Project Summary What Stabilizes Population Dynamics in...

Project Summary

What Stabilizes Population Dynamics in Nature? A New Framework for Quantifying the in situ Strength and Nonlinearity of Species Interactions

Project Overview The proposed research program will develop a new class of observational methods for

estimating the strength of predator-prey interactions in species-rich systems. These will be used to evaluate support for three theory-motivated hypotheses regarding the nonlinearity of generalist functional responses and the propensity of population dynamics to cycle. Observational and experimental implementations of the approach in stream communities of the Andrews Experimental Forest LTER will be used to quantitatively compare the degree to which prey-dependent, consumer-dependent and adaptive-foraging processes contribute to empirical levels of interaction nonlinearity. Empirically-derived insights will be integrated into abstracted mathematical models to develop general theory regarding the dynamics of specialist and generalist consumers.

Intellectual Merit Much of our theory regarding the regulation of ecological communities is built on the study

of species that exhibit periodic fluctuations in their abundance. These species are typically specialist consumers who feed on one or few prey and exhibit nonlinear functional responses. Most species in nature, however, are generalists that do not exhibit cycles. Our understanding of the mechanisms that regulate the dynamics of generalists is limited. This is due to the difficulty of measuring the strength and nonlinearity of interactions in nature’s species-rich and reticulate food webs. This limitation is widely acknowledged as a significant problem in the development of mathematical models with which to guide resource management and conservation practices. The proposed research program therefore promises significant advances in our conceptual and applied understanding of the mechanisms by which predator-prey interactions regulate the dynamics of species-rich communities. Indeed, the novel simplicity and broad applicability of the observational approach to be developed here promises a transformative new way to bridge mathematical theory and empirical data.

Broader Impacts Funding will support the education, mentoring, and training of undergraduate assistants, a

graduate student, and a postdoctoral researcher, and will initiate a first-time principal investigator’s research and teaching programs at Oregon State University (OSU). OSU draws many first generation undergraduate students primarily from within the state whose retention and mentoring in the biological sciences will be of high priority. Broader involvement with the local communities of Oregon will be achieved through an extensive collaboration with OSU’s Science, Math, Investigative Learning Experience (SMILE) elementary school program, annual community events at OSU’s Andrews Experimental Forest LTER, and the recruitment of summer high school field assistants from underrepresented groups. Research materials will be integrated as case studies in the development of two new courses and will be used to highlight the importance of mathematics to understanding the world around us. Both research and teaching results will be disseminated broadly to the scientific and education communities.�

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Project Description The nonlinear manner by which predator feeding rates respond to changes in prey abundance

underlies the dynamics of all predator-prey interactions. Understanding the empirical nature of these functional responses is central to food web theory and our knowledge of the processes controlling the dynamics of ecological communities (Abrams & Ginzburg 2000; McCann 2000). As such, functional responses are a linchpin in the development of mathematical models to guide resource management and conservation practices (Agrawal et al. 2007; Estes et al. 2011; Sinclair et al. 1998; Worm et al. 2009). However, our understanding of how the strength and nonlinear nature of predator-prey interactions affect community dynamics harbors two unresolved paradoxes: The Saturation Paradox – In manipulative experiments, most predators exhibit hyperbolic Holling type II-like functional responses, their feeding rate becoming saturated as prey abundance increases (Fig. 1a, Jeschke et al. 2004). It has long been recognized that such responses destabilize the dynamics of both simple predator-prey interactions and complex food webs (Hassell & May 1973; Oaten & Murdoch 1975). The negative density-dependence in the prey’s mortality rate that such responses elicit (Fig. 1b) leads to positive density-dependence in its growth rate causing large-amplitude population cycles (Fig. 1c) that increase the risk of stochastic extinctions (Rosenzweig 1971).

To explain food web persistence and the rarity of cyclic dynamics in nature (Kendall et al. 1999), ecologists typically invoke stabilizing but difficult-to-measure adaptive predator switching behavior, spatial prey refuges or behavior (often encapsulated by the sigmoid shape of type III-like functional responses, Fig. 1a) or intraspecific interference among predators (encapsulated by consumer-dependent functional responses) (Arditi & Ginzburg 2012; Fryxell et al. 2007; Kondoh 2003; Peacor & Cressler 2012; Sarnelle & Wilson 2008). However, switching, refuges, and consumer-dependence are only stabilizing below a threshold prey density (Fig. 1a, Murdoch & Oaten 1975). With prey densities above this threshold, these responses too are destabilizing as predator feeding rates become unable to control prey growth. In laboratory and field studies alike, this refuge density often falls well below the density attained by prey on the landscape (Englund & Leonardsson 2008; Middlemas et al. 2006). Thus, if saturating functional responses are both common and destabilizing, why are cyclic population dynamics so rare? The Prey Dynamics Paradox – Theory does suggest that, in contrast to single-prey predators, the feeding rates of generalists may effectively exhibit sigmoid (type III-like) responses to some prey species despite their underlying type II nature (McCann 2000; Murdoch & Oaten 1975). This mechanism requires negative covariance in prey dynamics and per capita interaction strengths sufficiently skewed towards weak interactions. Empirical interaction strength distributions typically are skewed towards weak interactions (Wootton & Emmerson 2005). However, time-series data indicate that the mechanism of apparent competition leading to negative covariance among prey is not exhibited by the prey populations of generalist predators; only specialist predators exhibit such consumer-resource driven dynamics (Murdoch et al. 2002). Thus, if the mechanisms proposed to prevent cycles for generalist predators are shown only by the prey of specialists, how do food webs that consist largely of generalist predators persist?

The research program proposed here will address these paradoxes by developing a new class of observational methods for estimating the empirical strength and nonlinearity of generalist predator-prey interactions in the field. To be tested are the hypotheses that, despite the inherently destabilizing nonlinearity of pairwise interactions, (H1) the feeding rates of generalist predators are not sufficiently saturated to elicit cyclic dynamics due to the non-

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additive effects of multiple prey on cumulative feeding rates; that (H2) the range of prey and predator densities experienced by generalists is too narrow to generate strong consumer-dependence; and that (H3) refuges, adaptive foraging, and consumer-dependence need not be invoked to explain the scarcity of cyclic predator-prey dynamics in nature.

Rationale and Significance There has been little empirical insight into the above-described paradoxes of predator-prey dynamics due to the difficulty of measuring species interactions in the field, particularly in the species-rich and reticulate food webs that are typical in nature:

First, population time-series rarely include all of a predator’s strong and weakly-linked prey. Insights have thus been limited to the strong interactions of specialist predators. Further, even species-poor time-series are rarely of sufficient length for the statistical fitting of models that include nonlinear, adaptive, or consumer-dependent terms. Formal model-comparison is thus biased towards the selection of linear models (Ives et al. 2010; Ives et al. 2003), even when populations are manipulated experimentally (Novak 2010).

Second, alternative methods for directly quantifying interaction strengths in the field assume linear type I functional responses (Fig. 1a, Novak & Wootton 2010). These offer limited insight because type I responses are neutrally stable (Murdoch et al. 2003), fail to incorporate the decrease in species-specific feeding rates inherent to feeding on multiple prey (Golubski & Abrams 2011), and cannot accommodate predator interference (Arditi & Ginzburg 2012).

Third, manipulative experiments are biased by their single-prey focus which artificially creates specialist predators and require a logistically unfeasible number of treatments for generalist predators (Okuyama & Bolker 2012; Tschanz et al. 2007), even when predator interference is not suspected. Further, they are difficult to extrapolate to natural communities by failing to address trait-mediated effects and the indeterminacy of indirect effects between species which are rampant and of equal importance to the more readily apparent direct effects (Menge 1995; Novak et al. 2011b; Wootton 1994; Yodzis 1988).

Fourth, recently popularized allometric methods for predicting interaction strengths on the basis of metabolic theory and predator-prey body-size ratios assume an absence of prey-preferences (Berlow et al. 2009; Williams et al. 2007). Further, by capitalizing on relationships emergent on a logarithmic-scale, they unavoidably lose the species-specific differences and spatiotemporal variation in interaction strengths whose effects can dominate community

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Figure 1. The strength and nonlinear form of predator functional responses (e.g., type II vs. type III in (a)) alter the density-dependent nature of the prey’s per capita mortality rate (b). Sufficiently strong and nonlinear functional responses may lead to limit cycles in predator-prey population dynamics (e.g., red intersection point of isoclines in (c)), but may be countered by sufficiently strong predator interference (blue intersection point in (c)). Multidimensional bifurcation analysis of generalized predator-prey models permit the use of empirically-estimated Bayesian posterior parameter distributions to infer the likelihood of cyclic dynamics in specialist versus generalist predator populations.

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dynamics (Kareiva & Levin 2002; Novak et al. 2011b). They are therefore unable to shed empirical light on the functional forms and potential importance of adaptive dynamics and consumer-dependence at scales most relevant to the field.

Thus, with a review of over 700 single-population time-series revealing that only 30% of species exhibit cyclic dynamics (Kendall et al. 1999), our current understanding of the mechanisms regulating the dynamics of the majority of species in nature is limited.

Overview of Research Approach A new approach for quantifying the strength of predator-prey interactions circumvents the aforementioned limitations of previous methods (developed by NSF DDIG to Novak and Wootton, DEB-0608092, Novak & Wootton 2008). Its observational nature avoids the obscurity of indirect effects, does not require time-series, and is logistically feasible even in species-rich systems. It also makes no assumptions regarding the prey population’s internal dynamics (see below), unlike experimental and time-series approaches (Novak & Wootton 2010). Requiring only knowledge of (i) species abundances, (ii) prey-specific clearance times (handling or digestion times, as appropriate), and (iii) two pieces of information derived from “snap-shot” diet surveys of focal predator populations (the fraction of feeding and not-feeding individuals, see below), the method enables the simultaneous estimation of a predator’s per capita attack rates on an arbitrary number of prey species. The method works on the same basis as the multispecies type II functional response and accounts for the decrease in species-specific feeding rates that accompanies a generalist predator’s feeding. A further appealing feature of the observational nature of the method is that it estimates the per capita attack rates in situ, in the context of all other co-occurring species interactions (i.e. competition, mutualism, trait-mediated effects, etc.).

Importantly, the observational method has also seen the empirical validation of its feasibility and accuracy, showing high concordance (as little as 5% discrepancy) between its estimates and those of independent field experiments (Novak 2010). Its estimates of prey-specific feeding rates have also shown concordance with those made on the basis of stable isotope ratios using a Bayesian mixing model (Yeakel et al. 2011b). To date, the method has been successfully applied to estimate the three-year time-averaged strengths of >180 interactions in six omnivorous food webs situated along a productivity gradient, thereby revealing the dynamic nature of food web topologies and interaction strengths which food web theory has largely assumed are constant (Novak 2013, see Results from Prior NSF Support).

The method’s snap-shot observational nature, however, also permits the measurement of per capita attack rates at finer scales. It thereby offers a means to quantify the spatiotemporal dynamics of functional responses and adaptive foraging directly. Further still, I have now determined that the same framework may in fact be extended to form a much broader class of observational methods suitable for estimating the parameters of a wide variety of alternative functional response forms (see Details of Research Approach, below). In particular, the observational approach can also be used to estimate the strength of predator interference, working equally well for ratio-dependent and more generalized consumer-dependent functional response forms (of which the type II is a special case). The observational framework thereby permits not only a quantification of the in situ, instantaneous magnitude of prey-specific per capita attack and interference rates, but also the direct, quantitative comparison of the degree to which prey-dependent, consumer-dependent, and adaptive foraging processes contribute to the nonlinearity of predator-prey interactions and thus the propensity of populations to cycle.

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Overview of Research Objectives The observational approach to quantifying interaction strengths provides the requisite basis on which to empirically confront the two paradoxes of current theory regarding the dynamics of generalist predators and the stability of their food webs. The research program proposed here seeks to resolve these paradoxes by accomplishing six specific objectives: a. Confronting variation, uncertainty, and concurrent feeding on multiple prey items -- Current implementation of the observational method uses non-parametric bootstrapping to obtain parameter confidence intervals. A proposed extension to a Bayesian formulation will permit the ability to more appropriately quantify and propagate uncertainty, consider spatiotemporal covariation in a hierarchical manner that is true to the data’s collection, and permit use of the observational framework in instances where predators consume multiple prey simultaneously. b. Simulation-based power analysis -- Individual-based simulations of predator populations will be used to inform fieldwork (see next) and meta-analyses (see below) by determining how species richness, sampling effort, and uncertainty in species abundance and clearance time estimates affect the method’s power in estimating parameters and the ability to detect density-dependent changes in attack rates over time and space. c. System-specific implementation -- Stream communities in Oregon State University’s Andrews Experimental Forest LTER will be used to evaluate support for the hypotheses among three predatory sculpin fishes. Prey-specific clearance times will be estimated in temperature-controlled laboratory facilities (Elliott & Persson 1978; Novak 2010). The abundances of prey, sculpins, and other predators will be surveyed across density gradients at 6 sites using electrofishing and Surber sampling (Novak et al. 2011a; Twardochleb et al. 2012). Snap-shot diet surveys will use non-destructive gastric lavage. All surveys will be performed on a quarter-annual basis to quantify seasonal attack rates, conditioned on the strength of consumer-interference, to determine the density-dependent nature of adaptive foraging prey preferences. d. System-specific experimental evaluation -- Snap-shot surveys of experimentally-manipulated sculpin populations under replicated density and prey-richness treatments will be used to directly test the hypotheses using an analytical relationship between functional response parameters and interaction nonlinearity. Density and richness treatments will be scaled to reflect and exceed the extremes observed in 49 years of community monitoring at the Andrews Experimental Forest. e. Assessing generality with meta-analysis -- The observational approach is well-suited for capitalizing on existing data. Contemporaneous surveys of abundances and predator diets abound for freshwater, terrestrial, and marine communities, with species-specific clearance times being readily available. Published and unpublished data sets will be acquired by contacting authors, assembled into a publicly-accessible online MySQL database, and used to investigate putative correlates of interaction nonlinearity and assess the generality of system-specific results. f. Theoretical synthesis -- Informed by objectives c-e, analyses of abstracted ordinary differential equation models (Novak 2008; Yeakel et al. 2011a) will be used to develop a general understanding of how the strength and form of prey self-regulation interact with empirically-relevant levels of trophic nonlinearity to affect the dynamics of specialist versus generalist predator-prey interactions. Our theory of predator-prey interactions has far outpaced its empirical assessment (Agrawal et al. 2007). Thus, in combination, the research objectives proposed here promise to offer significant advances in our understanding of the mechanisms that structure and regulate the dynamics of nature’s species-rich communities.

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Conceptual Framework Many definitions of the term interaction strength exist (reviewed in Berlow et al. 1999; Wootton & Emmerson 2005). Arguably the most general use of the term reflects the change seen in a prey’s abundance following a change in the abundance of a predator (Kareiva & Levin 2002). The rate, and thus magnitude and dynamical nature, of a prey’s response (dNi/dt) is governed by the rate and functional form of the predator’s feeding (its functional response, fij) and the rate and functional form of the prey’s predator-independent net growth rate (gi), both of which may be mediated by other species:�dNi

dt = gi(N)− fij(N , P )P . In turn, the predator’s reciprocal response (dPj/dt) depends on its cumulative feeding rates (�fij) and net mortality rate.

Theory indicates that strong and saturating feeding rates (i.e. high per capita attack rates and long handling times), in combination with high and negatively density-dependent prey growth rates, increase the propensity of (specialist) predator-prey interactions to exhibit cyclic dynamics (Fig. 1, McCann 2012; Rosenzweig 1971). Therefore, understanding the strength and nonlinear nature of functional responses and, in particular, the magnitude and density-dependence of the per capita attack rates, is key to understanding predator-prey interactions.�

Rationale for Hypotheses It is generally assumed that generalists do not exhibit cycles because they adaptively switch to alternative prey, changing their relative per capita attack rates whenever the abundance of a focal prey species is driven too low (e.g., Hanski et al. 1991; Murdoch et al. 2002; Rooney et al. 2006). This notion of weakly coupled generalist interactions that circumvent the effects of strong and saturating pairwise functional responses stems back to Elton (1927). Ratio- and other predator-dependent functional responses serve similarly to reduce the magnitude of the predator’s per capita attack rates when prey abundances are low (Arditi & Ginzburg 2012).

My alternative hypothesis is that prey-switching and predator interference, which certainly do occur in nature, are not necessary to explain the lack of cyclic dynamics in nature. That is, I propose a simpler hypothesis. Namely, that despite the inherently destabilizing nonlinearity of pairwise interactions, the feeding rates of generalist predators are not sufficiently saturated to elicit cyclic dynamics. This is due to a non-additive effect of prey richness on the overall nonlinearity of a predator’s functional response: a generalist predator will thereby experience a less saturated functional response than a specialist, even when they are feeding at the same total rate. As a result, the range of prey and predator densities experienced in species-rich food webs is too narrow to generate strong consumer-dependence.

My hypothesis stems from a combination of (i) field experiments showing linear predator effects despite a propensity for nonlinearity (Berlow 1999; Novak 2010; Wootton 1997) and (ii) preliminary simulations testing an analytical relationship between the effective linearity of a predator’s functional response and its cumulative feeding rate, for specialist versus generalist predators (Fig. 2).

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Figure 2. Preliminary simulations confirm a newly derived analytical relationship between the feeding rate and the effective linearity of a specialist predator’s functional response (dotted curves), and demonstrate that generalist predators exhibit less saturated functional responses even when feeding at the same total rate. The measure of effective linearity (eqn. 4a) varies from 0 (fully saturated) to 1 (linear type I functional response).

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Alternative Functional Response Formulations The nonlinearity of pairwise interactions is dependent on a predator’s functional response.

All functional response forms commonly used in ecology (and which are to be considered by the herein proposed research) may be viewed as special cases or extensions of the multispecies type II functional response on the basis of which the original observational approach of Novak & Wootton (2008) was derived (see Table 1 for summary). Specifically, the type II functional response assumes foraging rates are dependent only on prey densities. It is therefore a special case (with predator interference terms � = 0) of a prey- and consumer-dependent functional response (“BD response”, after Beddington 1975; DeAngelis et al. 1975):

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p γijpPp. (1) (Note that I have here generalized the classic BD response to an arbitrary number of interfering predator species whose strength of interference, �ijp, is both predator- and prey-specific. It is this most general functional response form for which the extension of the observational approach has now been developed (see below) and which will be applied in the research proposed here.) Table 1. Functional responses differ in the density-dependence of the per capita attack rates.

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eckjNk All additional functional response forms differ from the BD response in the assumed density-

dependent form of the per capita attack rates (c ~ c(N,P)) or the presence of consumer-dependence (� � 0). That is, the other functional responses may be obtained from the BD response by making the c attack rate parameters (= prey preferences, Chesson 1983) functions of prey and/or predator densities (Table 1). Thus the ratio-dependent functional response is an extreme case of consumer-dependence whereby the per capita attack rate depends on the predator’s abundance, c = c(P) = �P-m (Arditi & Ginzburg 2012). Similarly, the type III response is a case where the predator’s per capita attack rate is assumed to be a power-function of the prey’s abundance, c = c(N) = �Nq-1. The three most common ways that theoreticians have modeled adaptively foraging predators (reviewed by Valdovinos et al. 2010) assume that the rate at which per capita attack rates change (i.e. prey-switching) is controlled either by: (i) a replicator-based prey frequency-dependent fitness gradient (e.g., Kondoh 2003), (ii) a game theory-based allocation of equal effort maintained over all prey (e.g., Drossel et al. 2001), or (iii) an optimal foraging-based ranking of the preys’ energetic profitability that depends on their

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handling times, h (e.g. Beckerman et al. 2006). At the other, most simplest extreme, the type I functional response assumes near instantaneous handling times (h � 0) and thus practically unbounded proportional increases of the predator’s feeding rate as the focal prey’s density increases. Other potential functional response formulations, including those that incorporate adaptive prey behavior (Peacor & Cressler 2012) or space explicitly (Englund & Leonardsson 2008), are beyond the scope of this proposal but could be considered in future work.

Thus, the key to differentiating between alternative functional response formulations of the nonlinear nature of predator-prey interactions is how they predict the predator’s per capita attack rates to vary over time and space as a function of prey and predator densities. That is, the manner by which empirically estimated per capita attack rates and interference rates relate to prey- and predator densities can be used to distinguish among alternative functional response forms. The observational approach proposed here provides a novel means to measure these parameters and relationships. It thereby provides a means to address hypotheses H1-H3 by quantifying how prey-dependent, predator-dependent, and adaptive foraging processes contribute to the strength and nonlinearity of generalist interactions and their propensity to cause cycles.

A New Class of Observational Methods for Estimating Functional Response Parameters The observational approach introduced by Novak & Wootton (2008) capitalizes on the (relative) ease with which three different sources of data may be acquired:

(i) estimates of species abundances (Ni); (ii) estimates of prey-specific clearance times (hij, handling or digestion times, as appropriate). (iii) snap-shot diet surveys of focal predator populations that provide estimates of:

• the fraction of feeding individuals caught feeding on each prey species (Fij), • the fraction of all individuals (feeding and not feeding) caught feeding on each species (Aij).

The method uses estimates of these variables to calculate prey-specific per capita attack rates as

cij =FijAij

(Fij −Aij)hijNi. (2) As stated above, the method enables the simultaneous estimation of a predator j’s per capita attack rates on an arbitrary number of prey i species, having been derived on the same basis as the multispecies type II response. It thus accounts for the decrease in species-specific feeding rates that accompanies a generalist predator’s feeding. Its “snap-shot” nature means its estimates are effectively instantaneous measures of the predator’s per capita attack rates (as long as diet surveys are sufficiently short that prey abundances do not change over the survey period). By isolating the top-down component of a predator-prey pair’s interaction, it makes no assumptions regarding the prey’s predator-independent rate and form of density-dependence (gi). This is important because the prey species of generalist predators typically differ greatly in this aspect.

Fig. 3 serves to provide a more intuitive understanding of the approach’s success. It depicts the hypothetical feeding activities of eight predator individuals (indicated on the left-hand axis) consuming four different prey species through time. Intuition may be built as follows: If the predator population (and all its individuals) were to exhibit equal per capita attack rates on all four prey species (i.e. uniform prey preferences) and these prey species were equally abundant, then the likelihood of observing each prey species in a snapshot diet survey of the predator population would be proportional to their clearance times; prey with longer clearance times would be more likely to be observed than prey with shorter clearance times. Similarly, if both per capita attack rates and clearance times were to be uniform across all prey but their

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abundances differed, then each prey’s frequency in the predator population’s diet (and thus a snapshot diet survey) would be proportional to its abundance. The Fij and Aij terms of eqn. 2 (respectively the fractions of all feeding, and of all feeding and non-feeding individuals, observed in the process of feeding on each prey species) provide information on the predator population’s prey preferences, conditioned on prey abundances and clearance times. Their differences effectively convert the relative likelihood of observing the different prey species to absolute measures of the number of prey eaten per predator per prey available per time per area – corresponding to the units of theoretical predator-prey models.

The derivation of the method just detailed explicitly assumes a prey-dependent functional response (i.e. f=f(N) with c=c(0)). It can, however, by separately applied across multiple locations (in space or time) that differ in predator abundance; a regression of the location-specific attack rates on predator abundances provides a model-free estimate of predator interference rates (c=c(P)). Similarly, application to multiple locations differing in prey abundance (e.g., Novak 2013) provides model-free estimates of the density-dependence of prey-preferences appropriate to type III and adaptive foraging functional responses (c=c(N)).

That said, I have now determined that the same framework may also be used to derive explicit model-specific equations analogous to eqn. 2 for each of the alternative functional response models listed in Table 1. In particular, this may even be done for the most general prey- and predator-dependent BD functional response model (eqn. 1). For example, for a situation where a single predator j population experiences only intraspecific interference, the equations for the prey-specific attack rates and interference rates are as simple as:

cij =βij(1)βij(2)(Pj(1) − Pj(2))

βij(1)Pj(1) − βij(2)Pj(2) and γijj =

βij(2) − βij(1)

βij(1)Pj(1) − βij(2)Pj(2) , (3) where ß equals eqn. 2 and numbered subscripts refer to two locations or time-points differing in the predator j’s abundance. More generally, estimation of the parameters can be performed by simple matrix algebra: x = B-1b, where x is a vector containing all prey-specific per capita attack rates and all predator interference rates that are to be estimated, b is a vector of the location-specific �’s, and B is a matrix containing the appropriately arranged location-specific products of the �’s and predator abundances. In fact, parameters may be estimated not only for an arbitrary number of prey, but also for an arbitrary number of predator species as long as the number of locations, treatment replicates or time-points surveyed exceeds the number of interfering species, analogous to any regression framework.

Details of Research Objectives a. Confronting variation, uncertainty, and concurrent feeding on multiple prey items – Two operational issues have held back implementation of the observational method to a wider suite of data collection methods and predator feeding types than have been investigated to-date: (i) an

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�Figure 3. A snap-shot diet survey of 8 predator individuals (left axis) feeding on four prey species differing in their clearance rates (i.e. handling times). Right axis: Proposed hierarchical consideration of 3 individuals when feeding on multiple prey at a time (see Details of Research Objectives).�

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unsatisfactory treatment of the variation and uncertainty surrounding parameter point estimates, and (ii) a model-consistent but empirically-limiting restriction that predator individuals may only consume a single prey item at a time. Both of these issues can and will be addressed by reformulating the approach into a hierarchical Bayesian framework. Indeed, the Bayesian framework leads to exciting new territory in the estimation of interactions strengths, treating these as probabilistic distributions rather than mere point estimates (Yeakel et al. 2012). Variation and uncertainty: Previous implementations of the observational method have used non-parametric bootstrapping to obtain confidence intervals for attack rate point estimates. Although useful for assessing many aspects of uncertainty and spatiotemporal variation (Novak 2010, 2013; Yeakel et al. 2011b), the utility of this approach is limited. For example, small sample size-associated values of zero in diet- and abundance surveys often lead to over-inflated confidence intervals that include nonsensical estimates of zero (Novak 2010).

While parametric bootstrapping or a likelihood framework could avoid some of these issues, the proposed hierarchical Bayesian framework provides a more intuitive way of confronting variation and uncertainty. As true probability distributions, the posterior distributions of the Bayesian framework are also more useful for characterizing uncertainty in sensitivity analyses (Fig. 1d) and stochastic population models. The following examples illustrate why and how the Bayesian approach will be implemented. This objective will be co-led by Novak and the graduate student.

(i) Species abundances (Ni): Species abundances are typically estimated in some hierarchically nested fashion. For example, individuals of all encountered species are counted within quadrats (Surber samples) which are replicated within transects (stream reaches) which are replicated within sites (tributaries). Surveys are typically also repeated over time. Environmental covariates of interest for explaining variation in species interaction strengths over space or time (e.g., water temperature, habitat complexity, time-of-day) are typically collected at different levels of this hierarchy. Furthermore, the inherent patchiness of species distributions very often leads to values of zero (and larger variances than sample means) at lower levels of the hierarchy. These factors are ignored in previous implementations of the observational approach (and most other methods), potentially leading to biased inferences (Bunge & Fitzpatrick 1993; Clark 2005).

The proposed Bayesian framework will account for the lack of within-sample independence among species and will accommodate the hierarchical and patchy nature of the species abundances to provide robust inferences regarding level-specific (hyper)parameters and their uncertainty. For example, the model to be developed here will consider counts of prey individuals at the sample scale to be drawn from a zero-inflated negative binomial likelihood model, Ni|�=1 ~ NegBin(,) and � ~ Bern(p), for which the appropriate non-informative prior distributions for the mean (), over-dispersion (), and probability-of-zero (p) parameters are ~ Gamma(.01,.01), ~ Unif.(.1,10), and p ~ Unif.(0,1). With an appropriate hierarchical framework, the posterior uncertainty surrounding these and the associated hyper-parameters may be propagated across spatial and temporal levels in the calculation of attack rates.

(ii) Clearance-times (hij): Predator species can be classified into two feeding types (Jeschke et al. 2002): Those whose maximum feeding rate is set by their handling times (the time needed to capture, subdue and ingest a prey item), and those for whom it is set by their digestion times (the inverse of digestion rate). (My use of the term “clearance time” is meant to refer to either scenario.) Jeschke et al. (2002) have demonstrated that it is the larger of the two time intervals that controls predator-prey dynamics. Empirical clearance times estimates can be obtained in a

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variety of ways (Novak & Wootton 2008). In practice, however, they are best estimated by a combined observational and experimental approach. For example, in Novak (2013), I estimated the clearance times of 26 different predator-prey pairs using lab experiments in which ambient temperatures and the sizes of predator and prey individuals were varied systematically. Multiple regression coefficients derived from these lab experiments permitted me to infer the expected clearance times of all field-based feeding observations.

Unfortunately, consideration of the uncertainty surrounding regression-coefficients associated with the interval nature of observations (where exact feeding start and end-times are known only within a window of time) is challenging for the current procedure. That is, because continuous-time monitoring of predator feeding is typically not possible, data on clearance times are obtained by monitoring feeding activity at, for example, hourly intervals. The proposed Bayesian framework will avoid this limitation by considering the interval nature of the laboratory-based clearance time observations explicitly. More specifically, the uncertainty of clearance times (�2) may be estimated by considering them as conditional on the interval of time (l) in which their true start and end times occurred. The resulting joint posterior distribution allows for the existence of correlations among the predictor variables of temperature, prey- and predator-body sizes, and is easily integrated into the subsequent calculation of the attack rates. (iii) Diet surveys (Fij and Aij): The observational approach relies on snapshot diet surveys of focal predator populations to estimate the fraction of feeding individuals (Fij), and the fraction of all individuals (feeding and not feeding, Aij) observed in the process of feeding on each prey species. The natural model for representing these proportions of different prey species is the multinomial likelihood, assuming that each individual shares the same distribution of prey preferences. A dirichlet prior with unit concentration parameters would reflect the belief that all prey frequencies are equally likely. Concurrent feeding on multiple prey items: Previous applications of the observational approach have estimated the population-averaged attack rates of predator species whose individuals can only consume a single prey item at a time. Examples of suitable predators include intertidal invertebrates (whelks), arthropods (wolf spiders), reptiles (boa constrictors), birds (gulls), and mammals (sea otters). The reason for this is that the principles on which the method was derived explicitly assumes such single-prey-item-at-a-time feeding. Many more predator species, however, exhibit handling times that are effectively instantaneous (e.g., fishes). Instead, it is the process of digestion that can limit feeding rates (Armstrong & Schindler 2011; Jeschke 2007; Jeschke et al. 2002). Although gut contents surveys permit the determinations of prey frequencies, the common presence of multiple prey items in an individual’s gut incurs a bias in the estimation of per capita attack rates when using the current observational approach.

The proposed framework will overcome this limitation and extend the use of observational methods to predators consuming multiple prey simultaneously, as indicated on the right-hand axis of Fig. 3. This may be done by nesting individual-specific Fij terms (the proportional frequency of prey in the gut of an individual) within a hyper-parameter reflecting a population-level Fij value. The latter estimate may then be combined with the population-level Aij estimate (incorporating individuals with empty stomachs) to estimate population-level attack rates. b. Simulation-based power analysis – The appropriate application of any sample-based statistical method for making inferences regarding parameter estimates requires an understanding of the method’s accuracy (its bias with respect to a parameter’s true value or distribution) and its precision (the relationship between uncertainty and sample size). Novak & Wootton (2008)

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performed such an evaluation for the original observational approach using stochastic, non-spatial individual-based simulations. These simulations revealed two insights of key empirical utility: (i) the method is unbiased by variation in prey abundances or clearance times given sufficient diet sampling effort, and (ii) that the sufficiency of diet sampling effort and the associated precision of attack rate estimates can be judged by the degree to which predator-specific prey accumulation curves are saturated (analogous to species accumulation curves, Gotelli & Colwell 2001).

We propose to extend these simulations to incorporate multiple predator populations. We will thereby determine how the extent and magnitude of interference within and between predator species affect the accuracy and precision of the new prey- and predator-dependent observational approach (eqns. 3). Specifically, Novak and the graduate student will determine how (i) sampling effort (the number of focal predator individuals that are surveyed), (ii) diet richness, (iii) predator richness and interference levels, and (iv) the focal predator population’s level of feeding activity (A•j, emergent from all other parameters) influence the method’s accuracy and precision. I predict, for example, that a trade-off exists whereby stronger interference rates will both ease their estimation but also reduce the method’s power at estimating attack rates for a given sampling effort because the fraction of feeding individuals will be thereby be reduced. Following Novak & Wootton (2008), the simulated ranges, distributions and interdependencies of parameter values (abundances, handling times, attack rates and interference rates), prey- and predator richness levels, and feeding activity levels will be selected to reflect typical empirical levels. (Note: Future work may easily extend these simulations to investigate how accuracy and precision are affected by intraspecific diet specialization, the potential importance of which is increasingly recognized (Bolnick et al. 2011).) c. System-specific implementation – Experimental food web ecology of predator-prey interactions and functional responses has predominantly focused on the interactions of species pairs or modules, isolating these from the surrounding community. A central tenet of this proposal is that this artificially creates specialist consumers whose interactions are thereby strengthened (increasing attack rates) and inferred to be more nonlinear than actually experienced in nature. I hypothesize that the functional responses of generalist predators are far more linear, particularly in the range of species abundances experienced in nature (H2). I thus predict that the effects of prey refuges, adaptive foraging, and predator-interference are relatively weak (H3), such that attack rates are effectively density-independent (cij = cij(0), Table 1).

Novak and the postdoctoral researcher will test these predictions by quantifying the per capita attack rates and interferences rates of three freshwater sculpin species (Cottus bairdi, C. beldingi, and C. rhotheus) in the field. These species are common in streams of the Pacific Northwest (Roni 2002), are hypothesized to exhibit strong intra- and interspecific interference (Burgess 2001; Matheson & Brooks 1983; Quist et al. 2004), exhibit saturating functional responses in manipulative experiments of prey abundance (Soluk 1993), can exhibit strong effects on the abundance of their diverse macroinvertebrate prey (Brusven & Rose 1981; Cheever & Simon 2009), and are amendable to the experimental manipulation of their density due to their non-schooling, benthic life-histories (relevant to d. System-specific experimental manipulation). All three species co-occur at the HJ Andrews Experimental Forest LTER.

The three sources of data required for the observational approach will be obtained as follows: (i) The densities, Ni and Pj, and body size distributions of sculpins, their prey and other putative predators (salmonids and salamanders) will be estimated across 6 stream reaches (30m length), varying in community structure, using three-pass electrofishing and replicate Surber sampling (n

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= 6 per reach) (Novak et al. 2011a; Twardochleb et al. 2012). (ii) Concurrent diet surveys of captured individuals will use non-destructive gastric lavage (Foster 1977) to estimate reach-specific Fij and Aij terms. (iii) Clearance rates will be estimated (using models of exponential decay) for each predator-prey pair in lab facilities at OSU by flushing the stomachs of replicate individuals at set time intervals following a meal (n � 30, Elliott & Persson 1978). Predator:prey size ratios and aquarium temperatures will reflect seasonal ranges observed in the field. These lab-based relationships between clearance rates, temperature and body sizes will be used to calculate clearance times for field-based feeding observations (Novak 2010). Surveys will be performed quarter-annually (excluding mid-winter) over 3 years to quantify seasonal variation and density-dependence (adaptive foraging) in attack- and interference rates. Reach temperatures will be recorded year round at ½ hr. intervals using HOBO Data loggers.

The overall and relative contributions of prey- and predator-dependence to the effective linearity of each species’ functional response will be respectively assessed at each time-point by:

1

cij

dfijdNi

∣∣∣∣N,P and

1

cij

dfijdPj

∣∣∣∣N,P . (4)

These measures reflect the slope of the functional response with respect to prey i (eqn. 4a) or predator j’s (eqn. 4b) abundance relative to the slope of the functional response at its origin (cij). Values of 0 thereby indicate a functional response that is completely saturated with respect to a prey- or interfering predator’s abundance, while values of 1 indicate a functional response that is effectively linear (type I-like) in the range of observed species abundances (see also Fig. 2). d. System-specific experimental evaluation – If hypotheses H2-H3 are correct – that the range of species abundances experienced under natural conditions is too small to affect prey saturation and predator-interference in generalist predators despite the inherent nonlinearity of their prey-specific functional responses – then it should be possible to elicit this nonlinearity by manipulating species densities beyond their natural range. Novak and the postdoc will test this prediction using two orthogonal experiments targeting Cottus bairdi, the most abundant of the three sculpin species. Replicate artificial streams (n = 10) will be stocked with either (i) a varying density of C. bairdi only, or (ii) a constant density of C. bairdi but varying density of C. beldingi, each crossed with a treatment of high or low prey richness to manipulate specialist versus generalist diet diversity. Each individual’s stomach will be flushed after 2 and 10 elapsed days to estimate Fij and Aij terms, with day 2 prey abundances inferred from the rate of loss between the start and end of an experiment. Each experiment will be repeated twice in each of two summer field seasons with densities and high-prey richness levels respectively exceeding and reflecting the ranges observed in 49 years of community monitoring (HJ Andrews Experimental Forest Data Catalog).

If hypotheses H2-H3 are not correct, then (i) the proportion of feeding individuals, Aij, will decrease as the density of conspecific and interspecific individuals is increased, and (ii) the intercept of the relationship between effective linearity (eqns. 4) and predator density will not differ between high- and low prey richness treatments. These predictions will be tested using linear mixed-effects models (Novak 2010; Zuur et al. 2009). Additional artificial streams will be used in year 2 should statistical power (inferred from year 1) prove insufficient. e. Assessing generality with meta-analysis – Sculpins are an idea focal study system because their functional responses saturate and predator interference is expected to be strong. It is possible that these features make them atypical. Novak and the postdoc will therefore conduct a meta-analysis to assess the hypotheses more broadly (Hillebrand 2001; Koricheva et al. 2013;

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Nakagawa & Cuthill 2007). Indeed, the observational approach is well-suited for capitalizing on the wealth of predator diet surveys (Fij and Aij), species abundance surveys (Ni), and clearance time experiments (hij) that already exists for freshwater, terrestrial, and marine systems (see preliminary compilation of 148 publications following the References Cited section). Published and unpublished data sets will be identified with standardized search terms using the Web of Science, Google and Google Scholar, acquired by directly contacting authors where possible, assembled into a publicly accessible MySQL database, and used to estimate and create frequency distributions of the overall and relative contributions of prey- and predator-dependence to the effective linearity of specialist versus generalist functional responses (eqns. 4).

Putative predictors of effective linearity to be investigated include ecosystem type (Strong 1992), temperature (Rall et al. 2010), trophic level (excluding producer and herbivore levels), predator-prey size ratios (Rall et al. 2011), taxonomy, predator hunting mode (Schmitz 2008), and interaction dimensionality (Pawar et al. 2012). When not directly inferable for a given diet survey, clearance times will be estimated on the basis of allometric considerations (Rall et al. 2011; Sentis et al. 2013) or from studies of similar predator-prey pairs (e.g., Englund et al. 2011; Jackson et al. 1987; Lovei et al. 1990). Similarly, when not directly available for a given diet survey, species abundances will be drawn from published surveys of comparable habitats. f. Theoretical synthesis – Each of objectives c-e will inform hypotheses H1-H3 by quantifying how nonlinear the functional responses (fij) of generalist predators are with respect to the density of their prey and interfering predators, relative to those of specialist predators. In order to test hypothesis H1 – that the feeding rates of generalist predators are not sufficiently nonlinear to elicit cyclic dynamics – requires further that the rate and density-dependent nature of predator-independent prey growth rates (gi) be known for all prey species as well (see Conceptual Framework). This is admittedly a challenging empirical task, particularly because of the varied life history patterns that typify species-rich communities.

We therefore propose to use local bifurcation and isocline analysis of abstracted ordinary differential equations (Fig. 1c-d) to develop a general understanding of how the strength and density-dependent nature of prey self-regulation interact with our empirically-measured levels of functional response nonlinearity to affect the dynamics of specialist versus generalist predator-prey interactions (Novak 2008; Noy-Meir 1975; Yeakel et al. 2011a). We will do so using Generalized modeling (Gross et al. 2004; Gross & Feudel 2006; Gross et al. 2009) to which Yeakel et al. (2011a) provide a pedagogical introduction. This relatively new tool in dynamical systems theory circumvents the need to assume specific functional forms for the processes being considered (e.g., logistic or Ricker for gi, type II or BD for fij), by normalizing the variables and functions of standard ODEs to an assumed set of feasible steady states (N* > 0). Bifurcation analysis of generalized models need thereby consider only (i) the relative timescale of the predator-prey system’s dynamics (set by the magnitudes of gi and fij), and (ii) the nonlinearity of these functions (i.e. the partial derivatives of gi and fij, analogous to eqns. 4) at steady-state. A given generalized model thus often reflects a whole family of standard ODEs exhibiting similar degrees of nonlinear density-dependence in prey growth and the predator’s functional response.

Generalized modeling will therefore allow us to test hypothesis H1 directly, permitting us to contrast the domain of prey growth nonlinearity levels within which our empirically measured levels of functional response nonlinearity affect stable equilibria versus limit cycles (Fig. 1d). If the hypothesis is correct, then generalist functional responses will be exhibit a larger domain of stable equilibrium dynamics than will levels of nonlinearity associated with the functional responses of specialist predators. Numerical simulations will be used to confirm these results.

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Intellectual Merit Much of our theory regarding the regulation of ecological communities is built on the study of species exhibiting periodic fluctuations in their abundance. These species are typically specialist consumers who feed on one or few prey. Most species in nature, however, are generalists that do not exhibit cycles. Our understanding of the mechanisms that regulate generalist populations is limited. This is due to the difficulty of measuring the strength and nonlinearity of interactions in nature’s species-rich and reticulate food webs. This limitation is widely acknowledged as a significant problem in the development of mathematical models with which to guide resource management and conservation practices. Our proposed research program therefore promises significant advances in our conceptual and applied understanding of the mechanisms by which predator-prey interactions regulate the dynamics of their species-rich communities. Indeed, the novel simplicity and broad applicability of the observational approach to be developed here promises a transformative new way to bridge mathematical theory and empirical data.

Broader Impacts PI Novak is a starting professor at Oregon State University. The proposed research will therefore contribute to the initiation of a new lab, as well as providing support, field experience and quantitative training to locally-recruited high school students, undergraduate assistants, a PhD student and a postdoctoral researcher. Field work at the Andrews Experimental Forest LTER will coincide with annual community events for which lab members will create exhibitions that highlight the importance of mathematics for understanding the world around us. Two courses - Theoretical Ecology and Intro. to Ecology - will be developed using the scientific teaching principles PI Novak has learned in the NSF-funded Faculty Institutes for Reforming Sciences Teaching initiative, and will focus on improving students’ quantitative reasoning skills and confidence in mathematics using collaborative learning techniques. OSU draws students primarily from within the state, many of whom are first generation students. Thus the retention and mentoring of underrepresented groups in the biological sciences will be high priority. Research and teaching results (e.g., curricula, pre- and pre/post-assessments) will be disseminated via conferences and publications involving all personnel.

In addition, PI Novak, the postdoctoral researcher, and the graduate student will all collaborate extensively with OSU’s Science, Math, Investigative Learning Experience (SMILE) program to provide science and math enrichment for elementary school students. SMILE is a university - school partnership between OSU, 11 Oregon school districts and 4 charter schools, with an annual participation of more than 700 students. Its purpose is to increase the number of underrepresented and educationally underserved students graduating from high school qualified to enroll in college and pursue careers in science, math, health, engineering, and education.

We will work with SMILE in three ways: (i) contributing teaching materials to afterschool SMILE clubs that stimulate elementary school students’ interest in STEM content, careers, and academic engagement, (ii) contributing to the professional development of elementary school teachers –the afterschool club leaders – by engaging them in annual SMILE workshops, and (iii) supporting and participating in SMILE’s annual College Connection Events. PI Collay will use these activities to test the hypothesis that sustained connections to research and researchers increase teacher interest and confidence in science content, and increase student engagement. This will be assessed through annual pre/post-tests, teacher reflections, clubs logs, and workshop conversations with SMILE’s teacher community. (i) SMILE Clubs – SMILE currently organizes 9 elementary afterschool clubs, each with ~20

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students, advised by 18 public school teachers. For the last three years, these clubs have averaged 200 students: 62% female, 74% underrepresented minority, 26% low income white, and 53% first generation to college. The teaching materials we propose to contribute to these clubs will be directly related to the topics of our proposed research (i.e. food webs, population dynamics, etc.) and will be designed to pique student interest and awareness of nature, the science of ecology, and the contributions of mathematics and modeling. (ii) SMILE Workshops – A central tenant of the SMILE program is teacher professional development. A second core strategy for our proposed project is thus to provide such development for 15-18 elementary teachers – the afterschool SMILE club leaders – by engaging them in annual workshop sessions co-led by PIs Novak and Collay. The goals of these sessions will be to: (a) increase the teachers' science content knowledge, (b) increase their tools and strategies for engaging students in our 4th and 5th grade target groups, and (c) modeling 5-8 teaching activities for use in their clubs. These workshops also provide time for reflection and conversations that are crucial for nurturing SMILE’s teacher community. (iii) College Connection Events – Finally, we request funds to support and participate in SMILE’s annual College Connection Events. These events entail transporting club members to local college campuses (including OSU) to tour these campuses, laboratories and lecture halls, engage with scientists, and work in groups to complete challenging and fun STEM activities.

Project Timeline

OObjec t ive Bayesian reformulation Simulations Surveys Experiments Meta-analysis Theoretical

synthesis

TTerm F W S S F W S S F W S S F W S S F W S S F W S S

Year 1

Year 2

Year 3

Unfunded Collaborations The already-identified student (Chris Wolf, Masters in Statistics), who’s Ph.D. this grant will support, will be co-advised by Dr. Alix Gitelman in the Department of Statistics. Dr. Gitelman’s expertise lies in environmental statistics, particularly graphical and hierarchical Bayes models.

Results from Prior NSF Support DEB-0608092: J.T. Wootton and M. Novak. Total Award: $12,000; 10/01/06 – 09/30/08. Dissertation Research: Quantitative interaction strengths in omnivorous food webs across a gradient in primary productivity. Intellectual Merit – Trophic omnivores are central to our understanding of food webs but theory regarding their effects has far outpaced its empirical assessment. This research developed, tested, and employed a new approach for quantifying omnivorous interaction strengths and thereby assessed key predictions of intraguild predation theory in a series of species-rich food webs situated along a productivity gradient of New Zealand’s rocky shores. Broader Impacts – Research supported by this grant was presented at 9 professional meetings, resulted in 5 publications to date, and trained 4 undergraduate assistants in both the field and lab.

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References Cited

(Self-citations have been bolded)

Abrams P.A. & Ginzburg L.R. (2000). The nature of predation: prey dependent, ratio dependent or neither? Trends Ecol. Evol., 15, 337-341.

Agrawal A.A., Ackerly D.D., Adler F., Arnold A.E., Cáceres C., Doak D.F., Post E., Hudson P.J., Maron J., Mooney K.A., Power M., Schemske D., Stachowicz J., Strauss S., Turner M.G. & Werner E. (2007). Filling key gaps in population and community ecology. Frontiers in Ecology and the Environment, 5, 145-152.

Arditi R. & Ginzburg L.R. (2012). How species interact: altering the standard view of trophic ecology. Oxford University Press, Oxford.

Armstrong J.B. & Schindler D.E. (2011). Excess digestive capacity in predators reflects a life of feast and famine. Nature, 476, 84-87.

Beckerman A.P., Petchey O.L. & Warren P.H. (2006). Foraging biology predicts food web complexity. PNAS, 103, 13745-13749.

Beddington J.R. (1975). Mutual Interference Between Parasites or Predators and its Effect on Searching Efficiency. The Journal of Animal Ecology, 44, 331-340.

Berlow E.L. (1999). Strong effects of weak interactions in ecological communities. Nature, 398, 330-334.

Berlow E.L., Dunne J.A., Martinez N.D., Stark P.B., Williams R.J. & Brose U. (2009). Simple prediction of interaction strengths in complex food webs. Proc. Natl. Acad. Sci., 106, 187-191.

Berlow E.L., Navarrete S.A., Briggs C.J., Power M.E. & Menge B.A. (1999). Quantifying variation in the strength of species interactions. Ecology, 80, 2206-2224.

Bolnick D.I., Amarasekare P., Araujo M.S., Burger R., Levine J.M., Novak M., Rudolf V.H.W., Schreiber S.J., Urban M.C. & Vasseur D.A. (2011). Why intraspecific trait variation matters in community ecology. Trends Ecol. Evol., 26, 183-192.

Brusven M.A. & Rose S.T. (1981). Influence of substrate composition and supended sediment on insect predation by the Torrent sculpin, Cottus rhotheus. Can. J. Fish. Aquat. Sci., 38, 1444-1448.

Bunge J. & Fitzpatrick M. (1993). Estimating the Number of Species: A Review. Journal of the American Statistical Association, 88, 364-373.

Burgess J.A. (2001). Response of trout, sculpins, and salamanders to experimental manipulation of large wood in Cascade mountain streams. In: Fisheries and Wildlife. Oregon State University, p. 95.

Cheever B.M. & Simon K.S. (2009). Seasonal influence of brook trout and mottled sculpin on lower trophic levels in an Appalachian stream. Freshw. Biol., 54, 524-535.

Chesson J. (1983). The estimation and analysis of preference and Its relationship to foraging models. Ecology, 64, 1297-1304.

Clark J.S. (2005). Why environmental scientists are becoming Bayesians. Ecol. Lett., 8, 2-14. DeAngelis D.L., Goldstein R.A. & O'Neill R.V. (1975). A Model for Tropic Interaction.

Ecology, 56, 881-892. Drossel B., Higgs P.G. & McKane A.J. (2001). The Influence of Predator-Prey Population

Dynamics on the Long-term Evolution of Food Web Structure. J. Theor. Biol., 208, 91-107.

2 of 13�

Elliott J.M. & Persson L. (1978). The Estimation of Daily Rates of Food Consumption for Fish. J. Anim. Ecol., 47, 977-991.

Elton C.S. (1927). Animal Ecology. Sidwick and Jackson, London. Englund G. & Leonardsson K. (2008). Scaling up the functional response for spatially

heterogeneous systems. Ecol. Lett., 11, 440-449. Englund G., Öhlund G., Hein C.L. & Diehl S. (2011). Temperature dependence of the functional

response. Ecol. Lett., 14, 914-921. Estes J.A., Terborgh J., Brashares J.S., Power M.E., Berger J., Bond W.J., Carpenter S.R.,

Essington T.E., Holt R.D., Jackson J.B.C., Marquis R.J., Oksanen L., Oksanen T., Paine R.T., Pikitch E.K., Ripple W.J., Sandin S.A., Scheffer M., Schoener T.W., Shurin J.B., Sinclair A.R.E., Soulé M.E., Virtanen R. & Wardle D.A. (2011). Trophic Downgrading of Planet Earth. Science, 333, 301-306.

Foster J.R. (1977). Pulsed gastric lavage - efficient method of removing stomach contents of live fish. Progress. Fish-Cult., 39, 166-169.

Fryxell J.M., Mosser A., Sinclair A.R.E. & Packer C. (2007). Group formation stabilizes predator-prey dynamics. Nature, 449, 1041-1043.

Golubski A.J. & Abrams P.A. (2011). Modifying modifiers: what happens when interspecific interactions interact? J. Anim. Ecol., 80, 1097-1108.

Gotelli N.J. & Colwell R.K. (2001). Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness. Ecol. Lett., 4, 379-391.

Gross T., Ebenhoh W. & Feudel U. (2004). Enrichment and foodchain stability: the impact of different forms of predator-prey interaction. J. Theor. Biol., 227, 349-358.

Gross T. & Feudel U. (2006). Generalized models as a universal approach to the analysis of nonlinear dynamical systems. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 73, 016205-14.

Gross T., Rudolf L., Levin S.A. & Dieckmann U. (2009). Generalized Models Reveal Stabilizing Factors in Food Webs. Science, 325, 747-750.

Hanski I., Hansson L. & Henttonen H. (1991). Specialist Predators, Generalist Predators, and the Microtine Rodent Cycle. J. Anim. Ecol., 60, 353-367.

Hassell M.P. & May R.M. (1973). Stability in Insect Host-Parasite Models. The Journal of Animal Ecology, 42, 693-726.

Hillebrand H. (2001). Meta-analysis in Ecology. In: Encyclopedia of Life Sciences. John Wiley & Sons, Ltd.

Ives A.R., Abbott K.C. & Ziebarth N.L. (2010). Analysis of ecological time series with ARMA(p,q) models. Ecology, 91, 858-871.

Ives A.R., Dennis B., Cottingham K.L. & Carpenter S.R. (2003). Estimating community stability and ecological interactions from time-series data. Ecol. Monogr., 73, 301-330.

Jackson S., Duffy D.C. & Jenkins J.F.G. (1987). Gastric digestion in marine vertebrate predators: in vitro standards. Functional Ecology, 1, 287-291.

Jeschke J.M. (2007). When carnivores are “full and lazy”. Oecologia, 152, 357-364. Jeschke J.M., Kopp M. & Tollrian R. (2002). Predator functional responses: Discriminating

between handling and digesting prey. Ecol. Monogr., 72, 95-112. Jeschke J.M., Kopp M. & Tollrian R. (2004). Consumer-food systems: why type I functional

responses are exclusive to filter feeders. Biological Reviews, 79, 337-349. Kareiva P. & Levin S.A. (2002). The Importance of Species: Perspectives on Expendability and

Triage. Princeton University Press, Princeton.

3 of 13�

Kendall B.E., Briggs C.J., Murdoch W.W., Turchin P., Ellner S.P., McCauley E., Nisbet R.M. & Simon N.W. (1999). Why Do Populations Cycle? A Synthesis of Statistical and Mechanistic Modeling Approaches. Ecology, 80, 1789-1805.

Kondoh M. (2003). Foraging Adaptation and the Relationship Between Food-Web Complexity and Stability. Science, 299, 1388-1391.

Koricheva J., Gurevitch J. & Mengersen K. (2013). Handbook of Meta-analysis in Ecology and Evolution. Princeton University Press, Princeton, NJ.

Lovei G.L., Sopp P.I. & Sunderland K.D. (1990). Digestion rate in relation to alternative feeding in 3 species of polyphagous predators. Ecological Entomology, 15, 293-300.

Matheson R.E., Jr. & Brooks G.R., Jr. (1983). Habitat Segregation Between Cottus bairdi and Cottus girardi: An Example of Complex Inter- and Intraspecific Resource Partitioning. Am. Midl. Nat., 110, 165-176.

McCann K.S. (2000). The diversity–stability debate. Nature, 405, 228-233. McCann K.S. (2012). Food Webs. Princeton University Press. Menge B.A. (1995). Indirect Effects in Marine Rocky Intertidal Interaction Webs: Patterns and

Importance. Ecol. Monogr., 65, 21-74. Middlemas S.J., Barton T.R., Armstrong J.D. & Thompson P.M. (2006). Functional and

aggregative responses of harbour seals to changes in salmonid abundance. Proceedings of the Royal Society B-Biological Sciences, 273, 193-198.

Murdoch W.W., Briggs C.J., Nisbet R.M., Kendall B.E. & McCauley E. (2003). Natural enemy specialization and the period of population cycles - Reply. Ecol. Lett., 6, 384-387.

Murdoch W.W., Kendall B.E., Nisbet R.M., Briggs C.J., McCauley E. & Bolser R. (2002). Single-species models for many-species food webs. Nature, 417, 541-543.

Murdoch W.W. & Oaten A. (1975). Predation and population stability. Adv. Ecol. Res., 9, 1-130. Nakagawa S. & Cuthill I.C. (2007). Effect size, confidence interval and statistical significance: a

practical guide for biologists. Biological Reviews, 82, 591-605. Novak M. (2008). Trophic omnivory and the structure, strength, and nonlinear nature of

species interactions across a productivity gradient. In: Ecology and Evolution. University of Chicago, Ph.D. Chicago, p. 258.

Novak M. (2010). Estimating interaction strengths in nature: experimental support for an observational approach. Ecology, 91, 2394-2405.

Novak M. (2013). Trophic omnivory across a productivity gradient: intraguild predation theory and the structure and strength of species interactions. Proceedings of the Royal Society B: Biological Sciences, 280.

Novak M., Moore J.W. & Leidy R.A. (2011a). Nestedness patterns and the dual nature of community reassembly in California streams: a multivariate permutation-based approach. Global Change Biology, 17, 3714-3723.

Novak M. & Wootton J.T. (2008). Estimating nonlinear interaction strengths: an observation-based method for species-rich food webs. Ecology, 89, 2083-2089.

Novak M. & Wootton J.T. (2010). Using experimental indices to quantify the strength of species interactions. Oikos, 119, 1057-1063.

Novak M., Wootton J.T., Doak D.F., Emmerson M., Estes J.A. & Tinker M.T. (2011b). Predicting community responses to perturbations in the face of imperfect knowledge and network complexity. Ecology, 92, 836-846.

Noy-Meir I. (1975). Stability of grazing systems - application of predator-prey graphs. J. Ecol., 63, 459-481.

4 of 13�

Oaten A. & Murdoch W.W. (1975). Functional response and stability in predator-prey systems. Am. Nat., 109, 289-298.

Okuyama T. & Bolker B.M. (2012). Model-based, response-surface approaches to quantifying indirect interactions. In: Trait-Mediated Indirect Interactions (eds. Ohgushi T, Schmitz OJ & Holt RD). Cambridge University Press, pp. 186-204.

Pawar S., Dell A.I. & Van M.S. (2012). Dimensionality of consumer search space drives trophic interaction strengths. Nature, advance online publication.

Peacor S.D. & Cressler C.E. (2012). The implications of adaptive prey behavior for ecological communities: a review of current theory. In: Trait-Mediated Indirect Interactions (eds. Ohgushi T, Schmitz OJ & Holt RD). Cambridge University Press, pp. 186-204.

Quist M.C., Hubert W.A. & Isaak D.J. (2004). Factors affecting allopatric and sympatric occurrence of two sculpin species across a rocky mountain watershed. Copeia, 617-623.

Rall B.C., Kalinkat G., Ott D., Vucic-Pestic O. & Brose U. (2011). Taxonomic versus allometric constraints on non-linear interaction strengths. Oikos, 120, 483-492.

Rall B.C., Vucic-Pestic O., Ehnes R.B., Emmerson M. & Brose U. (2010). Temperature, predator–prey interaction strength and population stability. Global Change Biology, 16, 2145-2157.

Roni P. (2002). Habitat use by fishes and pacific giant salamanders in small western Oregon and Washington streams. Trans. Am. Fish. Soc., 131, 743-761.

Rooney N., McCann K., Gellner G. & Moore J.C. (2006). Structural asymmetry and the stability of diverse food webs. Nature, 442, 265-269.

Rosenzweig M.L. (1971). Paradox of Enrichment: Destabilization of Exploitation Ecosystems in Ecological Time. Science, 171, 385-387.

Sarnelle O. & Wilson A.E. (2008). Type III functional response in Daphnia. Ecology, 89, 1723-1732.

Schmitz O.J. (2008). Effects of Predator Hunting Mode on Grassland Ecosystem Function. Science, 319, 952-954.

Sentis A., Hemptinne J.L. & Brodeur J. (2013). Parsing handling time into its components: implications for responses to a temperature gradient. Ecology, 94, 1675-1680.

Sinclair A.R.E., Pech R.P., Dickman C.R., Hik D., Mahon P. & Newsome A.E. (1998). Predicting Effects of Predation on Conservation of Endangered Prey. Conserv. Biol., 12, 564-575.

Soluk D.A. (1993). Multiple Predator Effects - Predicting Combined Functional-Response of Stream Fish and Invertebrate Predators. Ecology, 74, 219-225.

Strong D.R. (1992). Are Trophic Cascades All Wet? Differentiation and Donor-Control in Speciose Ecosystems. Ecology, 73, 747-754.

Tschanz B., Bersier L.-F. & Bacher S. (2007). Functional responses: A question of alternative prey and predator density. Ecology, 88, 1300-1308.

Twardochleb L.A., Novak M. & Moore J.W. (2012). Using the functional response of a consumer to predict biotic resistance to invasive prey. Ecol. Appl., 22, 1162-1171.

Valdovinos F.S., Ramos-Jiliberto R., Garay-Narváez L., Urbani P. & Dunne J.A. (2010). Consequences of adaptive behaviour for the structure and dynamics of food webs. Ecol. Lett., 13, 1546-1559.

Williams R.J., Brose U. & Martinez N.D. (2007). Homage to Yodzis and Innes 1992: Scaling up feeding-based population dynamics to complex ecological networks. In: From Energetics

5 of 13�

to Ecosystems: The Dynamics and Structure of Ecological Systems (eds. Rooney N, McCann KS & Noakes DLG). Springer Dordrecht.

Wootton J.T. (1994). The nature and consequences of indirect effects in ecological communities. Annu. Rev. Ecol. Syst., 25, 443-466.

Wootton J.T. (1997). Estimates and tests of per capita interaction strength: Diet, abundance, and impact of intertidally foraging birds. Ecol. Monogr., 67, 45-64.

Wootton J.T. & Emmerson M. (2005). Measurement of interaction strength in nature. Annu Rev Ecol Evol Syst, 36, 419-444.

Worm B., Hilborn R., Baum J.K., Branch T.A., Collie J.S., Costello C., Fogarty M.J., Fulton E.A., Hutchings J.A., Jennings S., Jensen O.P., Lotze H.K., Mace P.M., McClanahan T.R., Minto C., Palumbi S.R., Parma A.M., Ricard D., Rosenberg A.A., Watson R. & Zeller D. (2009). Rebuilding Global Fisheries. Science, 325, 578-585.

Yeakel J., Stiefs D., Novak M. & Gross T. (2011a). Generalized modeling of ecological population dynamics. Theor Ecol, 2, 179-194.

Yeakel J.D., Guimarães P.R., Novak M., Fox-Dobbs K. & Koch P.L. (2012). Probabilistic patterns of interaction: the effects of link-strength variability on food web structure. J. Royal Soc. Interface, 9, 3219-3228.

Yeakel J.D., Novak M., Guimarães P.R., Jr., Dominy N.J., Koch P.L., Ward E.J., Moore J.W. & Semmens B.X. (2011b). Merging Resource Availability with Isotope Mixing Models: The Role of Neutral Interaction Assumptions. PLoS ONE, 6, e22015.

Yodzis P. (1988). The indeterminacy of ecological interactions as perceived through perturbation experiments. Ecology, 69, 508-515.

Zuur A.F., Ieno E.N., Walker N.J., Saveliev A.A. & Smith G.M. (2009). Mixed Effects Models and Extensions in Ecology with R. Springer, New York.

Preliminary Compilation of References for Meta-analysis

Abe, N. 1989. Prey value to the carnivorous gastropods Morula musiva (Kiener) and the two forms of Thais clavigera (Küster): effect of foraging duration and abandonment of prey. Malacologia 30:373-395.

Adlerstein, S. A., A. Temming, and N. Mergardt. 2002. Comparison of stomach contents of haddock (Melanogrammus aeglefinus) from the 1981 and 1991 North Sea International Stomach Sampling Projects. Ices Journal of Marine Science 59:497-515.

Allison, E. H., K. Irvine, A. B. Thompson, and B. P. Ngatunga. 1996. Diets and food consumption rates of pelagic fish in Lake Malawi, Africa. Freshwater Biology 35:489-515.

Andersen, N. G. 1999. The effects of predator size, temperature, and prey characteristics on gastric evacuation in whiting. Journal of Fish Biology 54:287-301.

Andersen, N. G. 2001. A gastric evacuation model for three predatory gadoids and implications of using pooled field data of stomach contents to estimate food rations. Journal of Fish Biology 59:1198-1217.

Andersen, N. G. 2012. Influences of potential predictor variables on gastric evacuation in Atlantic cod Gadus morhua feeding on fish prey: parameterization of a generic model. Journal of Fish Biology 80:595-612.

Andersen, N. G. and J. E. Beyer. 2005a. Gastric evacuation of mixed stomach contents in predatory gadoids: an expanded application of the square root model to estimate food rations. Journal of Fish Biology 67:1413-1433.

6 of 13�

Andersen, N. G. and J. E. Beyer. 2005b. Mechanistic modelling of gastric evacuation in predatory gadoids applying the square root model to describe surface-dependent evacuation. Journal of Fish Biology 67:1392-1412.

Andrade, J. P., K. Erzini, and J. Palma. 1996. Gastric evacuation and feeding in the gilthead sea bream reared under semi-intensive conditions. Aquaculture International 4:129-141.

Annett, C. and R. Pierotti. 1984. Foraging behavior and prey selection of the leather seastar Dermasterias imbricata. Marine Ecology-Progress Series 14:197-206.

Bayliss, D. E. 1982. Switching by Lepsiella vinosa (Gastropoda) in South Australian mangroves. Oecologia V54:212-226.

Bayne, B. L. and C. Scullard. 1978. Rates of feeding by Thais (Nucella) lapillus (L.). Journal of Experimental Marine Biology and Ecology 32:113-129.

Berg, C. W. and A. Temming. 2011. Estimation of feeding patterns for piscivorous fish using individual prey data from stomach contents. Canadian Journal of Fisheries and Aquatic Sciences 68:834-841.

Bernreuther, M., A. Temming, and J. P. Herrmann. 2009. Effect of temperature on the gastric evacuation in sprat Sprattus sprattus. Journal of Fish Biology 75:1525-1541.

Blackmore, G. R. 1998. The importance of feeding ecology in investigating accumulated heavy metal body burdens in Thais clavigera (Küster) (Mollusca: Neograstrapoda: Muricidae) in Hong Kong. The University of Hong Kong.

Blanco-Parra, M. D., F. Galvan-Magana, J. F. Marquez-Farias, and C. A. Nino-Torres. 2012. Feeding ecology and trophic level of the banded guitarfish, Zapteryx exasperata, inferred from stable isotopes and stomach contents analysis. Environmental Biology of Fishes 95:65-77.

Boelter, R. A., I. L. Kaefer, C. Both, and S. Cechin. 2012. Invasive bullfrogs as predators in a Neotropical assemblage: What frog species do they eat? Animal Biology 62:397-408.

Bostrom, M. K., O. Ostman, M. A. J. Bergenius, and S. G. Lunneryd. 2012. Cormorant diet in relation to temporal changes in fish communities. Ices Journal of Marine Science 69:175-183.

Brown, K. M. 1997. Size-specific aspects of the foraging ecology of the southern oyster drill Stramonita haemastoma (Kool 1987). Journal of Experimental Marine Biology and Ecology 214:249-262.

Brown, K. M. and J. E. J. Alexander. 1994. Group foraging in a marine gastropod predator: benefits and costs to individuals. Marine Ecology Progress Series 112.

Calver, M. C. and R. D. Wooller. 1982. A technique for assessing the taxa, length, dry weight and energy content of the arthropod prey of birds. Australian Wildlife Research 9:293-301.

Carroll, M. L. and D. S. Wethey. 1990. Predator foraging behavior: effect of a novel prey species on prey selection by a marine intertidal gastropod. Journal of Experimental Marine Biology and Ecology 139:101-117.

Chow, C.-y. 2004. Foraging behaviour of Thais clavigera. The University of Hong Kong. Collier, A., J. B. Keiper, and L. P. Orr. 1998. The invertebrate prey of the northern leopard frog,

Rana pipiens, in a northeastern Ohio population. Ohio Journal of Science 98:39-41. Connell, J. H. 1961. Effects of Competition, Predation by Thais lapillus, and Other Factors on

Natural Populations of the Barnacle Balanus balanoides. Ecological Monographs 31:61-104. Coulson, L. A., C. Perrin, D. G. Roberts, T. E. Minchinton, and D. J. Ayre. 2011. Can limited

dispersal or biotic interaction explain the declining abundance of the whelk, Morula marginalba, at the edge of its range? Biological Journal of the Linnean Society 103:849-862.

7 of 13�

Davis, A. M., M. L. Blanchette, B. J. Pusey, T. D. Jardine, and R. G. Pearson. 2012. Gut content and stable isotope analyses provide complementary understanding of ontogenetic dietary shifts and trophic relationships among fishes in a tropical river. Freshwater Biology 57:2156-2172.

Dayton, P. K., R. J. Rosenthal, L. C. Mahen, and T. Antezana. 1977. Population structure and foraging biology of the predaceous chilean asteroid Meyenaster gelatinosus and the escape biology of its prey. Marine Biology 39:361-370.

De B. Dunkin, S. and R. N. Hughes. 1984. Behavioural components of prey-selection by dogwhelks, Nucella lapillus (L.), feeding on barnacles, Semibalanus balanoides (L.), in the laboratory. Journal of Experimental Marine Biology and Ecology 79:91-103.

Dickman, C. R. 1995. Diets and habitat preferences of 3 species of Crocidurine shrews in arid South Africa. Journal of Zoology 237:499-514.

Dickman, C. R., S. E. J. Daly, and G. W. Connell. 1991. Dietary relationships of the barn owl and Australian kestrel on islands off the coast of western Australia. Emu 91:69-72.

Elliott, J. M. 1991. Rates of gastric evactuation in piscivorous brown trout, Salmo trutta. Freshwater Biology 25:297-305.

Eloranta, A. P., R. Knudsen, and P. A. Amundsen. 2013. Niche segregation of coexisting Arctic charr (Salvelinus alpinus) and brown trout (Salmo trutta) constrains food web coupling in subarctic lakes. Freshwater Biology 58:207-221.

Emlen, J. M. 1966. Time, energy and risk in two species of carnivorous gastrophods. University of Washington, Seattle.

Facendola, J. J. and F. S. Scharf. 2012. Seasonal and Ontogenetic Variation in the Diet and Daily Ration of Estuarine Red Drum as Derived from Field-Based Estimates of Gastric Evacuation and Consumption. Marine and Coastal Fisheries 4:546-559.

Fahrig, L., G. R. Lilly, and D. S. Miller. 1993. Predator stomachs as sampling tools for prey distribution, Atlantic cod (Gadus morhua) and Capelin (Mallotus villosus). Canadian Journal of Fisheries and Aquatic Sciences 50:1541-1547.

Fairweather, P. G. 1985. Differential predation on alternative prey, and the survival of rocky intertidal organisms in New South Wales. Journal of Experimental Marine Biology and Ecology 89:135-156.

Fairweather, P. G. and A. J. Underwood. 1983. The apparent diet of predators and biases due to different handling times of their prey. Oecologia 56:169-179.

Fairweather, P. G. and A. J. Underwood. 1991. Experimental removals of a rocky intertidal predator: variations within two habitats in the effects on prey. Journal of Experimental Marine Biology and Ecology 154:29-75.

Feder, H. M. 1959. The Food of the Starfish, Pisaster-Ochraceus, Along the California Coast. Ecology 40:720-724.

Feeney, W. E., O. M. Lonnstedt, Y. Bosiger, J. Martin, G. P. Jones, R. J. Rowe, and M. I. McCormick. 2012. High rate of prey consumption in a small predatory fish on coral reefs. Coral Reefs 31:909-918.

Ferry, K. H. and M. E. Mather. 2012. Spatial and Temporal Diet Patterns of Subadult and Small Adult Striped Bass in Massachusetts Estuaries: Data, a Synthesis, and Trends across Scales. Marine and Coastal Fisheries 4:30-45.

Fisher, J. A. D. 2008. Using polyclonal antibodies to detect predation by dogwhelks Nucella lapillus (L.). Journal of Experimental Marine Biology and Ecology 361:28-35.

8 of 13�

Gales, R. P. 1987. Validation of stomach flushing technique for obtaining stomach contents of penguins. Ibis 129:335-343.

Garrido, S. and A. G. Murta. 2011. Interdecadal and spatial variations of diet composition in horse mackerel Trachurus trachurus. Journal of Fish Biology 79:2034-2042.

Gaymer, C. F., C. Dutil, and J. H. Himmelman. 2004. Prey selection and predatory impact of four major sea stars on a soft bottom subtidal community. Journal of Experimental Marine Biology and Ecology 313:353-374.

Gaymer, C. F. and J. H. Himmelman. 2008. A keystone predatory sea star in the intertidal zone is controlled by a higher-order predatory sea star in the subtidal zone. Marine Ecology Progress Series 370:143-153.

Gaymer, C. F., J. H. Himmelman, and L. E. Johnson. 2001. Use of prey resources by the seastars Leptasterias polaris and Asterias vulgaris: a comparison between field observations and laboratory experiments. Journal of Experimental Marine Biology and Ecology 262:13-30.

Gil, D. G. and H. E. Zaixso. 2007. The relation between feeding and reproduction in Anasterias minuta (Asteroidea: Forcipulata). Marine Biology 3:256-264.

Glorioso, B. M., J. H. Waddle, M. E. Crockett, K. G. Rice, and H. F. Percival. 2012. Diet of the invasive Cuban Treefrog (Osteopilus septentrionalis) in pine rockland and mangrove habitats in South Florida. Caribbean Journal of Science 46:346-355.

Green, S. J., J. L. Akins, A. Maljkovic, and I. M. Cote. 2012. Invasive Lionfish Drive Atlantic Coral Reef Fish Declines. PLoS ONE 7.

Greene, H. W. and J. A. Rodriguez-Robles. 2003. Feeding ecology of the California mountain kingsnake, Lampropeltis zonata (Colubridae). Copeia:308-314.

Hall, R. O., M. F. Dybdahl, and M. C. VanderLoop. 2006. Extremely high secondary production of introduced snails in rivers. Ecological Applications 16:1121-1131.

Hall, R. O., J. B. Wallace, and S. L. Eggert. 2000. Organic matter flow in stream food webs with reduced detrital resource base. Ecology 81:3445-3463.

Hampton, P. M., N. Haertle, S. F. Dartez, and C. Monteiro. 2009. Prey of the broad-banded watersnake (Nerodia fasciata) and the diamondback watersnake (Nerodia rhombifer). Southwestern Naturalist 54:521-523.

Hart, R. K., M. C. Calver, and C. R. Dickman. 2002. The index of relative importance: an alternative approach to reducing bias in descriptive studies of animal diets. Wildlife Research 29:415-421.

Hayward, R. S. and M. E. Bushmann. 1994. Gastric evacuation rates for juvenile Largemouth bass. Transactions of the American Fisheries Society 123:88-93.

He, E. Q. and W. A. Wurtsbaugh. 1993. An empirical model of gastric evacuation rates for fish and an analysis of digestion in piscivorous brown trout. Transactions of the American Fisheries Society 122:717-730.

Hynes, H. B. N. 1950. The Food of Fresh-Water Sticklebacks (Gasterosteus aculeatus and Pygosteus pungitius), with a Review of Methods Used in Studies of the Food of Fishes. Journal of Animal Ecology 19:36-58.

Jackson, S., D. C. Duffy, and J. F. G. Jenkins. 1987. Gastric digestion in marine vertebrate predators: in vitro standards. Functional Ecology 1:287-291.

Jensen, H., M. Kiljunen, and P. A. Amundsen. 2012. Dietary ontogeny and niche shift to piscivory in lacustrine brown trout Salmo trutta revealed by stomach content and stable isotope analyses. Journal of Fish Biology 80:2448-2462.

9 of 13�

Jeschke, J. M., M. Kopp, and R. Tollrian. 2002. Predator functional responses: Discriminating between handling and digesting prey. Ecological Monographs 72:95-112.

Jones, P. C., R. B. King, K. M. Stanford, T. D. Lawson, and M. Thomas. 2009. Frequent Consumption and Rapid Digestion of Prey by the Lake Erie Watersnake with Implications for an Invasive Prey Species. Copeia:437-445.

Kapuscinski, K. L., J. M. Farrell, and B. A. Murry. 2012. Feeding Strategies and Diets of Young-of-the-Year Muskellunge from Two Large River Ecosystems. North American Journal of Fisheries Management 32:635-647.

Karlsen, J. D. and N. G. Andersen. 2012. Does the cylinder model of gastric evacuation predict observed evacuation of mixed meals of prey of contrasting geometries in a piscivorous fish? Journal of Fish Biology 80:166-180.

Kearney, M. 2003. Diet in the amphisbaenian Bipes biporus. Journal of Herpetology 37:404-408. Knudsen, R., A. Siwertsson, C. E. Adams, M. Garduno-Paz, J. Newton, and P. A. Amundsen.

2011. Temporal stability of niche use exposes sympatric Arctic charr to alternative selection pressures. Evolutionary Ecology 25:589-604.

Kok, O. B. 1996. Diet composition of different carnivores in the Free State, South Africa. South African Journal of Science 92:393-398.

Krofel, M., D. Huber, and I. Kos. 2011. Diet of Eurasian lynx Lynx lynx in the northern Dinaric Mountains (Slovenia and Croatia) Importance of edible dormouse Glis glis as alternative prey. Acta Theriologica 56:315-322.

Krog, C. and N. G. Andersen. 2009. Are the dynamics of gastric evacuation of natural prey in a piscivorous flatfish different from what is going on in a gadoid? Journal of Fish Biology 75:1831-1844.

Labropoulou, M., A. Machias, N. Tsimenides, and A. Eleftheriou. 1997. Feeding habits and ontogenetic diet shift of the striped red mullet, Mullus surmuletus Linnaeus, 1758. Fisheries Research 31:257-267.

Landenberger, D. E. 1968. Studies on Selective Feeding in Pacific Starfih Pisaster in Southern California. Ecology 49:1062-1075.

Legler, J. M. and L. J. Sullivan. 1979. Application of stomach flushing to lizards and anurans. Herpetologica 35:107-110.

Legler, N. D., T. B. Johnson, D. D. Heath, and S. A. Ludsin. 2010. Water Temperature and Prey Size Effects on the Rate of Digestion of Larval and Early Juvenile Fish. Transactions of the American Fisheries Society 139:868-875.

Locke, S. A., G. Bulte, M. R. Forbes, and D. J. Marcogliese. 2013. Estimating diet in individual pumpkinseed sunfish Lepomis gibbosus using stomach contents, stable isotopes and parasites. Journal of Fish Biology 82:522-537.

López, M. S., R. Coutinho, C. Ferreira, and G. Rilov. 2010. Predator-prey interactions in a bioinvasion scenario: differential predation by native predators on two exotic rocky intertidal bivalves. Marine Ecology Progress Series 403:101-112.

Louda, S. M. 1979. Distribution, movement and diet of the snail Searlesia dira in the intertidal community of San Juan Island, Puget Sound, Washington. Marine Biology 51:119-131.

Lovei, G. L., P. I. Sopp, and K. D. Sunderland. 1990. Digestion rate in relation to alternative feeding in 3 species of polyphagous predators. Ecological Entomology 15:293-300.

Mah, C. L. and D. B. Blake. 2012. Global Diversity and Phylogeny of the Asteroidea (Echinodermata). PLoS ONE 7:e35644.

10 of 13�

Mauzey, K. P. 1966. Feeding behavior and reproductive cycles in Pisaster ochraceus. Biological Bulletin 131:127-&.

Mauzey, K. P., Birkelan.C, and P. K. Dayton. 1968. Feeding Behavior of Asteroids and Escape Responses of Their Prey in Puget Sound Region. Ecology 49:603-&.

McClintock, J. B. and J. M. Lawrence. 1985. Characteristics of foraging in the soft-bottom benthic starfish Luidia clathrata (echinodermata: Asteroidea): prey selectivity, switching behavior, functional responses and movement patterns. Oecologia 66:291-298.

McMillan, S., A. K. Kuusk, A. Cassel-Lundhagen, and B. Ekbom. 2007. The influence of time and temperature on molecular gut content analysis: Adalia bipunctata fed with Rhopalosiphum padi. Insect Science 14:353-358.

McWilliam, R. A., T. E. Minchinton, and D. J. Ayre. 2013. Despite prolonged association in closed populations, an intertidal predator does not prefer abundant local prey to novel prey. Biological Journal of the Linnean Society 108:812-820.

Memmott, J., N. D. Martinez, and J. E. Cohen. 2000. Predators, Parasitoids and Pathogens: Species Richness, Trophic Generality and Body Sizes in a Natural Food Web. Journal of Animal Ecology 69:1-15.

Menge, B. A. 1972. Foraging strategy of a starfish in relation to actual prey availability and environmental predictability. Ecological Monographs 42:25-50.

Menge, B. A. 1976. Organization of the New England Rocky Intertidal Community: Role of Predation, Competition, and Environmental Heterogeneity. Ecological Monographs 46:355-393.

Menge, J. L. 1974. Prey selection and foraging period of the predaceous rocky intertidal snail, Acanthina punctulata. Oecologia 17:293-316.

Menge, J. L. and B. A. Menge. 1974. Role of Resource Allocation, Aggression and Spatial Heterogeneity in Coexistence of Two Competing Intertidal Starfish. Ecological Monographs 44:189-209.

Mikkelsen, B., T. Haug, and K. T. Nilssen. 2002. Summer diet of grey seals (Halichoerus grypus) in Faroese waters. Sarsia 87:462-471.

Miller, M. A. and M. E. Holey. 1992. Diets of Lake trout inhabiting nearshore and offshore Lake michigan environments. Journal of Great Lakes Research 18:51-60.

Modica, L., A. Bozzano, F. Velasco, G. Albertelli, and I. Olaso. 2011. Predation, feeding strategy and food daily ration in juvenile European hake. Marine Ecology Progress Series 440:177-189.

Morton, B. 2006. Diet and predation behaviour exhibited by Cominella eburnea (Gastropoda: Caenogastrapoda: Neogastrapoda) in Princess Royal Harbour, Albany, Western Australia, with a review of attack strategies in the Buccinidae. Molluscan Research 26:39-50.

Morton, B. 2010. Predator-prey interactions between a population of Nucella lapillus (Gastropoda: Muricidae) recovering from imposex and Mytilus galloprovincialis (Bivalvia: Mytilidae) on the south-east coast of England. Journal of the Marine Biological Association of the United Kingdom 90:671-681.

Nadeau, M., M. A. Barbeau, and J.-C. BrÍthes. 2009. Behavioural mechanisms of sea stars (Asterias vulgaris Verrill and Leptasterias polaris M¸ller) and crabs (Cancer irroratus Say and Hyas araneus Linnaeus) preying on juvenile sea scallops (Placopecten magellanicus (Gmelin)), and procedural effects of scallop tethering. Journal of Experimental Marine Biology and Ecology 374:134-143.

11 of 13�

Navarrete, S. 1995. Effects of interactions between predators, variable predation regimes, and species body size on rocky intertidal communities : comparative and experimental approaches. Oregon State University.

Navarrete, S. A. and T. Manzur. 2008. Individual- and population-level responses of a keystone predator to geographic variation in prey. Ecology 89:2005-2018.

Navarrete, S. A. and B. A. Menge. 1996. Keystone predation and interaction strength: interactive effects of predators on their main prey. Ecological Monographs 66:409-429.

Nifong, J. C., A. E. Rosenblatt, N. A. Johnson, W. Barichivich, B. R. Silliman, and M. R. Heithaus. 2012. American Alligator Digestion Rate of Blue Crabs and Its Implications for Stomach Contents Analysis. Copeia:419-423.

Nilsson, P. A. and C. Bronmark. 2000. The role of gastric evacuation rate in handling time of equal-mass rations of different prey sizes in northern pike. Journal of Fish Biology 57:516-524.

Nishino, M. and K. Kawabata. 2003. Gastric evacuation in koayu Plecoglossus altivelis altivelis examined in aquaria. Fisheries Science 69:819-822.

Paine, R. T. 1963. Trophic Relationships of 8 Sympatric Predatory Gastropods. Ecology 44:63-73.

Paine, R. T. 1969. The Pisaster-Tegula interaction: Prey patches, predator food preference, and intertidal community structure. Ecology 50:950-961.

Paine, R. T. 1976. Size-Limited Predation - Observational and Experimental Approach with Mytilus-Pisaster Interaction. Ecology 57:858-873.

Paine, R. T. 1988. Road Maps of Interactions or Grist for Theoretical Development? Ecology 69:1648-1654.

Palmer, A. R. 1984. Prey selection by thaidid gastropods: some observational and experimental field tests of foraging models. Oecologia V62:162-172.

Palmer, A. R. 1988. Feeding Biology of Ocenebra-Lurida (Prosobranchia, Muricacea) - Diet, Predator-Prey Size Relations, and Attack Behavior. Veliger 31:192-203.

Parker, M. S. 1993. Size-selective predation on benthic macroinvertebrates by stream-dwelling salamander larvae. Archiv Fur Hydrobiologie 128:385-400.

Perry, D. M. 1985. Function of the shell spine in the predaceous rocky intertidal snail Acanthina spirata (Prosobranchia: Muricacea). Marine Biology 88:51-58.

Quinlan, T. G., M. C. Calver, and G. T. Smith. 1993. Immunological determination of digestive rates in the syntopic scorpions Urodacus armatus Pocock and Urodacus noaehollandiae Peters. Oecologia 95:459-462.

Richardson, T. D. and K. M. Brown. 1990. Wave exposure and prey size selection in an intertidal predator. Journal of Experimental Marine Biology and Ecology 142:105-120.

Rodriguez-Robles, J. A. and H. W. Greene. 1999. Food habits of the long-nosed snake (Rhinocheilus lecontei), a 'specialist' predator? Journal of Zoology 248:489-499.

Rogers, J. B. and C. C. Burley. 1991. A sigmoid model to predict gastric evacuation rates in smallmouth bass, Mircropterus dolomieui) fed juvenile salmon. Canadian Journal of Fisheries and Aquatic Sciences 48:933-937.

Romano, A., S. Salvidio, R. Palozzi, and V. Sbordoni. 2012. Diet of the newt, Triturus carniflex (Laurenti, 1768), in the flooded karst sinkhole Pozzo del Merro, Central Italy. Journal of Cave and Karst Studies 74:271-277.

Sagarese, S. R., R. M. Cerrato, and M. G. Frisk. 2011. Diet Composition and Feeding Habits of Common Fishes in Long Island Bays, New York. Northeastern Naturalist 18:291-314.

12 of 13�

Sanford, E. 1999. Oceanographic Influences on Rocky Intertidal Communities: Coastal Upwelling, Invertebrate Growth Rates, and Keystone Predation. Oregon State University.

Saunders, R. J., A. J. Fowler, and B. M. Gillanders. 2012. The use of food resources by 0+snapper, Chrysophrys auratus, from northern Spencer Gulf, South Australia. Marine and Freshwater Research 63:680-686.

Scharf, F. S., R. M. Yetter, A. P. Summers, and F. Juanes. 1998. Enhancing diet analyses of piscivorous fishes in the Northwest Atlantic through identification and reconstruction of original prey sizes from ingested remains. Fishery Bulletin 96:575-588.

Scolding, J. W. S., C. A. Richardson, and M. J. Luckenbach. 2007. Predation of cockles (Cerastoderma edule) by the whelk (Buccinum undatum) under laboratory conditions. Journal of Molluscan Studies 73:333-337.

Sokolowiez, C. C., L. Ayres-Peres, and S. Santos. 2007. Diel activity and digestion time of Aegla longirostri (Crustacea, Decapoda, Anomura). Iheringia Serie Zoologia 97:235-238.

Spight, T. M. 1977. Diversity of Shallow-Water Gastropod Communities on Temperate and Tropical Beaches. The American Naturalist 111:1077-1097.

Spight, T. M. 1978. Temporal change in a tropical rocky shore snail community. Veliger 21:137-143.

Stefansson, G. and O. K. Palsson. 1997. Statistical evaluation and modelling of the stomach contents of Icelandic cod (Gadus morhua). Canadian Journal of Fisheries and Aquatic Sciences 54:169-181.

Steinarsdóttir, M. B., A. Ingólfsson, and E. Ólafsson. 2009. Trophic relationships on a fucoid shore in south-western Iceland as revealed by stable isotope analyses, laboratory experiments, field observations and gut analyses. Journal of Sea Research 61:206-215.

Sugiura, S. and T. Taguchi. 2012. Estimating the feeding habits of largemouth bass and bluegill around Noda Lake, a satellite lake of Lake Biwa, based on stomach contents and fecal DNA. Nippon Suisan Gakkaishi 78:43-53.

Sullivan, L. J. 2010. Gut evacuation of larval Mnemiopsis leidyi A. Agassiz (Ctenophora, Lobata). Journal of Plankton Research 32:69-74.

Taylor, J. D. and A. Lewis. 1995. Diet and radular morphology of Peristernia and Latirolagena (Gastropoda: Fasciolariidae) from Indo-Pacific coral reefs. Journal of Natural History 29:1143 - 1154.

Temming, A. and J. P. Herrmann. 2001a. Gastric evacuation in horse mackerel. I. The effects of meal size, temperature and predator weight. Journal of Fish Biology 58:1230-1245.

Temming, A. and J. P. Herrmann. 2001b. Gastric evacuation of horse mackerel. II. The effects of different prey types on the evacuation model. Journal of Fish Biology 58:1246-1256.

Temming, A. and J. P. Herrmann. 2003. Gastric evacuation in cod - Prey-specific evacuation rates for use in North Sea, Baltic Sea and Barents Sea multi-species models. Fisheries Research 63:21-41.

Tomiyama, T. and Y. Kurita. 2011. Seasonal and spatial variations in prey utilization and condition of a piscivorous flatfish Paralichthys olivaceus. Aquatic Biology 11:279-288.

Town, J. C. 1980a. Diet and Food Preference of Inter-Tidal Astrostole-Scabra (Asteroidea, Forcipulata). New Zealand Journal of Marine and Freshwater Research 14:427-435.

Town, J. C. 1980b. Movement, morphology, reproductive periodicity, and some factors affecting gonad production in the seastar Astrostole scabra (Hutton). Journal of Experimental Marine Biology and Ecology 44:111-132.

13 of 13�

Town, J. C. 1981. Prey Characteristics and Dietary-Composition in Inter-Tidal Astrostole-Scabra (Echinodermata, Asteroidea). New Zealand Journal of Marine and Freshwater Research 15:69-80.

Townsend, C. R., R. M. Thompson, A. R. McIntosh, C. Kilroy, E. Edwards, and M. R. Scarsbrook. 1998. Disturbance, resource supply, and food-web architecture in streams. Ecology Letters 1:200-209.

Tuttle, K. N. and P. T. Gregory. 2009. Food Habits of the Plains Garter Snake (Thamnophis radix) at the Northern Limit of Its Range. Journal of Herpetology 43:65-73.

van Rijn, P. C. J., F. M. Bakker, W. A. D. van der Hoeven, and M. W. Sabelis. 2005. Is arthropod predation exclusively satiation-driven? Oikos 109:101-116.

Vigg, S., T. P. Poe, L. A. Prendergast, and H. C. Hansel. 1991. Rates of consumption of juvenile salmonids and alternative prey by Northern Squawfish, Walleyes, Smallmouth bass, and Channel catfish in John Day resevoir, Columbia river. Transactions of the American Fisheries Society 120:421-438.

Ward, S. and G. P. Quinn. 1988. Preliminary investigations of the ecology of the intertidal predatory gastropod Lepsiella vinosa (Lamarck) (Gastropoda Muricidae). Journal of Molluscan Studies 54:109-117.

West, L. 1986. Interindividual variation in prey selection by the snail Nucella (=Thais) emarginata. Ecology 67:798-809.

West, L. 1988. Prey selection by the tropical snail Thais melones: a study of interindividual variation. Ecology 69:1839-1854.

Wieters, E. A. 2000. The consequences of variable recruitment of prey for predators. San Jose State University, Moss Landing.

Witman, J. D., M. Brandt, and F. Smith. 2010. Coupling between subtidal prey and consumers along a mesoscale upwelling gradient in the Galápagos Islands. Ecological Monographs 80:153-177.

Wong, M. C. and M. A. Barbeau. 2005. Prey selection and the functional response of sea stars (Asterias vulgaris Verrill) and rock crabs (Cancer irroratus Say) preying on juvenile sea scallops (Placopecten magellanicus (Gmelin)) and blue mussels (Mytilus edulis Linnaeus). Journal of Experimental Marine Biology and Ecology 327:1-21.

Wong, M. C., J. d'Entremont, and M. A. Barbeau. 2012. An approach for quantifying effects of multiple predators that forage on different time scales. Journal of Experimental Marine Biology and Ecology 420-421:100-109.

Woodward, G., D. C. Spiers, and A. G. Hildrew. 2005. Quantification and resolution of a complex, size-structured food web. Advances in Ecological Research 36:85-135.

Yamamoto, T. 2004. Prey composition and prey selectivity of an intertidal generalist predator, Muricodrupa fusca (Küster) (Muricidae). Marine Ecology 25:35-49.

York, M. M., D. K. Rosenberg, and K. K. Sturm. 2002. Diet and food-niche breadth of Burrowing Owls (Athene cunicularia) in the Imperial Valley, California. Western North American Naturalist 62:280-287.

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