Quantitative analysis of harmonic convergence in mosquito auditory...

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ResearchCite this article: Aldersley A, Champneys A,Homer M, Robert D. 2016 Quantitative analysis

of harmonic convergence in mosquito auditory

interactions. J. R. Soc. Interface 13: 20151007.http://dx.doi.org/10.1098/rsif.2015.1007

Received: 20 November 2015

Accepted: 14 March 2016

Subject Category:Life Sciences Mathematics interface

Subject Areas:biomathematics, biophysics, systems biology

Keywords:bioacoustics, acoustic signal processing,

hearing, active audition

Author for correspondence:Martin Homer

e-mail: [email protected]

& 2016 The Authors. Published by the Royal Society under the terms of the Creative Commons AttributionLicense http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the originalauthor and source are credited.

Quantitative analysis of harmonicconvergence in mosquito auditoryinteractions

Andrew Aldersley1, Alan Champneys2, Martin Homer2 and Daniel Robert3

1Bristol Centre for Complexity Sciences, University of Bristol, Bristol BS8 1TR, UK2Department of Engineering Mathematics, University of Bristol, Bristol BS8 1UB, UK3School of Biological Sciences, University of Bristol, Bristol BS8 1TQ, UK

MH, 0000-0002-9848-1409

This article analyses the hearing and behaviour of mosquitoes in the context ofinter-individual acoustic interactions. The acoustic interactions of tetheredlive pairs of Aedes aegypti mosquitoes, from same and opposite sex mosquitoesof the species, are recorded on independent and unique audio channels,together with the response of tethered individual mosquitoes to playbacks ofpre-recorded flight tones of lone or paired individuals. A time-dependent rep-resentation of each mosquitos non-stationary wing beat frequency signature isconstructed, based on Hilbert spectral analysis. A range of algorithmic tools isdeveloped to automatically analyse these data, and used to perform a robustquantitative identification of the harmonic convergence phenomenon. Theresults suggest that harmonic convergence is an active phenomenon, whichdoes not occur by chance. It occurs for live pairs, as well as for lone individualsresponding to playback recordings, whether from the same or opposite sex.Malefemale behaviour is dominated by frequency convergence at a widerrange of harmonic combinations than previously reported, and requires partici-pation from both partners in the duet. New evidence is found to show thatmalemale interactions are more varied than strict frequency avoidance.Rather, they can be divided into two groups: convergent pairs, typified bytightly bound wing beat frequencies, and divergent pairs, that remain widelyspaced in the frequency domain. Overall, the results reveal that mosquitoacoustic interaction is a delicate and intricate time-dependent active processthat involves both individuals, takes place at many different frequencies, andwhich merits further enquiry.

1. IntroductionCollective motion in groups of mosquitoes and other swarming dipterans hasbeen the subject of much recent study [16], as it has for many other animals[711]. At the heart of these investigations is a fundamental question: what isthe nature of the interactions between individuals within the group that producesuch emergent behaviours? This paper aims to explore this question from theperspective of measurement and analysis of the interactions; specifically, weinvestigate the auditory interactions between pairs of mosquitoes.

Audition has long been known to be central to mosquito interaction. Malemosquitoes of many species form swarms that attract females, who approachindividually to locate a mate [1219]. Being part of a swarm increases the like-lihood of any individual male encountering a female [20]. Once a potential mateis located, males orient themselves according to flight tones produced byfemales [2125]. The males hearing apparatus is tuned to actively and non-linearly respond to the tonal signal of a passing female, amplifying her weaksound and thus enhancing his ability to track and pursue her [2628]. Aswell as performing the tasks of detection and positional resolution, mosquitoes

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may also use the characteristic sounds of their neighboursto inform mate choice and infer gender and/or speciesidentification [2933].

At a pairwise level, mosquitoes participate in an ani-mated frequency-based interaction, known as harmonicconvergence [30]. This was first reported by Gibson &Russell [29], who observed an increase in the variability ofwing beat frequencies of pairs of males and females, of thespecies Toxorhynchites brevipalpis, when compared with soloflight. Significantly, opposite sex pairs of these mosquitoesdisplayed an apparent effort to converge their wing beatsto a common frequency value. Subsequent studies havedemonstrated similar flight frequency matching behavioursin other species of mosquito: Culex quinquefasciatus [31],Aedes aegypti [30] and Anopheles gambiae [33].

Mosquito wings have numerous vibrational modes, produ-cing acoustic signals that comprise a high-energy fundamentalfrequency and multiple, successively weaker, harmonic over-tones [34,35]. The wing beat frequencies of male and femaleT. brevipalpis occupy broadly similar ranges, and thusfrequency-based interactions take place at the fundamentalflight frequency, yet this is not the case for other species,which display a greater degree of sexual dimorphism. Insuch mosquitoes, convergence of wing beat frequencies hasbeen observed to take place at the lowest shared harmonicovertone, typically the male second and female third flightfrequency component [30,31].

While a great deal of progress has been made in ourunderstanding of acoustic signalling and processing in mos-quitoes, a quantitative description of their flight frequencybehaviours remains lacking. This is particularly true ofharmonic convergence, which has no formal definition,and for which several interpretations have been given inthe literature (e.g. [31,33,36,37]). Moreover, while it hasbeen stated that there is little doubt that frequency conver-gence occurs [38], it has not yet been quantitativelydemonstrated that it is indeed an active behaviour, andnot simply a random, passive, occurrence that results bychance, because insects occupy a common band of frequencyspace. For example, the male A. aegypti has a fundamentalwing beat frequency approximately 50% higher than that ofthe female. When flying in a pair, the individuals may there-fore be expected to have a natural overlap around the regionof the males second and females third harmonic com-ponents, without any active flight frequency modulationbeing necessary.

Previous studies have typically visualized mosquito flighttones using a spectrogram representation of wing beatfrequency [2931,33,36,37]. Such Fourier-based approachesdemand a trade-off between resolution in the time andfrequency domains, and are inherently difficult to extractaccurate data from [34]; it is therefore quite possible thatthere exist aspects of mosquito frequency interactions whichmay not be apparent when analysed in this way.

In this study, we seek to address these concerns, andconsolidate and expand upon existing knowledge of mos-quito bioacoustics by providing a thorough quantitativeevaluation of high-quality audio recordings of tethered livemosquito pairs, as well as of tethered individuals subjectedto playback recordings. We apply Hilbert spectral analysis[34] to calculate instantaneous frequency time series, whichyields acoustic interaction data at a higher timefrequencyresolution than has previously been reported. This more

accurate analysis generates data that in turn motivate thedevelopment of tools enabling the quantitative characteriz-ation of mosquito acoustic behaviours. In particular, weinvestigate how the acoustic interactions of malemalepairsof which investigations are sparsecompare tothose of opposite sex pairs. We also test, quantify, andexpand on the phenomena reported in [30], where bothmale and female mosquitoes were found to harmonicallyconverge to a playback stimulus (i.e. a non-interactivesound signal) of the opposite sex. We aim to provide robuststatistical evidence to determine whether harmonic con-vergence between mosquito pairs is indeed a genuinephenomenon and, if so, identify the different ways it can beobserved (in both the frequency and time domains), quantifyhow likely it is to occur, and how behaviour differs acrossa population.

Here, we describe a series of experiments designed toinvestigate pairwise interactions between opposite andsame sex mosquitoes. We introduce analytical tools devel-oped to probe communication in the frequency domain,with a particular emphasis on the reliable detection ofunique convergence events. Finally, we discuss the impli-cations of our findings in the context of new experimentalapproaches to characterize swarm dynamics and mosquitomating behaviour.

2. Experimental methods2.1. Mosquito husbandryA colony of the species A. aegypti was initiated using labora-tory eggs obtained from the London School of Hygiene andTropical Medicine. Mosquitoes were developed in containersfilled with de-oxygenated water in a humidity controlledenvironment, held at approximately 268C. Pupae were routi-nely extracted into vials, which were then placed open insecured flight cages, running on a D16 : N8 circadian cycle.Emerged adults were fed a diet of 1020% glucose solution.

2.2. Preparation and test conditionsWe recorded flight tones of live mosquitoes less thanone-week old following the procedure outlined in [34]. Testsubjects were anaesthetized for 1020 s using a stream ofcarbon dioxide gas and tethered to the rounded end of anentomological stainless steel pin (gauge 000). After allowingsufficient time for recovery (around 15 min), mosquitoeswere introduced to the experimental arena. Insects were posi-tioned upright in such a way as to mimic their natural flightpositions. Flight was initiated either by gently blowing oneach mosquito or by stroking its legs. Acoustic emissionswere recorded using two electret condenser microphones(FG-23329-C05, Knowles Electronics), one placed directlyunderneath each animal. The acoustic sampling frequencywas set at 40 kHz. Flight tones were recorded on separatechannels, logged simultaneously using a custom-built inte-grating amplifier (based on a published circuit design [39]),prior to being passed into a National Instruments (NationalInstruments, Austin, TX, USA) USB data acquisition device.Data were logged digitally using LabVIEW SignalExpress(National Instruments).

Temperature, humidity and lighting conditions weremonitored and controlled throughout experimental trials.

http://rsif.royalsocietypublishing.org/

to data logging

10 mm

20 mm

Figure 1. Schematic of experimental set-up for live pairwise recordings;flight tones of each mosquito are recorded on separate channels viamicrophones placed directly below each insect.


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Recordings were carried out in a soundproofed booth toreduce noise effects from external sources. Care was takento minimize disturbance of the mosquitoes visual field bypointing them towards the rear of the darkened enclosure.

Note that the effect of tethering on the biomechanicsof mosquito flight is uncertain [40], despite its wide-spread use in studies involving insect flight kinematics[2931,33,36,37,41]. While the pin itself does not createresonance artefacts (see, e.g. supplementary material of[30]), there is evidence that tethering results in a decrease inmosquito wing beat frequency compared with free flight[30,35,42]. Furthermore, there may be differences in fre-quency composition of the flight tone between hoveringand forward flight, and the variation of wing beat phasearound the mosquito implies that orientation in free flight(fixed in our tethered experiments) may also be important[35]. While an analysis of mosquito communication in naturalconditions is clearly a major goal, the number of variables infree flight and the challenging nature of the experimentsmotivate the simpler tethered experiments we undertakehere, in the belief that at least some aspects of free flightbehaviour are preserved in tethered individuals.

2.3. Experimental procedureOur experiments had two areas of focus. First, we studiedacoustically mediated behavioural interactions between livepairs of same and opposite sex mosquitoes. Next, we investi-gated the response of individual mosquitoes to playbacks ofpre-recorded flight tones. The methods employed for eachscenario are detailed below.

2.3.1. Live pairwise recordingsOpposite and same sex pairs of mosquitoes were positionednext to each other at a distance of around 20 mm; figure 1shows a schematic of the experimental set-up. This is wellwithin their range of acoustic detection [27], but beyond thereach of physical contact. After stimulating flight in bothindividuals, the sounds produced by each were recordedfor a duration of 60 s.

Between experiments, mosquitoes were kept in isolatedcontainers to minimize extra-recording acoustic interaction.In some instances, multiple recordings were taken from thesame pair; a minimum time of 10 min was left betweensuch repeat trials.

In these tests, data were recorded from each subject onan independent audio channel [34], in contrast to single-microphone techniques used in all previous studies (e.g.[2931,33,35]). Significantly, our protocol [34], based on theHilbert transform, enables rapid and accurate quantificationof the wing beat frequency of the mosquitoes.

2.3.2. Playback recordingsLive male and female mosquitoes were subjected to a mixtureof pre-recorded flight tones of lone and paired conspecifics,drawn at random from an archive developed earlier byAldersley et al. [34]. Tethered individuals were placed40 mm in front of and facing a loudspeaker, through whichplayback tones were fed at a sound pressure level of 86 dB,which approximates the intensity of a female mosquitoacoustic emissions measured at 20 mm [27]. Mosquitoeswere recorded for 5 s prior to the introduction of the playback

stimulus, which lasted for 60 s, followed by a further 5 s oflone, stimulus free, flight.

3. Development of analytical tools3.1. Data preprocessing and frequency extractionThe study of behavioural interactions relies fundamentallyon a detailed spectral and temporal representation of eachmosquitos flight sequences. We apply the concept of instan-taneous frequency, obtained via Hilbert spectral analysis [43],to our collection of audio recordings. The key advantage ofHilbert spectral analysis is that it yields a time series ofinstantaneous wing beat frequency, with the same samplingrate as the original data. Thus, it achieves a significantimprovement over other techniques in both the time andfrequency resolution; in particular, short-time fast Fouriertransforms are fundamentally limited by an inherent timefrequency trade-off and are unable to capture the rapidmodulations in frequency exhibited by mosquito flight tones.

Data were processed according to the methodologydetailed in [34], briefly summarized as follows. To isolatethe fundamental frequency component, a time-varying filteris applied to the raw acoustic waveform associated with agiven mosquito. The instantaneous frequency, vi(t), canthen be determined via Hilbert transformation. Higherharmonic frequencies are obtained by integer multiplicationof the fundamental; such a linear relationship betweenovertones has been shown to hold even during periods of fre-quency modulation [35], and is also valid in the datapresented here.

This approach yields mosquito acoustic interaction datawith a time and frequency resolution at the sampling rateused during data acquisition (40 kHz). An automated processis then used to detect and remove portions of the recordingsduring which mosquitoes temporarily cease flight [34], theabsence of a flight tone in the signal being detrimental toquantitative analysis.

3.2. Detecting frequency convergenceIn Aedes aegpyti mosquitoes, harmonic convergence hasbeen reported to take place most commonly at the malesecond and female third frequency overtone, and to a lesserdegree at the male first and female second overtone [30].Malemale pairs of mosquitoes, on the other hand, interactat the level of the fundamental frequency component.


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In general, interactions in the frequency domain occur oversome range that is shared by the mosquitoes in the pair,and are apparent at integer ratios between their fundamentalflight frequencies.

Here, we take an approach similar to that of [31,33], inwhich fundamental wing beat frequency ratios betweenmosquitoes were used to explore convergent relationshipsbetween mosquitoes. Constant flight frequency ratios indi-cate a fixed frequency relationship between the mosquitoes;when located at rational fractions (with small integernumerator and denominator), this points towards harmonicconvergence. For pairs of signals vi(t),vj(t), we calculatethe instantaneous ratio between them, using the lowerfrequency as the denominator. The ratio is uniquely deter-mined because the signals vi(t) are of the fundamentalfrequency component. The resultant time series serves anumber of functions. Firstly, by looking at the distributionof frequency ratios at the population level, we are able toidentify common occurrences in the frequency behavioursof our experimental cohort. Secondly, ratios can be used toconsistently assign convergence events within individualpairs. Both of these ideas are developed further below.

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3.2.1. The randomization protocolA key aim of this study is to establish frequency convergenceas an active or passive phenomenon, i.e. do mosquitoes makean effort to converge at harmonic frequencies, or does thisobservation simply result from chance? One way to answerthis question is to compare the distribution of frequencyratios between opposite and same sex pairs to those ofnon-interactive pairs.

Consider pairing the recording of a male mosquito inlone flight with that of a female also flying solo (data con-tained in the F and C groups, respectively, as summarizedin table 1). These mosquitoes are in no way interacting withone another, and should indeed be beating their wings inaccordance with their rest state, typified by a flight fre-quency distributed approximately normally [34]. However,by combining their wing beat frequency traces, we create adataset which can be subjected to the same analysis as thatgenerated by a live pair (the FC dataset). Apparent conver-gence in such pairs can be considered truly random, sincethere is no way for these mosquitoes to have modulatedtheir flight frequencies in response to a neighbour.

Permuting across lone recordings of male and femalemosquitoes in this manner supplies a population ofrandom pairs (N 68) that can be used to benchmarkconvergence between the interactive pairs that we haverecorded, by comparing the prevalence of that behaviourbetween the real and artificial pairs. We are not aware ofthe use of any such re-sampling techniques in the mosquitobioacoustics literature to date.

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3.3. Classifying individual convergence eventsFor pairwise mosquito interactions, frequency convergenceevents must be quantified in a robust and unbiasedmanner, a need that was highlighted by previous studies[31,33,36,37]. A framework is developed here to consistentlydetect frequency convergence in mosquitoes, with the aimof facilitating more straightforward comparisons betweenfuture acoustic studies in various species.


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Figure 3. Using PAA to identify harmonic convergence in mosquito pairs.(a) Determine the ratio of fundamental flight frequencies between the paired mos-quitoes, and take the PAA using a window of size w 0.5 s. Shaded regionindicates convergence tolerance d +1% about the integer ratio 3 : 2 (1.5).(b) Convergent behaviour is assigned a binary state value according to whetherthe frequency ratio PAA lies on the interval r+d%, here [1.485, 1.515].A value of 1 indicates convergence. The start and end indices of each convergenceevent (green and red markers, respectively) are then logged, using criteria t1 s Dt 1 s (i.e. each event must be at least 1 s long and distinct events areseparated by more than 1 s). (c) Visualization of the prescribed convergenceevents in the time frequency plane, at the male (blue) and female (red)second and third harmonic overtones, respectively.


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3.3.1. The piecewise aggregate approximationOne of the most fundamental challenges in any investigationinvolving time-series data is to identify features and similaritiesacross the database of interest. This is particularly true for high-resolution, high-dimensionality, noisy data, categorizations,which can certainly be applied to the time series presentedhere. Consequently, there has been much interest in the develop-ment of data-mining algorithms that can be used to classifywhole time series, or subsets therein, according to some particu-lar criteria. The piecewise aggregate approximation (PAA)[44,45] offers a simple yet powerful means to reduce the dimen-sionality of a time series, which can aid us greatly in prescribingwing beat frequency convergence between mosquitoes. Anoutline of the PAA now follows.

Consider a time series X of length n as a set of discretepoints such that X x1, . . ., xn, that we wish to reduce to a rep-resentation of dimension N, where 1 N n and, typically,n mod N 0: The reduced form of X in N-dimensionalspace is denoted X x1, . . . , xN : Using PAA, the ith elementof X is then determined as

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In essence, a given time series is divided into N equally sizedframes, and the mean value of each is calculated. A vector ofthe combined means becomes the reduced representationof the original data (an illustrative example is given in figure 2).

3.3.2. Applying piecewise aggregate approximation to frequency-based mosquito interactions

As described earlier, harmonic convergence is characterized bythe maintenance of a fixed integer ratio between the funda-mental frequencies of two mosquitoes in a pair. This process,however, is inherently affected by noise, a fact that becomesobvious when analysing the highly temporally-resolved datathat we have obtained here (an example is shown infigure 3). Hence, it can be difficult to assess where convergencebegins and ends and how long individual events are. Redu-cing the dimensionality of our data via PAA (applied to theinstantaneous frequency data obtained from Hilbert spectralanalysis) helps simplify this process. While being computa-tionally inexpensive and easy to implement, PAA rivalsother more sophisticated dimensionality reduction techniques(such as wavelet and Fourier decompositions) [44,45], andcomfortably satisfies the requirements for this classificationtask. Thus, it has the twin benefits of reducing the

computational cost of our study, and of improving the robust-ness of the detection of harmonic convergence to noise.

It is important to bear in mind that identifying conver-gence events necessarily requires certain restrictions to beimposed upon the data. We determine the PAA represen-tation of the ratio of fundamental wing beat frequencies forthe pair using a window of size w. Convergence events arelabelled as contiguous time intervals of duration t, greaterthan some threshold t, for which the reduced ratio iswithin a given tolerance d of some integer fraction. Uniqueevents are separated by a time period Dt. As convergenceis rarely perfect, the tolerance parameters t and d are essen-tial to the classification process. Here, we use parametersw 0.5 s, d +1%, t 1 s and Dt 1 s, which robustlydetect convergence events.

A graphical overview of how PAA is used in the contextof detecting harmonic convergence events between pairs ofmosquitoes is provided in figure 3. Using this routine, weare able to perform an automated and quantitative searchfor harmonic convergence in our various combinations ofmosquito pairs. Once such convergent intervals have beenidentified, the full-resolution frequency data (i.e. withoutPAA) are used for further analysis.

4. Results4.1. Summary statisticsThe numbers and different types of paired recordingsobtained during the investigation are presented in table 1,


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Figure 4. Examples of harmonic convergence, viewed in the form of a frequency time plot. Convergence is typified by one or both of the mosquitoes altering theirwing beat frequency so that harmonic components approximately converge to some low integer ratio, for a period lasting up to tens of seconds. The relevantfrequency components are shown with zoomed-in frequency axis (over the same time) below. The data presented here are extracted using Hilbert spectral analysis,and show convergence at female : male integer ratios of (a) 3 : 2 and (b) 2 : 1. At this resolution the imperfect nature of frequency convergence between the insectsis apparent.


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along with statistics for lone male (F) and lone female (C)mosquito populations. As in previous studies [30,35,46],tethered male A. aegypti consistently flew at a higher funda-mental frequency than females (691.2 versus 479.8 Hz forlone insects, and 673.5 versus 465.5 Hz across all recordings,MannWhitney U-test: p 1010), and also displayedgreater spread between their average fundamental flightfrequencies (s.d. 90.5 versus 31.3 Hz, Levenes test: p ,1025). While the male population tends to occupy a broadersection of frequency space, variation between individuals(sinter) was significantly greater than that within any givenrecording of an individual (sintra).

4.2. Convergence in opposite sex pairsThe analytical techniques outlined in 3 allow us to go farbeyond this summary analysis, and to analyse the data toprovide quantitative measures of harmonic convergence.This permits a much more detailed investigation of frequencyinteractions at both individual and population level than hashitherto been possible. We begin by analysing acoustic datacollected from live (FC) and all playback (FCP and CFP)opposite sex pairs of A. aegypti.

4.2.1. Time frequency representationFigure 4 presents examples of instantaneous frequency data(for the fundamental and higher harmonics) as a function oftime, for mosquitoes in two sample recordings from the FCcohort. In each instance, the phenomenon of harmonic con-vergence is visible, as is the possibility that it is mediatedthrough frequency modulation by both sexes during theinteraction. It is clear, at this resolution, that an exact matchof harmonic components is rarely achieved. Figure 4 alsoshows that convergence can take place at multiple harmoniccombinations even in the same species; in this case, at thefemale third and male second harmonic (figure 4a), andfemale second harmonic and male fundamental frequency(figure 4b), an observation that is consistent with previouslyreported findings for A. aegypti (e.g. [30]).

An alternative perspective on the harmonic convergencephenomenon, permitted by our high-quality data, is shown

in figure 5. Here, data at convergent harmonic overtonesare aggregated over short time intervals to produce snapshotdistributions of wing beat frequency, plotted in a waterfallfashion against time. Steady flight is characterized by asharp-peaked frequency distribution, whereas transient orerratic modulations of flight frequency tend to produce abroader shape. Harmonic convergence, then, can be typifiedby a gradually increasing overlap between the frequencydistributions of the pair (as can be seen in figure 5), akin toshared information between the mosquitoes. This overlap,a, between distributions a and b, is quantifiable accordingto the following metric:

a 1Pm

i1 jai bijPmi1 ai bi

, 4:1

where m is the number of bins used to generate frequencyhistograms. Frequency overlap is plotted as a function oftime adjacent to the distributions (figure 5). Interestingly,convergence is markedly imperfect in the overlap mea-sure, with distribution overlaps as low as 3040%, with amaximum in this case of around 80%.

4.2.2. Convergent behaviours across the populationIn each of the datasets presented in figure 4, one wouldexpect that an inspection of the distributions of the female :male flight frequency ratios would show peaks aroundvalues of 1.5 and 2 (respectively, for figure 4a,b). But whatcan be said of the rest of our experimental data?

In general, the use of frequency ratios is an efficientmeans to examine convergence behaviours in mosquitopairs, as it reduces the scope of the timefrequency searchspace, and condenses the information from all harmonic over-tones into a single one-dimensional time series. Moreover, itallows us to aggregate and compare data from across theexperimental population, as it gives a standardized represen-tation of the acoustic interaction field that is independentof the exact wing beat frequencies displayed by the individ-uals in the pair. Finally, it does not require any priorknowledge as to the ratios at which convergence may ormay not occur. Aedes aegypti mosquitoes can detect sounds


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Figure 5. Waterfall plot showing the evolution of wing beat frequency distributions (left) of male (second harmonic, blue) and female (third harmonic, red)mosquitoes, and overlap fraction (right), as functions of time, for a live male female pair (taken from dataset FC) during a period of harmonic convergence.Distributions and overlaps are calculated using a window size of 1 s at a frequency resolution of 1 Hz.


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at frequencies up to around the fifth male harmonicarange that extends to several thousand Hertzusing differ-ence tones corresponding to the separation between themosquitos own wing beat and that of its partner [47].

Figure 6a shows the distribution of frequency ratios for alllive malefemale pairs recorded (FC dataset, n 43),together with that of artificial pairs generated by combiningrecordings of males (F dataset, n 27) and females (C data-set, n 19) in solo flight. If convergence were a chancephenomenon, one would anticipate that the shapes of thesedistributions would be broadly similar. However, theshapes of the distributions are markedly different: there are

numerous peaks at integer ratios between the actual pairsthat do not appear in the artificially paired mosquito data.This is strong evidence that frequency convergence viawing beat modulation is indeed an active process carriedout by mosquitoes. Not only this, it suggests that frequencyconvergence is a two-way phenomenon that requires feed-back from both participants in the duet; that is, a mosquitomodulates its wingbeats differently when a partner alsomodulates theirs. However, it is also hypothetically possiblethat a physical interaction between local airborne pressurevariations driven by and influencing the mechanical beatingof the wings is responsible for harmonic convergence, at


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01:1 5:4 4:3 3:2

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paired lone

paired lone

P

P

(a)

(b)

Figure 6. Distribution of fundamental flight tone ratios between fundamen-tal frequencies for (a) all live paired male female mosquitoes and (b)individual males (blue) and females (red) subjected to playback sounds ofthe opposite sex. Common harmonic ratios (+1%) are indicated byshaded vertical bars. In each graph, shaded grey area indicates the distri-bution of fundamental frequency ratios for random combinations ofrecordings of opposite-sex solo mosquitoes, i.e. those that are not interactingwith one another. The live paired data from (a) are also presented in (b), forcomparison.


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least in part. We cannot, based on our data, rule out thishypothesis, which we discuss further in 5.

Our methodology enables the identification of differentmodes of convergence between male and female A. aegypti(figure 6a). While interactions at female : male frequencyratios of 3 : 2 and 2 : 1 have been observed before in this species[30,37], our analysis indicates that harmonic convergencemay also take place at fundamental frequency ratios of 1 : 1,4 : 3, 5 : 3 and 5 : 4. Note that we have excluded harmonic fre-quencies above the male fourth and female fifth due to thelow energy content in the acoustic signal [35] and the low sen-sitivity of the mosquito hearing organ beyond this range [47].Therefore, the rather prominent peak at the ratio 7 : 6 (* infigure 6a) is not included in our analysis of convergence.

4.2.3. Playback recordingsFigure 6b shows the frequency ratio distribution obtainedwhen individual tethered live male or female mosquitoeswere subjected to playback recordings of the opposite sex(CFP and FCP datasets, respectively, n 34 in bothcases). Both sexes displayed the ability to converge to theplayback tones, as evidenced by the occurrence of numerouspeaks at integer ratios.

Males exposed to playbacks of females show prominentconvergent relationships at frequency ratios of 5 : 4, 4 : 3and 3 : 2, whereas for females stimulated by the sounds ofmales peaks appear at 4 : 3, 3 : 2, 5 : 3 and, arguably, 2 : 1(figure 6b). The distributions of frequency ratios for both theFCP and CFP datasets differ from those of randomly associ-ated lone pairs (although the FCP to a lesser degree), and

peaks occur, on the whole, at the same locations as the liveFC pairs (figure 6a), with the exception of 1 : 1. One immedi-ate implication of these findings is that both male and femaleA. aegypti are able to converge their flight tones to playbacksounds of the opposite sex. On the other hand, neither of theplayback distributions closely matches that of the live pairs,indicating differences in behaviour between unidirectionaland bidirectional opposite-sex auditory interactions.

4.3. Wing beat frequency interactions in male malepairs

Mosquito flight frequency convergence has been studied pri-marily as a precursor to malefemale copulation [3337],and as a result the behavioural interactions of malemalepairs have received notably less attention. Despite this,frequency convergence behaviours that are qualitatively analo-gous to those of opposite sex pairs have been observed betweenmales [29], and indeed are also present within our data (oneexample is shown in figure 7a); this would also be consistentwith the physical interaction hypothesis. For same sex pairs,convergence events may be characterized by frequency hunt-ing [29], typified by rapid frequency modulations performedby one or both males when in close frequency proximity to apartner, followed by frequency divergence (figure 7b). Thishas led to the conclusion that pairs of male mosquitoes donot perform frequency convergence, and tend to avoid eachother acoustically [31,32]. Here, we see a more dynamic picture,that can include both frequency convergence and avoidancebehaviour (figure 7c).

Through inspection of the distribution of fundamentalwing beat frequency ratios for malemale pairs (FF dataset,n 30, figure 7d ), we find two peaksat 1.02 and 1.09neither of which are at integer ratios. Note that in [31],pairs of male C. quinquefasciatus displayed prominent fre-quency ratios at similar values of 1.07 and 1.13. Comparingthese recordings to artificial pairs generated by combininglone individuals (from the F dataset), we find that neitherpeak from the frequency ratios of the actual pairs is presentin that of the non-interactive pairs (figure 7d ). Indeed, thebimodality of the distribution of ratios in our experimentaldata, coupled with the equivalently dual-peaked nature ofmale pairs in [31], suggests that there may be some active sig-nificance to these values when transformed into frequencyspace. Moreover, there is a significant component in thedistribution of actual pairs around the integer ratio of 1 : 1,indicating that live male pairs spend a greater amount oftime in a state akin to frequency convergence than onewould expect if such interactions were random.

Acoustic interactions between male mosquitoes take placeabout the fundamental frequency component, and not athigher harmonics as for opposite sex pairs. It is thereforeuseful to consider how the ratios identified (figure 7d ) mani-fest themselves in frequency space. Figure 7e shows thedistribution of absolute instantaneous separations, in thefrequency domain, between each pair of males in the exper-imental population. Again the distribution is bimodal,suggesting that, when paired with a member of the samesex, males tend to exist in one of two states in terms oftheir frequency separation: 020 Hz (near-convergence), or4060 Hz (fixed divergence). Once again, these modes of be-haviour are not apparent in the artificially created pairs.When the cohort is split into two groupsthose in which


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7000 5 10 15

time (s) frequency ratio20 25 30

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0 5 10 15time (s) frequency separation (Hz)

20 25 30 250200150100500

frequency separation (Hz)250200150100500

0.8 1.00.9 1.1 1.2 1.3 1.4 1.5

630

590

550

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630

wi(

Hz)

wi(

Hz)

wi(

Hz)

**

paired lone

paired lone

convergent pairsnon-convergent pairs

(a)

(b)

(c)

(d)

(e)

( f )

Figure 7. (a c) Sample time frequency spectra of male male pairs, showing the fundamental flight component only. A variety of behaviours is observed,including apparent sustained convergence qualitatively identical to that of male female duets (a), brief convergence, hunting [29], and divergence (b), andprolonged frequency modulation (c). (d ) The distribution of ratios between fundamental frequencies for paired males (solid line), plotted along with the equivalentdistribution for combinations of males in solo flight (shaded). Pair ratios peak at non-integer values (1.02, 1.09, *): the bimodal peak is not present in theratio distribution for non-interactive pairs. (e) The distribution of absolute frequency separations between fundamental frequency components for paired males(shaded), plotted along with the equivalent distribution for combinations of males in solo flight (solid line). Peaks occur in the region of 0 20 and 40 60 Hz, suggestive of a dual-state interaction. ( f ) Splitting the male male population into convergent and non-convergent pairs largely accounts for thebimodality observed in (e).


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at least one convergence event is identified (using the algor-ithm described in 3.3), and those in which no convergenceis observedwe are able to account for the bimodality inthe frequency separation distribution (figure 7f ). Males thatconverge spend much of their time at a wing beat frequencyseparation less than 25 Hz apart, whereas the separation forpairs that do not converge tends to be greater than or equalto 50 Hz.

4.4. Prevalence of convergence within the populationThe analysis presented above strongly suggests that harmonicconvergence between pairs of mosquitoes is a genuinephenomenon performed by both sexes, and furthermore thatconvergence is possible at several different frequency ratios.However, the question still remains of just how likely harmonicconvergence is to be observed, either in the time-domain for agiven pair of mosquitoes, or at all across a population. Toanswer this, we use the algorithms described in 3 to consist-ently capture individual harmonic convergence events withinour experimental data, and compute statistics across them.

We begin by conducting a systematic and automa-ted search for convergence among all mosquito pairs at theharmonic integer ratios identified above (1 : 1, 5 : 4, 4 : 3, 3 : 2,5 : 3 or 2 : 1 for female : male, and 1 : 1 for male : male). A sum-mary of the numbers of experimentally observed convergenceevents is presented in table 2. We see that convergence isubiquitous for both male and female mosquitoes, whether

they are in live pairs or subjected to a playback recording, ofeither the same or opposite sex.

4.5. Convergence duration and harmonic combinationsHaving identified unique convergence events within therecordings, statistics of their duration across all pairedinteraction types can be computed. Figure 8a shows thedistribution of convergence durations, aggregated on a per-recording basis, for the live opposite sex (FC), all oppositesex liveplayback (FC[P]) and same sex (FF) pair types.The mean and median convergence time, per recording, areapproximately equal for the opposite sex arrangements (bothin live and playback form), which also show long tails in theirdistributions, indicating the presence of long convergence dur-ations in these recordings. Same sex pairs, on the other hand,show both a shorter median and mean convergence durationthan opposite sex pairs and a much narrower range(i.e. malemale pairs spend less time in a convergent state,per recording, than malefemale ones).

Analysis of individual convergence events reveals a highdegree of skew in the data (figure 8b), most prominentlyfor the live opposite sex and playback recordings. Mostinstances of convergence are short, while a small number arenotably longer which tends to heavily distort group means.A KruskalWallis test for equality did not indicate a significanteffect of pair type on the duration of individual convergenceevents ( p . 0.05), although we do observe a decreasing mean


Tabl

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Sum

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FP),

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4337

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7%)

26(7

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316


13:20151007

10


(+s.e.) convergence time across live opposite sex, playbackand same sex pairs 4.36+0.44 s, 3.53+0.25 s and 2.76+0.37 s for FC, FC[P] and FF, respectively).

Our data also invite a more detailed investigation of thedifferent convergence types identified, illustrated schematicallyin figure 9. The most common harmonic ratios for convergencein live malefemale pairs, in decreasing order of occurrence(percentage of recordings in which a convergence type wasobserved), were 3 : 2 (35%), 5 : 3 (30%), 4 : 3 (16%), 2 : 1 (14%),and 5 : 4 and 1 : 1 (both 8%). Using instead a tally of individualconvergence events (as illustrated in figure 9a), the ratio 5 : 3becomes the most frequent (accounting for 33% of uniqueinstances), followed by 3 : 2 (21%), with the remaining orderpreserved. Convergence at the fundamental (i.e. 1 : 1), typicallyassociated with same sex interactions, was observed only in asingle pair of opposite sex mosquitoes (from which repeatrecordings were taken).

For males played the sounds of females (FCP), harmonicratios of 3 : 2 (42%), 4 : 3 (35%) and 5 : 4 (27%) were detectedmost frequently in recordings, although in terms of totalconvergence events 4 : 3 ranked highest (40%), then 5 : 4(31%) and 3 : 2 (26%). Harmonic convergence at ratios of 5 : 3,1 : 1, and 2 : 1 was observed twice, once, and not at all, respect-ively. Conversely, for live females subjected to male playbacks(CFP), the ratio 4 : 3 was most common both in terms ofits prevalence within recordings and as a proportion ofthe total number of convergence events (correspondingly36 and 32%), followed closely by 3 : 2 (27 and 29%) and 5 : 3(24 and 19%). For this dataset, fundamental frequencyconvergence was not observed.

Across all interaction types, the harmonic ratio at whichconvergence took place produced no statistically significantdifference in the length of the event (KruskalWallis test,p . 0.05).

4.6. Convergence and flight tone variabilityThe data we have collected are inherently non-stationary. It istherefore useful to also consider local features when investi-gating their properties, which may be of behaviouralsignificance at shorter timescales. For example, mosquitoesin pairs have been reported to increase the variability oftheir wing beat frequencies when compared with thoseflying alone [31,33]. The resolution of our data allows us toinvestigate this phenomenon in greater detail, and answerthe question of whether the wing beat frequency propertiesof mosquitoes change as a function of whom their partneris, or how they are interacting with that partner.

To address this, we compute short-time variations inindividual mosquitoes flight tones. We calculate a movingmean and variance (using a rectangular sliding window oflength Dt 0.25 s) for each wing beat frequency trace, anduse these to compute a local coefficient of variation, cv(t) s(t)/m(t), i.e. the ratio of the (instantaneous) standarddeviation to the (instantaneous) mean. The coefficient ofvariation, which is a dimensionless quantity, measuresspread within a dataset in a standardized way, normalizedagainst the diversity in population means. Since differentmosquitoes typically have widely varying mean wing beatfrequencies, the coefficient of variation is a more appropriatetool for comparing flight tone dispersion across a populationthan the standard deviation. As for other measures of spread,a low value of cv signifies low variability.


10040 n = 37 n = 59 n = 14

30

20

interaction type

10

0

[P]

[P]

80

60

40

20

%ev

ents

g

00 5 10

g (s)

g(s)

15 20

(a) (b)

Figure 8. (a) Boxplots showing the distribution of per-recording aggregated convergence durations (g(s)) for live opposite sex (FC), live playback opposite sex(FC[P]) and male male pairs (FF). Horizontal lines within each box represent the median, while dots show the mean. The lower and upper edges of theboxes represent, respectively, the lower and upper quartiles of the aggregated convergence times. The boxplot whiskers give the minimum and maximum of eachdistribution. Values above each box indicate the number of recordings in which convergence was observed. (b) Proportion of convergence events of duration greaterthan g for unique instances of convergence in the three different recording types.


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Figure 10 shows the distribution of local coefficientsof variation for convergent male and female mosquitoes inthe various recording types. Male A. aegypti (figure 10a)paired with a female (live or playback) show peaks in theircv distributions at lower values than males flying alone,whereas for males paired with another male the converseis true. Female mosquitoes (figure 10b) coupled with a livepartner also displayed slightly lower dispersion thanthe solo case. When in the presence of a male playback,however, females show a significantly greater degree oflocal frequency variation.

The implication here is that when interacting with afemale stimulus, male mosquitoes, in general, vary their localflight tones less than when flying alone. The same can besaid for females paired with a live male mosquito. Same sexmale pairs, however, show a larger amount of local spread.More fundamentally, these results again show the significantbehavioural difference between live and playback interaction.

5. Conclusion and discussionIn this study, we have provided the first comprehensive, rig-orous and quantitative investigation into wing beat frequencyinteractions between tethered pairs of mosquitoes. To achievethis, we recorded the flight tones of live mosquitoes coupledwith various different acoustic stimuli: a live individual of theopposite sex, a pre-recorded playback of the opposite sex and(in the case of male subjects) a live individual of the same sex.In contrast to previous research into auditory communicationbetween mosquitoes [2931,33], we recorded mosquitoes onseparate digital audio channels, for longer time periods (60 s),obtaining data with significantly higher resolution than thathas been achieved before. Furthermore, by generating timeseries of individual frequency components, and subjectingthem to a suite of quantitative tools, we were able to preci-sely define and investigate the phenomenon of harmonicconvergence for the first time.

5.1. Analysis of the populationOur data suggest that harmonic convergence is a real andactive phenomenon, which relies on the ability of both indi-viduals to modulate their wing beat frequencies in response

to sounds produced by their partner. There is an alternative,physical, hypothesis to explain the harmonic convergencephenomenon, namely a physical interaction betweenairborne pressure variations and the mechanical beatingof the wing system, which merits some discussion atthis point. In another dipteran, the fruit fly Drosophilamelanogaster, wingbeat is generated myogenically bystretch-activated muscles and hence independently fromdirect neural input [41]. Their wingbeat has been shown tosynchronize to an external stimulus [41]. Could this mechan-ism also drive rhythmic coupling between mosquito pairs,despite their sound emission profiles being quite differentfrom those of other flies [35]? We cannot, based on ourdata, rule out this physical interaction hypothesis. However,it has been demonstrated that deafened mosquitoes (bothmale and female) are incapable of harmonically convergingto a playback stimulus tone [29,30]. In addition, deafenedmales will not attempt to copulate at all with nearby females[22], and flight tone convergence is behaviourally implicatedin a given males mating success [36,37]. These observationspoint towards a coupling between sensory and locomotivemechanisms in mosquitoes, and that individual control andmanipulation of wing beat frequencies, and the observed con-vergence of flight tones, is a result of active processes. Newexperiments with tethered mosquitoes, in which one (or both)individual is deafened, could address this issue and furtherour understanding of mosquito bioacoustics.

We observe a significant difference between the frequencyratio distributions of live mosquito pairs, when compared withthose of non-interacting, artificial pairs. We generated thelatter by combining individual recordings from a database oflone mosquito recordings; this process of randomization isreadily applicable to other coupled time-series data gatheredin behavioural studies.

In the case of live opposite-sex pairs, significant peakswere found at multiple integer ratios, which were not appar-ent in the control dataset. This indicates that live male andfemale mosquito pairs do indeed spend a substantial timein a state of frequency convergence, actively maintainingthat state. We find significant peaks at previously reportedfemale : male frequency ratios of 3 : 2 and 2 : 1 [30,37], andalso at previously unseen ratios of 1 : 1, 5 : 4, 4 : 3 and 5 : 3.These new harmonic ratios do fall within the known acoustic


0.08

0.06

0.04

0.02

0

0.08

norm

aliz

ed c

ount

norm

aliz

ed c

ount

0.06

0.04

0.02

00 3 6

cv (103)9 12 15

P

P

(a)

(b)

Figure 10. The distribution of coefficients of variation, cv, for convergent (a)male and (b) female A. aegypti in different pair types. Shaded regions showthe corresponding distributions for lone males/females (the F and Cdatasets).

1215

12

9

6

3

0

15

12

9

6

2

0

15

12

9

6

2

01 : 1 5 : 4 4 : 3 3 : 2 5 : 3 2 : 1

n =

g(s)

g(s)

g(s)

6 20 23 37 13

1n =

30 38 25 2 0

0n =

14 40 36 24 12

frequency ratio

(a)

(c)

(b)

Figure 9. Boxplots of convergence duration (g(s)) for unique convergenceevents at different harmonic combinations in the (a) live opposite-sex pair(FC) (b) live male, playback female (FCP) and (c) live female, playbackmale (CFP) cohorts. Numbers at the top of each axis indicate the detectedfrequency of each harmonic configuration within the recordings. As infigure 8a, box lines give (in descending order) the upper quartile, medianand lower quartile of the convergence times, and circular markers give themean.


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detection range of the mosquito hearing system [47], andthere is no reason to discount them.

Male and female mosquitoes played back the soundsof conspecifics also displayed convergence at the samefundamental ratios as the live duets, although at differentintensities. The ratio distribution of males listening to pre-recorded females is somewhat similar to that of the artificialpair data. By contrast, data from live females paired withmale playback recordings indicates considerable convergenceto the playback stimulus. This provides further evidence ofactive female participation in frequency convergence events,and of differences between male and female responses toauditory stimuli.

When paired with a member of the same sex, male mos-quitoes have been demonstrated to frequency avoid[29,31,32], but the data reported here reveal that their inter-action is more complicated than this. Our analysis offundamental wing beat frequency distribution betweenmales indicates a mix of convergence and avoidance. Furtherinvestigation of this phenomenon, which does not feature inthe analysis of combined lone males, indicates that live malemale pairs occupy two different states in the frequencydomain: males that converge spend much of their time at a

wing beat frequency less than 25 Hz apart, whereas the sep-aration for pairs that do not converge tends to be over 50 Hz.

5.2. Analysis of individual convergence eventsFrequency convergence was a ubiquitous feature of acousticinteractions between mosquito pairs in all experimentalarrangements tested. We observed at least one convergenceevent in 86% of recordings of live opposite sex pairs, and in87% of playback tests. This is markedly higher than the conver-gence rate of 67% reported for A. aegypti in [30], probablybecause our analysis considers a wider range of harmonicratios for potential convergence. In live pairs, convergencewas most commonly observed in recordings at a female :male harmonic combination of 3 : 2, followed closely by 5 : 3.Convergence at other ratios (1 : 1, 5 : 4, 4 : 3 and 2 : 1) wasobserved, but was less pronounced. For playback recordings,overall, 4 : 3 was marginally more widespread than 3 : 2,yet both ratios stood out from other convergence types.

For malemale pairs, the convergence rate was 47%: con-vergence takes place less frequently between same sex pairsthan opposite sex. However, across each of the three treat-ment groups, where convergence was detected within agiven recording, it tended to be repeated at a similar rate.That is, in convergent datasets, multiple instances werefound in over 70% of all pair recordings, whether same oropposite sex, live or playback. Thus, when a convergent fre-quency interaction takes place between males, it is just aslikely to be repeated as in a malefemale pair. Again, thisdoes not indicate a strictly avoidant response of males toone another.

There is no statistically significant effect of interactiontype (live opposite/same sex pair or opposite sex playback)or harmonic frequency combination on the duration ofindividual convergence events. The majority of conver-gence events in all pair types are short (less than or equalto 1.5 s). In opposite sex pairs, a greater proportion are leng-thier; this could be symptomatic of hunting behavioursdescribed in same sex pairs [29], whereby males quicklymodulate their wing beat frequencies between transientbouts of convergence.



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5.3. Implications for future researchIt is pertinent to consider mosquito flight tone behaviours inthe broader context of their ecology. It has been shown thatthe ability of a male to match his flight frequency to that ofa female is a genetically inheritable trait [37], and may beused by females to assess male fecundity [36]. Furthermore,the presence of harmonic convergence between a pair wasfound to be positively correlated with successful copula-tion, and that females were less likely to reject males whodemonstrated an ability to converge [37]. Convergence mayalso confer sub-species recognition and membership inmixed-form populations of An. gambiae [33]. It is unclear,however, exactly what factors lead to or initiate convergence.The nature of the information contained within the con-vergent signal remains elusive. For instance, do differentconvergence types, or lengths, produce different successrates? Or does the accuracy of the convergence event trans-mit information between the individuals about their qualityin the context of sexual selection? Even basic consequencesof a change in the wing beat frequency of a mosquito, suchas whether there is an alteration of speed or directionof flight, are poorly understood; such questions must beaddressed before the collective behaviour of groups canbe fully comprehended.

The data suggest that, during convergence, pairs of malesmore accurately match their flight frequencies than pairs ofthe opposite sex. But why do males converge at all? Malemosquitoes are stimulated by a range of sound frequencies(rather than a fixed pitch), and any tone within that rangecould elicit some sort of copulatory response [22]. In a naturalswarm environment, auditory interactions are time-limitedby the spatio-temporal aspects of free flight. As acoustic

signalling plays a crucial role in mating behaviour, rapidgender identification is important to reduce the number ofwasted pursuits. It may be that males use such dynamicfrequency cues to inform their decision-making within thecollective swarm aggregation. Indeed, such a notion hasrecently been proposed in another swarming insect species:midges [48].

Understanding the responses of one male to his neigh-bours is critical if we are to gain insights into the dynamicsof swarming in mosquitoes. Our analysis presents somenovel possibilities as to what occurs when males interactwith members of the same and opposite sex, and generatesmany new research questions concerning mosquito bioacous-tics. Clearly, the informational content of the convergentsignal remains unknown, be it for pairs or more complexassociations within a swarm. Only by pursuing such avenues,and applying rigorous analytical tools, can we begin to fullyappreciate the role of sound in mosquito ethology.

Data accessibility. Mosquito auditory interaction data: University ofBristol data.bris Research Data Repository (http://dx.doi.org/10.5523/bris.1a44saul2ijj31u0raipvlims6).Authors contributions. A.A. designed the study, carried out the labora-tory work and collected the data, performed data analysis, andwrote the first draft of the manuscript. D.R., M.H. and A.C. conceivedand designed the study, and contributed to data analysis. All authorsanalysed and interpreted the results, edited and critically revised themanuscript, and gave final approval for publication.Competing interests. We have no competing interests.Funding. D.R. is supported by the Royal Society London. A.A.was funded by the UK Engineering and Physical Sciences ResearchCouncil (EP/E501214/1).Acknowledgements. The authors thank Katie Lucas for helpfuldiscussions and advice.

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Quantitative analysis of harmonic convergence in mosquito auditory interactionsIntroductionExperimental methodsMosquito husbandryPreparation and test conditionsExperimental procedureLive pairwise recordingsPlayback recordings

Development of analytical toolsData preprocessing and frequency extractionDetecting frequency convergenceThe randomization protocol

Classifying individual convergence eventsThe piecewise aggregate approximationApplying piecewise aggregate approximation to frequency-based mosquito interactions

ResultsSummary statisticsConvergence in opposite sex pairsTime-frequency representationConvergent behaviours across the populationPlayback recordings

Wing beat frequency interactions in male-male pairsPrevalence of convergence within the populationConvergence duration and harmonic combinationsConvergence and flight tone variability

Conclusion and discussionAnalysis of the populationAnalysis of individual convergence eventsImplications for future researchData accessibilityAuthors contributionsCompeting interestsFunding

AcknowledgementsReferences

Quantitative analysis of harmonic convergence in mosquito auditory...

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