Productivity, biodiversity, and pathogens influence theglobal hunter-gatherer population densityMiikka Tallavaaraa,1, Jussi T. Eronena,b, and Miska Luotoa

aDepartment of Geosciences and Geography, University of Helsinki, FI-00014 Helsinki, Finland; and bBIOS Research Unit, FI-00170 Helsinki, Finland

Edited by Robert L. Kelly, University of Wyoming, Laramie, WY, and accepted by Editorial Board Member Richard G. Klein December 6, 2017 (received forreview September 4, 2017)

The environmental drivers of species distributions and abundancesare at the core of ecological research. However, the effects ofthese drivers on human abundance are not well-known. Here, wereport how net primary productivity, biodiversity, and pathogenstress affect human population density using global ethnographichunter-gatherer data. Our results show that productivity hassignificant effects on population density globally. The most impor-tant direct drivers, however, depend on environmental conditions:biodiversity influences population density exclusively in low-productivity regions, whereas pathogen stress does so in high-productivity regions. Our results also indicate that subtropical andtemperate forest biomes provide the highest carrying capacity forhunter-gatherer populations. These findings document that envi-ronmental factors play a key role in shaping global populationdensity patterns of preagricultural humans.

hunter-gatherers | population density | pathogens | human ecology |structural equation modeling

Questions related to the environmental drivers of speciesdistributions and abundances have been at the core of

ecology throughout its history. However, these questions haverarely been addressed for preindustrial human populations, de-spite the fact that these populations provide a rare opportunityto investigate drivers of the distribution and abundance of asingle species along global environmental gradients. Recent ar-chaeological studies have correlated long-term human pop-ulation dynamics and major dispersal and range shift events withclimate changes (1–5), but their results are mixed regarding thesignificance of climate in shaping human population processes.Ethnographic data provide finer-scale information about pre-industrial human populations and their environments, poten-tially allowing more conclusive analyses. However, even forhunter-gatherers, ethnographic studies about the ecological de-terminants of population patterns are relatively few (6–9), de-spite hunter-gatherers’ close dependence on their immediateenvironment and wild resources.Here, we use global ethnographic hunter-gatherer data (10,

11) to explore the effects of key environmental variables onhuman population densities. These variables are net primaryproductivity (NPP) calculated as a function of the annual meantemperature and annual precipitation; biodiversity as surrogatedby a combination of mammal, bird, and vascular plant richness;and environmental pathogen stress as a combination of pathogenrichness and the severity of exposure (Materials and Methods andFig. S1). In previous work, only the effects of productivity onhuman population densities have been assessed. These studiessuggest that both primary and secondary productivity have, atleast regionally, positive effects on hunter-gatherer populationdensity as well as on population home ranges (6–9). Such posi-tive effects are expected, because hunter-gatherers access fooddirectly from their surroundings, which vary widely in energyavailability (12). Although hunter-gatherers depend on the pro-ductivity of wild plant and animal species, they appropriate onlya small fraction of the production and in this regard, more

resemble other land mammals of their size than they do humansof modern industrialized societies (13).However, the amount of available food may not be all that

matters in controlling hunter-gatherer abundance, as biodiversitycan also play a role. Biodiversity influences ecosystem stability,such that with increasing levels of diversity, the temporal vari-ance of ecosystem productivity tends to decrease and the tem-poral mean of ecosystem productivity tends to increase (14, 15).A current consensus is that higher biodiversity can enhance thetemporal stability of aggregate ecosystem properties, such asbiomass and productivity, but its effect on stability of individualpopulations remains controversial (15, 16). The stabilizing effectof biodiversity may come through processes like asynchrony inthe responses of species to environmental variation (17). Forhunter-gatherers, increased stability of ecosystem-level biomassproduction caused by higher biodiversity decreases subsistence-related risk, which can positively affect hunter-gatherer populationdensities.In contrast to the effects of productivity and biodiversity, the

effects of pathogens on hunter-gatherer abundance are negative.A well-known example is the demographic shock among NativeAmericans caused by infectious diseases after European contact(18, 19). Beyond the effects of such dramatic epidemiologicalevents, we postulate that the background level of pathogen stressspecific to each environment also influences human populationdensity. Studies in animal ecology have shown that pathogens

Significance

Because of complex cumulative culture, human populations areoften considered to be divorced from the environment and notbe under the same ecological forcing as other species. How-ever, this study shows that key environmental parameters netprimary productivity, biodiversity, and environmental patho-gen stress have strong influence on the global pattern ofhunter-gatherer population density. Productivity and bio-diversity exert the strongest influence in high and midlati-tudes, whereas pathogens become more important in tropics.The most suitable conditions for preagricultural humans arefound in temperate and subtropical biomes. Our results showthat cultural evolution has not freed human hunter-gatherersfrom strong biotic and abiotic forcing.

Author contributions: M.T. and M.L. designed research; M.T. performed research; M.T.and M.L. contributed new reagents/analytic tools; M.T., J.T.E., and M.L. analyzed data;and M.T., J.T.E., and M.L. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. R.L.K. is a guest editor invited by theEditorial Board.

Published under the PNAS license.

Data deposition: The data and scripts reported in this paper have been deposited in theZenodo repository, https://doi.org/10.5281/zenodo.1069786.

See Commentary on page 1137.1To whom correspondence should be addressed. Email: miikka.tallavaara@helsinki.fi.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1715638115/-/DCSupplemental.

1232–1237 | PNAS | February 6, 2018 | vol. 115 | no. 6 www.pnas.org/cgi/doi/10.1073/pnas.1715638115

Dow

nloa

ded

by g

uest

on

Janu

ary

2, 2

022

can have negative effects on hosts’ abundance (20–22), and weexpect that this applies to human populations as well.Previously, Binford (10) has suggested that resource abun-

dance and stability as well as pathogens would have playedan important role in constraining hunter-gatherer populationgrowth. However, Binford (10) does not analyze this hypothesiswith the data, whereas our study presents a test of the jointeffect of NPP, biodiversity, and pathogens on hunter-gathererpopulations.We use structural equation modeling to reveal the potentially

hierarchical effects of NPP, biodiversity, and environmentalpathogen stress (23) (Materials and Methods). This method al-lows us to explore the network of variables and thus, the indirecteffects of the explanatory variables. In addition to its direct effecton hunter-gatherer population density, NPP may have an indirecteffect mediated by biodiversity. Although the actual mechanismis still debated, plant and animal richness is related to productivity,and these relationships are predominantly positive and monotonic(24, 25). Furthermore, pathogen richness follows the same lat-itudinal pattern as biodiversity in general, and this pattern ismost likely related to temperature and precipitation (26). Thus,climate-based NPP may also have an indirect effect on populationdensity through pathogen stress. However, human pathogenrichness is also related to the richness of alternative hosts (27).Consequently, the effects of climate-based NPP on populationdensity can be simultaneously mediated by both biodiversity andpathogen stress. This hypothesizedx network of variables is il-lustrated in Fig. 1.In addition, we provide a geographical interpretation of en-

vironmental effects on population density by modeling a distri-bution map of the relative contributions of the limiting effects ofNPP, biodiversity, and pathogen stress on global hunter-gathererpopulation density. We also model a potential distribution ofglobal hunter-gatherer population density itself as a function of thethree environmental variables. These maps are based on the com-bination of two regression modeling techniques and are projectionsto current environmental conditions assuming that the globe ispopulated by hunter-gatherers only (Materials and Methods).

ResultsVisual inspections and breakpoint analysis of the bivariate re-lationship between climate-based NPP and hunter-gathererpopulation density indicate an NPP threshold of ∼1,360 g/m2

per year, above which the population density becomes largelyindependent of additional increases in annual productivity (Fig.2A). However, above the same threshold, NPP exhibits a strong

predictive power of pathogen stress (Fig. 2B). This raises thequestion as to whether the leveling off of hunter-gatherer pop-ulation density in high-productivity environments is related toincreased pathogen stress.To further analyze these potentially complex relationships

between variables, we used structural equation modeling. Toease interpretability of the direct and indirect effects, we builtseparate models with identical structure (Fig. 1) for the low- andhigh-productivity environments delineated by the NPP thresholdidentified in the breakpoint analysis.The structural equation modeling results strongly indicate

different constraints between the low- and high-productivity en-vironments. In the low-productivity environments, biodiversityhas the strongest direct effect on hunter-gatherer populationdensity followed by NPP, whereas the effect of pathogen stress isnot statistically significant (Fig. 3A, Fig. S2A, and Table S1). Inthe high-productivity regions, however, the importance of theexplanatory variables is reversed. Here, pathogen stress has thestrongest effect, and NPP still has relatively high direct and in-direct effects, but biodiversity is no longer significant (Fig. 3B,Fig. S2B, and Table S1).Because of its indirect effect through biodiversity, NPP has the

strongest total effect (combined direct and indirect effects) onpopulation density in low-productivity regions (Table S1). Inhigh-productivity regions, the total effect of NPP is weaker thanthe direct effect of pathogens (Table S1).As a cross-check to the structural equation modeling results

regarding the direct controls of hunter-gatherer populationdensity, we fit a linear model to the whole data (i.e., the datawere not split into low- and high-productivity environments as in

++

Net primary productivity

ytisrevidoiB

Population density

ssert

sne

goh t

aP

-+

++

Fig. 1. Structural equation metamodel showing hypothesized expectationsabout the relationships among NPP, biodiversity, environmental pathogenstress, and hunter-gatherer population density. Blue arrows indicate positiveeffects, and red arrows indicate negative effects.

−1

0

1

2

3

4

5

−1

−0.5

0

0.5

0 1500

5.6

2.2

-1.6

-0.98

-0.82

0.65

500 1000 2000 2500

ytisnednoitalu po

P)

mk001/#(

gole

2

sser t

sne

g oht

aP

s sert

sne

goht

aP

ytis nednoitalupo

P

NPP (g/ /year)m2

Low-productivity High-productivityβNPP = p =-0.0002, 0.5βNPP = p ≤0.003, 0.0001

βNPP = p ≤0.0006, 0.0001βNPP = p =0.00007, 0.2

1372 ± 103.4 (S.E.)

1349 ± 118.0 (S.E.)

A

B

Fig. 2. Contrasting effects of NPP on hunter-gatherer population densityand pathogen stress. (A) Relationship between NPP and hunter-gathererpopulation density. Bubble size reflects the magnitude of pathogen stress. Abivariate piecewise regression model (black curve) explains 44% of thevariation in population density. (B) Relationship between NPP and pathogenstress. Bubble size reflects hunter-gatherer population density. A bivariatepiecewise regression model (black curve) explains 29% of the variation inpathogen stress. A and B also show linear model breakpoints, their SEs, andthe mean of these breakpoints (1,360 g/m2 per year), which is used to definethe low- (n = 234) and high-productivity (n = 66) environments. In addition,A and B show coefficients of NPP and their P values in regressions betweenNPP, population density, and pathogen stress in low- and high-productivityenvironments.

Tallavaara et al. PNAS | February 6, 2018 | vol. 115 | no. 6 | 1233

ANTH

ROPO

LOGY

ECOLO

GY

SEECO

MMEN

TARY

Dow

nloa

ded

by g

uest

on

Janu

ary

2, 2

022

the structural equation modeling). In this model, we includedinteraction terms between biodiversity and NPP and betweenpathogen stress and NPP. The model shows the same pattern ofdirect effects of biodiversity and pathogen stress on populationdensity as the structural equation modeling (Fig. 3 C and D, Fig.S3, and Table S2): the effect of biodiversity decreases as NPPincreases, and the effect of pathogens becomes stronger as NPPincreases. This strongly supports our structural equation mod-eling results regarding the different controls of population den-sity in low- and high-productivity environments.The modeled geographical distribution of the relative limiting

effects of NPP, biodiversity, and pathogens on hunter-gathererpopulation density suggests that, among the three variables,environmental pathogen stress has the strongest limiting effecton population density in the tropics and subtropics (Fig. 4 A andE). In contrast, NPP and biodiversity constrain hunter-gathererpopulation density in mid- and high latitudes (Fig. 4 A, C, andD). These two factors tend to be colimiting, especially in highlatitudes. NPP assumes a more dominant role in North Americaand in northernmost Eurasia, whereas biodiversity assumes amore dominant role in dry regions and in midlatitude Eurasia.(Fig. 4 A, C, and D).Given the effects of NPP, biodiversity, and pathogen stress,

the potential global distribution of hunter-gatherers highlightspreviously known areas of high hunter-gatherer abundance, suchas the western coast of North America and the eastern andnortheastern coasts of Australia (10, 11) (Fig. 4B and Fig. S4).However, the map also suggests a number of areas with poten-tially high hunter-gatherer abundances that have been occupiedby agricultural populations from at least the late mid-Holoceneonward and that are not well-represented in the historical eth-nographic data on hunter-gatherers (Fig. 4B and Fig. S4). Theseareas include southwestern Mexico, southeastern North Amer-ica, Western Europe, Southeast Asia, and Papua New Guinea.The highest predicted mean population densities are in tem-perate oceanic forest biome followed by subtropical humid for-ests, temperate continental forests, and tropical rainforests (Fig.

4F). However, the differences between these highly suitable bi-omes are small. When interpreting these results, one has to keepin mind that the global projection takes into account only theeffects of three variables that reflect the influence of terrestrialenvironments on hunter-gatherers. Many coastal hunter-gathererpopulations have been dependent on aquatic resources, espe-cially in high latitudes, where terrestrial productivity is relativelylow (10, 11). Thus, it is possible that the global projection ofpopulation density would change if productivity of aquatic en-vironment is taken into account.

Discussion and ConclusionOur results show that NPP has significant positive effects onhunter-gatherer abundance globally. However, there is no singledeterminant of the large-scale variation in abundance. Rather,the most influential direct drivers of population density arecontext-dependent. Biodiversity affects population density mostlyin the low-productivity environments, whereas pathogen stress,which has insignificant effects in areas of low productivity, is acrucial constraint on population density in the high-productivitysettings, especially the tropics. The insignificant effect of biodi-versity on hunter-gatherer population density in high-productivityenvironments is not totally unexpected, as ecosystem propertiestend to have a saturating response to increasing species richness(14, 15). In high-productivity settings, which often coincide withhigh biodiversity, increasing diversity does not increase ecosystemstability; consequently, the response of hunter-gatherer populationdensity to biodiversity seems to saturate as well.As such, our results indicate that the factors affecting hunter-

gatherer abundance on a global scale are similar to those con-trolling global-scale biodiversity: macroscale studies on biodiversityindicate that, in high-latitude regions, productivity is limiting di-versity (30–32), whereas in the tropics, biotic interactions becomea more important driver (33). In the case of hunter-gatherers,abundance and stability of resources limit population density inthe low-productivity environments, whereas species interactions,

NPP

BiodiversityR = 0.442

PathogensR = 0.082

log Pop. densityeR = 0.372

0.661(0.0001)

0.330(0.002)

NPP

BiodiversityR = 0.272

PathogensR = 0.472

log Pop. densityeR =0.502

0.685(0.0006)

0.523(0.0001)

-0.965(-3.085)

0.583(0.002)

0.341(8.098)

Low-productivity (N=234) High-productivity (N=66)B C

D

NPP

Biodive

rsity

gole

ytisned.poP

NPP

Pathogens

gole

ytisned.poP

A

(1.087)0.289

Fig. 3. Relationships between variables. (A) Structural equation modeling of low-productivity environments (NPP ≤ 1,360 g/m2 per year). (B) Structuralequation modeling of high-productivity environments (NPP > 1,360 g/m2 per year). In A and B, NPP is considered an exogenous variable. Arrow widths andaccompanying numbers indicate the relative effects (standardized regression coefficients) of different variables. Unstandardized coefficients are shown inparentheses. Gray arrows indicate statistically nonsignificant relationships, and the red arrow indicates a negative effect. Effects are based on the componentmodels including only statistically significant relationships (α = 0.05). Regression planes show how population density responses to the joint effects of NPP andbiodiversity (C) and of NPP and pathogen stress (D) in the linear model fit to the whole data (i.e., data are not split into low- and high-productivity envi-ronments as in the structural equation modeling). These model results correspond to the structural equation modeling results about direct effects of bio-diversity and pathogens. In C and D, red lines indicate the NPP threshold separating low- and high-productivity environments in the structural equationmodeling.

1234 | www.pnas.org/cgi/doi/10.1073/pnas.1715638115 Tallavaara et al.

Dow

nloa

ded

by g

uest

on

Janu

ary

2, 2

022

as represented in this study by pathogen stress, become moreimportant in controlling population density in the high-pro-ductivity environments. Similarities in the patterns of limitingfactors of hunter-gatherer population density and global bio-diversity might suggest similarities in the underlying mechanismsas well.However, because we do not have direct measures of pathogen

prevalence among individual study populations, we cannotcompletely rule out spurious relationships between pathogenstress and hunter-gatherer population density. Due to generallylow population densities, it has been suggested that the preva-lence of pathogens, such as influenza and measles viruses, andPlasmodium and Trypanosoma parasites is low among hunter-gatherers (34). In addition, it has been argued that high rates ofmobility prevent the accumulation of fecal and other waste athunter-gatherer dwelling sites, leading to a low prevalence ofsoil-transmitted helminths (35, 36). Even if hunter-gatherers areless susceptible to pathogens than farmers who live under similarconditions of environmental pathogen stress, our findings nev-ertheless indicate that the interaction between pathogens andhunter-gatherers is sufficient to create a significant negative ef-fect on hunter-gatherer abundance.By suggesting that subtropical and temperate biomes can

sustain the highest hunter-gatherer population densities, ourresults corroborate the earlier untested hypothesis of Binford(10) regarding the role of resources and pathogens in creatingoptimal conditions for hunter-gatherers in temperate and sub-tropical biomes. Based on our results, it seems that, in sub-tropical and temperate biomes, there is an optimum tradeoffbetween the opposing effects of resource availability and path-ogens: at the higher-productivity end, negative biotic interactions

are too limiting, whereas at the lower-productive end, resourcesare too limiting. However, a large fraction of the area of thesehighly suitable biomes has been occupied by agricultural pop-ulations since at least the late mid-Holocene. It has been arguedthat stable environments with high resource abundance andrichness provide favorable conditions for the innovation andadoption of agriculture (37, 38). Thus, it is understandable thatthe most suitable environments for hunter-gatherers are alsoamong the first ones to support agriculture. Furthermore, po-tentially high hunter-gatherer population densities in these areasmight have facilitated the innovation, spread, and developmentof the new subsistence technology. Alternatively, high hunter-gatherer population density itself, resulting in population packing,and reduced options for mobility might have forced hunter-gath-erer populations toward agriculture (10, 39). Regardless of thefavored explanation, by showing that hunter-gatherer populationdensity and the abundance and stability of their resources arestrongly linked, our results highlight the difficulty in distinguishingbetween environmental and demographic causes of the sub-sistence change. Given hunter-gatherers’ well-documented abilityto affect species communities (40), we can nevertheless assumethat the higher the hunter-gatherer abundance that a given biomecan potentially sustain, the stronger the impact of anthropo-genic drivers on the biome has been even before the transitionto agriculture.In summary, our analyses revealed that NPP, biodiversity, and

environmental pathogen stress interact to impose complex andvarying limitations on hunter-gatherer population density indifferent parts of the world. These findings highlight the key rolethat environmental factors play in shaping the global populationdensity patterns of preagricultural humans. Although cultural

ytisnedno italupo

P)

mk001/#(

gole

2

Pathogens

Biodiversity

NPP

-1

1

3

5ytisnednoitalupo

P)

mk001/#(

gole

2

0.00.20.40.60.81.0

tceffegniti

miL

0.00.20.40.60.81.0

tceff

egn

i tim i

L

ssertsnegohtapfotceffegnitimiLytisrevidoibfotceffegnitimiLPPNfotceffegnitimiL

Population density1 3 5 7 9 11 13 15 17 19

1 3 5 7 9 11 13 15 17 19

1 3 5 7 9 11 13 15 17 19 1 3 5 7 9 11 13 15 17 19

█ Polar: 1Boreal: 2 tundra woodland, 3 mountain system, 4 coniferous forest█Temperate: 5 desert, 6 steppe, 7 mountain system, 8. continental forest, oceanic forest█Subtropical: 10 desert, 11 steppe, 12 mountain system, 13 dry forest, 14 humid forest█Tropical: 15 desert, 16 shrubland, 17 mountain system, 18 dry forest, 19 moist forest,█20 rainforest

Different biomes

A B

-1.4

0.2

1.9

3.5

5.1

C ED

F

Fig. 4. Global projection of hunter-gatherer population density and environmental constraints thereof under current conditions. (A) Geographical distri-bution of the limiting effects of NPP, biodiversity, and pathogen stress on population density. Red, green, and blue indicate dominant limiting effects ofpathogens, NPP, and biodiversity, respectively. The higher the limiting effect of a variable, the farther away that it is from its optimal value. For example,pathogen stress is limiting in the Mediterranean region, although the pathogen stress there is lower than in sub-Saharan Africa. This is because the NPP andbiodiversity are close to their optimum values in the Mediterranean region, leaving the constraining role to pathogens. (B) Map of predicted populationdensities. (C–F) Relative limiting effects of NPP (C), biodiversity (D), and pathogen stress (E) and predicted population density (F) in different ecological zones.Global ecological zones are according to the FAO (28, 29). In the box-and-whisker plots (C–F), the black horizontal lines represent the medians, the filledcircles represent the means, the boxes cover the interquartile ranges, and the whiskers represent the minimums and maximums of the distributions.

Tallavaara et al. PNAS | February 6, 2018 | vol. 115 | no. 6 | 1235

ANTH

ROPO

LOGY

ECOLO

GY

SEECO

MMEN

TARY

Dow

nloa

ded

by g

uest

on

Janu

ary

2, 2

022

evolution has made humans enormously potent ecosystem en-gineers and has enabled humans to survive under a varietyconditions (for example, by extracting energy in low-productivityenvironments and compiling knowledge on medical plants tofight against pathogens), it has not freed hunter-gatherer pop-ulations from biotic and abiotic forcing. We can, therefore, as-sume that spatial and temporal variability in this forcing has beenimportant for our biological and cultural evolution as well.

Materials and MethodsData. All data manipulation and analyses were conducted using R statisticalsoftware (41). The R script and the datasets are freely available at the Zenodorepository (https://doi.org/10.5281/zenodo.1069786), which makes it possibleto reproduce this study. SI Materials and Methods gives more details re-garding datasets and methods.

We extracted the annual mean temperature and annual precipitationvalues from the WorldClim.org database (42), and based on these values, wecalculated climatic NPP using the empirical Miami model (43) (Fig. S1A). TheMiami model, although relatively simple, has been shown to give reasonableestimates of NPP in current climatic and vegetation conditions (44) (SIMaterials and Methods). Instead of using satellite-based values, we decidedto use climate-based NPP estimates to avoid the potential problems causedby recent human appropriations of NPP and to reach an estimate that re-flects more natural levels of NPP.

We used combined mammal, bird, and vascular plant richness as a sur-rogate of overall biodiversity. Global mammal and bird richness data wereextracted from the BiodiversityMapping.org database (45). Global nativevascular plant richness data are model based, because native plant species’ranges are insufficiently documented in most regions of the world (46, 47).We interpolated plant richness data to cover the same global grid with thesame spatial resolution as the NPP and mammal and bird richness data usinginverse distance weighting interpolation with the “gstat” package in R (48–50) (SI Materials and Methods and Fig. S5 A and B). The biodiversity variablewas calculated as an average of the scaled animal (mammal + bird) andplant richness (Fig. S1B).

The estimations of environmental pathogen stress are based on obser-vations of the local pathogen conditions prevailing among 186 nonindustrialsocieties around the globe (51–53). These societies form the Standard Cross-Cultural Sample (www.worldcultures.org/) (54). We used the pathogenprevalence index, which is an average of the z scores of the prevalence of10 pathogens (malaria, dengue, filariae, typhus, trypanosomes, leishmania-sis, schistosomes, plague, leprosy, and spirochetes). We interpolated thepathogen data to cover the same global grid and the same spatial resolutionas the NPP and biodiversity data using kriging interpolation and an expo-nential variogram model with the gstat package in R (48–50) (SI Materialsand Methods and Figs. S1C and S5 C and D). We assume that the globalinterpolation of the pathogen data reflects the relative pathogen stresslevels in the local environments of the study populations.

The hunter-gatherer population density data were combined from twoethnographic datasets compiled by Binford (10) and Kelly (11), with theaddition of Saami in northern Europe from another source (55). To reducethe uncertainty related to ethnographic population density estimates, if apopulation was present in both datasets, we averaged the populationdensity values from both sources. When a hunter-gatherer population waspresent in only one of the datasets, we used the value given by that dataset(SI Materials and Methods and Fig. S6). For each population in the data, weextracted the values of the environmental explanatory variables fromthe global environmental layers of NPP, biodiversity, and environmentalpathogen stress.

To analyze biomewise differences in population density, we used the Foodand Agriculture Organization of the United Nations (FAO) Global EcologicalZones data on the distribution of 20 natural vegetation zones (28, 29)available at www.fao.org/geonetwork/srv/en/main.home?uuid=2fb209d0-fd34-4e5e-a3d8-a13c241eb61b.

Methods. Visual inspections of the relationships between NPP and the loge

population density of hunter-gatherers and between NPP and environ-mental pathogen stress indicated shifts in the effects of NPP. This impressionwas confirmed using breakpoint analysis with the segmented package inR, which allows for the fitting of piecewise linear regression models andprovides estimates of breakpoints (56, 57). This package uses an iterativemodel-fitting algorithm. We did not provide any starting values for thebreakpoint parameters, which means that the algorithm used the median ofthe predictor variable as a starting value for breakpoint estimation. The

Davies test (58) included in the segmented package was performed to testwhether the difference between the slopes before and after the estimatedbreakpoint was different from zero. We calculated the mean of the two NPPbreakpoints (for population density and pathogen stress) and used this valueto distinguish between low- and high-productivity environments.

Structural equation modeling is an approach that interprets informationabout the observed correlations between system components to evaluatepotentially complex causal relationships (23). The approach begins withhypothesizing the underlying structure of causal pathways in the system (aconceptual model or metamodel). Then, this structure is translated into re-gression equations, and finally, these equations are evaluated against datato support or refute the hypothesized structure. Through this process,structural equation modeling provides an understanding of the nature andmagnitude of direct and indirect effects in a system (23), which in our case, iscomposed of three environmental factors and human population density.

Here, we performed structural equation modeling as a piecewise esti-mation of local relationships, in which the parameters are estimated sepa-rately for each regression equation (59). The fit of the structure of thepiecewise model is evaluated using a test of directed separation, withFisher’s C as the test statistic (59, 60). This test indicates whether missingpaths between variables in a system should be included in the model. Weperformed modeling using the R package piecewiseSEM, which allows forthe automated fitting of lists of structured equations and goodness-of-fittests for full and component models (59). For the sake of interpretability, wefit separate models for low- and high-productivity environments.

We beganwith themodels (for low- and high-productivity environments) thatomitted the direct effects of NPP on loge population density. For low- and high-productivity structural equation models, the goodness-of-fit test strongly in-dicated that the direct effect of NPP should be included. In such saturatedmodels, however, the effect of pathogen stress on population density (lowproductivity) and the effect of biodiversity on both pathogen stress and pop-ulation density (high productivity) were nonsignificant. After omitting theseeffects, the goodness-of-fit test indicated that the structural equation models fitthe data well in both low- and high-productivity environments.

However, after adjusting the P values for spatial autocorrelation (61) (SIMaterials and Methods), the effect of NPP on pathogen stress turned out tonot be statistically significant in the low-productivity environments. There-fore, we omitted this effect from the final structural equation model, al-though Fisher’s C indicated a lower fit than for the model that included theeffect of NPP on pathogen stress.

For global projections of hunter-gatherer population density, we used tworegression methods: ordinary least squares linear regression model (LM) (Fig.S3 and Table S2) and support vector regression (SVR) (62–64). Both of thesemodels included interaction terms between biodiversity and NPP and be-tween pathogen stress and NPP. LM and SVR produce highly similar pre-dictions (Fig. S7). However, because fitting algorithms are different (62–64),their predictions are not identical, and therefore, these techniques arecomplementary (Fig. S7). Neither of the techniques seem to extrapolate, andthe predicted values are within the boundaries of the original hunter-gatherer data (Fig. S7). In the context of global prediction and extrapola-tion, we nevertheless feel that it safer to use a combination of two tech-niques instead of single technique.

We fit global models using NPP, biodiversity, and pathogen stress aspredictors of loge population density. SVR was implemented with the e1071package in R (65). The LM and SVR (with linear kernel) models were trainedwithout splitting the ethnographic data into low- and high-productivitysubsets. After the training, we used model algorithms to predict the loge pop-ulation density using global environmental data. We calculated the mean of thepredictions of the LM and SVR models and used this average as our globalprojection of hunter-gatherer population densities as shown in Fig. 3B. Theperformance of the averaged (LM and SVR) model was evaluated using h-blockcross-validation (SI Materials and Methods) (66, 67); h-block cross-validated (h =500 km) prediction root mean squared error is 1.26, and R2 is 0.46. These metricsindicate that the model is performing well with the unseen data.

The limiting effect of a predictor variable is calculated as the differencebetween the population density of the prediction, in which the given pre-dictor is set to its optimum value, and the “true” prediction (see above), inwhich all of the predictor variables are allowed to vary. The larger the dif-ference, the stronger the limiting effect of the predictor. The map of thelimiting effects of NPP, biodiversity, and pathogen stress was constructed bydetermining the optimum values of each predictor in the averaged (LM andSVR) model. The optimum value of a predictor is the value where the loge

population density reaches its highest value in the ethnographic data, asseen in the response shapes of the averaged (LM and SVR) model. We thencreated three global datasets, in which one predictor variable at a time was

1236 | www.pnas.org/cgi/doi/10.1073/pnas.1715638115 Tallavaara et al.

Dow

nloa

ded

by g

uest

on

Janu

ary

2, 2

022

set to its optimum and the other two predictors were allowed to vary. Next,we produced three global projections of population density using thesedatasets. From these projections, we subtracted the true prediction. Theresulting differences were scaled to vary between 0 and 255. The final mapwas produced using the plotRGB function in the “raster” package in R (68).As humans have had profound impact on biodiversity, the limiting effect ofbiodiversity may be artificially high in certain regions. This is because bio-diversity in these regions is further away from its optimum value than itwould be without the recent human influence.

For biomewise comparisons, we rasterized the biome dataset (see above)and aligned it with the global projected limiting effects and the population

density data. This allowed us to extract information about the distribu-tions of the limiting effects and the loge population density in differentbiomes. For the biomewise comparisons, the limiting effects were scaledto sum to unity.

ACKNOWLEDGMENTS. We thank M. Fortelius, J. Kankaanpää, R. L. Kelly,T. Rankama, and three anonymous reviewers for their constructivecritique. M.T. and J.T.E. acknowledge financial support from the KoneFoundation. J.T.E. acknowledges this as a contribution to the IntegrativeClimate Change Biology Programme under International Union ofBiological Sciences.

1. Kelly RL, Surovell TA, Shuman BN, Smith GM (2013) A continuous climatic impact onHolocene human population in the RockyMountains. Proc Natl Acad Sci USA 110:443–447.

2. Shennan S, et al. (2013) Regional population collapse followed initial agriculturebooms in mid-Holocene Europe. Nat Commun 4:2486.

3. Tallavaara M, Luoto M, Korhonen N, Järvinen H, Seppä H (2015) Human population dy-namics in Europe over the last glacial maximum. Proc Natl Acad Sci USA 112:8232–8237.

4. Goldberg A, Mychajliw AM, Hadly EA (2016) Post-invasion demography of prehistorichumans in South America. Nature 532:232–235.

5. Timmermann A, Friedrich T (2016) Late pleistocene climate drivers of early humanmigration. Nature 538:92–95.

6. Birdsell JB (1953) Some environmental and cultural factors influencing the structuringof Australian aboriginal populations. Am Nat 87:171–207.

7. Baumhoff MA (1963) Ecological Determinants of Aboriginal California Populations(Univ of California Press, Berkeley, CA).

8. Keeley LH (1988) Hunter-gatherer economic complexity and “population pressure”: Across-cultural analysis. J Anthropol Archaeol 7:373–411.

9. Hamilton MJ, Milne BT, Walker RS, Brown JH (2007) Nonlinear scaling of space use inhuman hunter-gatherers. Proc Natl Acad Sci USA 104:4765–4769.

10. Binford LR (2001) Constructing Frames of Reference: An Analytical Method forArchaeological Theory Building Using Ethnographic and Environmental Data Sets(Univ of California Press, Berkeley, CA).

11. Kelly RL (2013) The Lifeways of Hunter-Gatherers: The Foraging Spectrum (CambridgeUniv Press, Cambridge, UK), 2nd Ed.

12. Hamilton MJ, Burger O, Walker RS (2012) Human ecology. Metabolic Ecology, edsSibly RM, Brown JH, Kodric-Brown A (Wiley, Chichester, UK), pp 248–257.

13. Burger JR, Weinberger VP, Marquet PA (2017) Extra-metabolic energy use and therise in human hyper-density. Sci Rep 7:43869.

14. Loreau M (2000) Biodiversity and ecosystem functioning: Recent theoretical advances.Oikos 91:3–17.

15. Hooper DU, et al. (2005) Effects of biodiversity on ecosystem functioning: A consensusof current knowledge. Ecol Monogr 75:3–35.

16. Tilman D, Isbell F, Cowles JM (2014) Biodiversity and ecosystem functioning. Annu RevEcol Evol Syst 45:471–493.

17. de Mazancourt C, et al. (2013) Predicting ecosystem stability from community com-position and biodiversity. Ecol Lett 16:617–625.

18. Llamas B, et al. (2016) Ancient mitochondrial DNA provides high-resolution Time scaleof the peopling of the Americas. Sci Adv 2:e1501385.

19. O’Fallon BD, Fehren-Schmitz L (2011) Native Americans experienced a strong populationbottleneck coincident with European contact. Proc Natl Acad Sci USA 108:20444–20448.

20. Patterson JEH, Neuhaus P, Kutz SJ, Ruckstuhl KE (2013) Parasite removal improvesreproductive success of female North American red squirrels (Tamiasciurus hudsoni-cus). PLoS One 8:e55779.

21. Hochachka WM, Dhondt AA (2000) Density-dependent decline of host abundanceresulting from a new infectious disease. Proc Natl Acad Sci USA 97:5303–5306.

22. Hudson PJ, Dobson AP, Newborn D (1998) Prevention of population cycles by parasiteremoval. Science 282:2256–2258.

23. Grace JB (2006) Structural Equation Modeling and Natural Systems (Cambridge UnivPress, Cambridge, UK).

24. Gillman LN, Wright SD (2006) The influence of productivity on the species richness ofplants: A critical assessment. Ecology 87:1234–1243.

25. Cusens J, Wright SD, McBride PD, Gillman LN (2012) What is the form of the pro-ductivity-animal-species-richness relationship? A critical review and meta-analysis.Ecology 93:2241–2252.

26. Guernier V, Hochberg ME, Guégan J-F (2004) Ecology drives the worldwide distri-bution of human diseases. PLoS Biol 2:e141.

27. Dunn RR, Davies TJ, Harris NC, Gavin MC (2010) Global drivers of human pathogenrichness and prevalence. Proc Biol Sci 277:2587–2595.

28. FAO (2001) Global Ecological Zoning of the Global Forest Resources Assessment 2000.Final Report (Food and Agriculture Organization of the United Nations, Rome).

29. FAO (2012) Global Ecological Zones for FAO Forest Reporting: 2010 Update (Food andAgriculture Organization of the United Nations, Rome).

30. Currie DJ (1991) Energy and large-scale patterns of animal- and plant-species richness.Am Nat 137:27–49.

31. Badgley C, Fox DL (2000) Ecological biogeography of North American mammals:Species density and ecological structure in relation to environmental gradients.J Biogeogr 27:1437–1467.

32. Hortal J, Rodríguez J, Nieto-Díaz M, Lobo JM (2008) Regional and environmentaleffects on the species richness of mammal assemblages. J Biogeogr 35:1202–1214.

33. Schemske DW, Mittelbach GG, Cornell HV, Sobel JM, Roy K (2009) Is there a latitudinalgradient in the importance of biotic interactions? Annu Rev Ecol Evol Syst 40:245–269.

34. Froment A (2001) Evolutionary biology and health of hunter-gatherer populations.Hunter-Gatherers: An Interdisciplinary Perspective, Biological Society Symposium Se-ries, eds Panter-Brick C, Layton RH, Rowley-Conwy P (Cambridge Univ Press, Cam-bridge, UK), pp 236–266.

35. London D, Hruschka D (2014) Helminths and human ancestral immune ecology: Whatis the evidence for high helminth loads among foragers? Am J Hum Biol 26:124–129.

36. Page AE, et al. (2016) Reproductive trade-offs in extant hunter-gatherers suggestadaptive mechanism for the neolithic expansion. Proc Natl Acad Sci USA 113:4694–4699.

37. Smith BD (2011) A cultural niche construction theory of initial domestication. BiolTheory 6:260–271.

38. Zeder MA (2012) The broad spectrum revolution at 40: Resource diversity, intensification,and an alternative to optimal foraging explanations. J Anthropol Archaeol 31:241–264.

39. Rosenberg M (1990) The mother of invention: Evolutionary theory, territoriality, andthe origins of agriculture. Am Anthropol 92:399–415.

40. Boivin NL, et al. (2016) Ecological consequences of human niche construction: Ex-amining long-term anthropogenic shaping of global species distributions. Proc NatlAcad Sci USA 113:6388–6396.

41. R Core Team (2017) R: A Language and Environment for Statistical Computing.Version 3.3.3. Available at https://www.R-project.org/. Accessed March 6, 2017.

42. Hijmans RJ, Cameron SE, Parra JL, Jones PG, Jarvis A (2005) Very high resolution in-terpolated climate surfaces for global land areas. Int J Climatol 25:1965–1978.

43. Lieth H (1973) Primary production: Terrestrial ecosystems. Hum Ecol 1:303–332.44. Adams B, White A, Lenton TM (2004) An analysis of some diverse approaches to

modelling terrestrial net primary productivity. Ecol Modell 177:353–391.45. Jenkins CN, Pimm SL, Joppa LN (2013) Global patterns of terrestrial vertebrate di-

versity and conservation. Proc Natl Acad Sci USA 110:E2602–E2610.46. Kreft H, Jetz W (2007) Global patterns and determinants of vascular plant diversity.

Proc Natl Acad Sci USA 104:5925–5930.47. Ellis EC, Antill EC, Kreft H (2012) All is not loss: Plant biodiversity in the anthropocene.

PLoS One 7:e30535.48. Zimmerman D, Pavlik C, Ruggles A, ArmstrongMP (1999) An experimental comparison of

ordinary and universal kriging and inverse distance weighting. Math Geol 31:375–390.49. Pebesma EJ (2004) Multivariable geostatistics in S: The gstat package. Comput Geosci

30:683–691.50. Gräler B, Pebesma EJ, Heuvelink G (2016) Spatio-temporal interpolation using gstat. R

J 8:204–218.51. Low BS (1994) Pathogen intensity cross-culturally. World Cult 8:24–34.52. Cashdan E, Steele M (2013) Pathogen prevalence, group bias, and collectivism in the

standard cross-cultural sample. Hum Nat 24:59–75.53. Cashdan E (2014) Biogeography of human infectious diseases: A global historical

analysis. PLoS One 9:e106752.54. Murdock GP, White DR (1969) Standard cross-cultural sample. Ethnology 8:329–369.55. Itkonen TI (1948) Suomen lappalaiset vuoteen 1945. Ensimmäinen osa. (WSOY, Por-

voo, Finland).56. Muggeo VMR (2003) Estimating regression models with unknown break-points. Stat

Med 22:3055–3071.57. Muggeo VMR (2008) Segmented: An R package to fit regression models with broken-

line relationships. R News 8:20–25.58. Davies RB (1987) Hypothesis testing when a nuisance parameter is present only under

the alternatives. Biometrika 74:33–43.59. Lefcheck JS (2016) piecewiseSEM: Piecewise structural equation modelling in R for

ecology, evolution, and systematics. Methods Ecol Evol 7:573–579.60. Shipley B (2000) A new inferential test for path models based on directed acyclic

graphs. Struct Equ Model Multidiscip J 7:206–218.61. Moran PAP (1950) Notes on continuous stochastic phenomena. Biometrika 37:17–23.62. Drucker H, Burges CJC, Kaufman L, Smola AJ, Vapnik V (1997) Support vector re-

gression machines. Advances in Neural Information Processing Systems 9, edsMozer MC, Jordan MI, Petsche T (MIT Press, Cambridge, MA), pp 155–161.

63. Vapnik VN (1998) Statistical Learning Theory (Wiley, New York).64. Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Stat Comput 14:199–222.65. Meyer D, Dimitriadou E, Hornik K, Weingessel A, Leisch F (2015) e1071: Misc Functions

of the Department of Statistics (e1071), TU Wien. R Package Version 1.6-7. Availableat CRAN.R-project.org/package=e1071. Accessed January 1, 2017.

66. Telford RJ, Birks HJB (2009) Evaluation of transfer functions in spatially structuredenvironments. Quat Sci Rev 28:1309–1316.

67. Salonen JS, et al. (2016) Calibrating aquatic microfossil proxies with regression-tree ensembles:Cross-validation with modern chironomid and diatom data. Holocene 26:1040–1048.

68. Hijmans RJ (2016) raster: Geographic Data Analysis and Modeling. R Package Version2.5-8. Available at https://CRAN.R-project.org/package=raster. Accessed January 1,2017.

Tallavaara et al. PNAS | February 6, 2018 | vol. 115 | no. 6 | 1237

ANTH

ROPO

LOGY

ECOLO

GY

SEECO

MMEN

TARY

Dow

nloa

ded

by g

uest

on

Janu

ary

2, 2

022