Structural equation modeling as a tool to investigate correlates of extra-pair paternity in birds
Structural equation modeling as a tool to investigate correlates of extra-pair paternity in birds
Nicholas M. A. Crouch 0 1
Roberta J. Mason-Gamer 0 1
0 Dept. of Biological Sciences, University of Illinois at Chicago , 840 West Taylor St., MC066, Chicago, IL 60607 , United States of America, 2 Department of Zoology, The Field Museum , 1400 S. Lake Shore Drive, Chicago, IL 60605 , United States of America
1 Editor: Tim A. Mousseau, University of South Carolina , UNITED STATES
Identifying relationships between variables in ecological systems is challenging due to the large number of interacting factors. One system studied in detail is avian reproduction, where molecular analyses have revealed dramatic variation in rates of extra-pair paternityÐ the frequency with which broods contain individuals sired by different males. Despite the attention the topic has received, identification of ecological predictors of the observed variation remains elusive. In this study we evaluate how structural equation modelingÐwhich allows for simultaneous estimation of covariation between all variables in a modelÐcan help identify significant relationships between ecological variables and extra-pair paternity. We estimated the correlation of eight different variables using data from 36 species of passerines by including them in six different models of varying complexity. We recover strong support for species with lower rates of male care having higher rates of extra-pair paternity. Our results also suggest that testes size, range size, and longevity all potentially have a relationship with rates of extra-pair paternity; however, interpretation of this result is more challenging. More generally, these results demonstrate the utility of applying structural equation modeling to understanding correlations among interacting variables in complex biological systems.
Data Availability Statement: All relevant data are
within the paper and its Supporting Information
Funding: The authors received no specific funding
for this work.
Competing interests: The authors have declared
that no competing interests exist.
Variation in species mating systems can influence a range of ecological and evolutionary
processes, including: strength of sexual selection, population demographics and variation in
species traits [1±6]. Identifying ecological predictors of why mating systems in some taxa are so
variable is therefore a major area of research. The application of molecular techniques to avian
mating systems has revealed that socially-monogamous species, with a male and female paired
at a nesting site, are infrequently genetically monogamousÐchicks from a single brood are
frequently sired by multiple males [7±10]. Numerous hypotheses have been generated to explain
how extra-pair copulations may improve the fitness of individuals [11±14], but despite the
considerable research, identification of ecological predictors of the observed variation remains
Rates of extra-pair paternity (EPP) vary dramatically between avian species. There are some
species where EPP is perhaps non-existent, for example in Carolina wrens (Thryothorus
]). However, it appears uncommon for species to show no evidence of EPP, with
most species showing low-levels of EPP [
]. Some species show extremely high rates of EPP,
with most broods fathered by more than one male. For example, approximately three-quarters
of broods of the Superb fairy-wren (Malurus cyaneus) are associated with multiple males [
This variation is not ubiquitously between distantly related taxa, members of the same genus
can show similarly disparate rates of EPP [
Numerous abiotic and biotic factors have been suggested to explain interspecific variation
in EPP (reviews by [
8, 9, 18
]). These are wide ranging and include, but are not limited to, song
performance , parental care [
], male brightness [
], and clutch size [
]. Despite the
number of potential explanatory variables there is no clear consensus as to whether one can
uniformly explain avian EPP. This is partly due to the ability of closely related taxa being
similar in explanatory variables, but differing in their rates of EPP. For example, the blue tit (Parus
caeruleus) and coal tit (Parus ater) have comparable testes size [
], suggested to influence
rates of EPP [
], yet the rates of EPP in the coal tit are over double that seen in the blue tit [
Variation in life history between closely related taxa is not the only reason why identifying
correlates of EPP is problematic. Additional challenges include, for example: a large number of
explanatory factors ; methodological differences between studies; sampling bias in studied
]; and the potential for explanatory factors to covary, potentially leading to
overidentification of explanatory factors . Many studies that seek to identify ecological correlates
of extra-pair paternity either focus on specific species, employ phylogenetic comparative
methods, or apply meta-analytical techniques to try and parse out trends. Although these methods
can give tremendous insight into statistically complex problems, there are still possible sources
of error. For example, a potential limitation of multivariate statistical techniques is that if a
model contains a series of confounding variablesÐmultiple interactions between dependent
variablesÐthen potential signal between two traits of interest may be lost [
In this study we evaluate structural equation modeling (SEM) as a method to estimate
whether eight important life history and morphological variables are correlated with EPP.
SEM allows the specification of multiple predictive pathways between model variables to
account for their influence on each other [26±28]. We derived six models representing
different hypotheses about the relationships between variables, and compared their relative
performance in explaining the data using a variety of model fitting techniques. We appraise the
suitability of SEM for examining EPP by discussing the results of these analyses in the context
of previous research.
Materials and methods
We gathered data for 36 species of passerines (Passeriformes) from 15 families (Table 1) from
a variety of sources. Levels of EPP are both higher and more variable in passerines compared
to non-passerines . We obtained EPP data, defined as the percentage of broods containing
offspring sired by multiple males, from [
] and [
]. If a species was repeated between the
two studies, we followed the more recent values [
]. We used percentage of broods to define
EPP rather than percentage of young as these data were available for a larger number of taxa.
These two approaches to defining EPP are highly correlated (Pearson r = 0.93, n = 19, data
]), and so the results are unlikely to be unaffected by which is used. We collected data
on four potentially explanatory factors which have previously suggested to influence EPP:
2 / 14
Great reed warbler
Common reed bunting
European pied flycatcher
Eurasian blue tit
EPP is percentage of broods containing offspring sired by multiple males using data [
body size (grams ), longevity (years [
]), male provisioning (percentage of broods fed
by male ), and testes size (residual from regression between testes size and body size [
To these we added two potentially co-varying variables: range size (polygon size [
altitude range (maximumÐminimum values from across range ). Finally, we added two
variables which are potentially sexually selected traits, therefore possibly involved in EPP, that are
highly variable across the study taxa: range in clutch size (maximumÐminimum clutch size
 and song complexity.
PLOS ONE | https://doi.org/10.1371/journal.pone.0193365
3 / 14
We quantified a single metric for song complexity for each species before performing the
SEM analyses in order to minimize model complexity given the low sample size of this study.
Song complexity was defined using eight components of avian song, quantified from
recordings downloaded from the online database xeno-canto (xeno-canto.org). Using the package
warbleR  in the statistical program R  we measured: spectral entropy (complexity of the
audio elements), spectral flatness (distribution of energy across spectral bands), modulation
index (accumulated absolute difference between adjacent measurements of fundamental
frequencies divided by the frequency range) and bandwidth (maximumÐminimum frequency)
of each recording. Additionally, we quantified song duration using the program Audacity 
and the total number of notes, and number of unique notes, via visual inspection of recording
sonograms from xeno-canto. Finally, we quantified trill rate by dividing the total number of
notes produced by song length. We analyzed between 2 and 5 recordings for each species from
disparate locations in their ranges. The recordings were not taken from the same location as
the studies quantifying EPP for that species. We calculated the mean value for each of the eight
elements of song complexity from all the recordings analyzed. Using the mean component
values, we calculated a single overall metric for song complexity for each species as the sum of the
score on each individual component, with each component scaled to be weighted equally.
We limited the analysis to eight potential explanatory factors, because including too many
factors can potentially over-parameterize the models. These eight factors were chosen
primarily on data availability, but they are also among those most frequently associated with
differences in EPP [
]. However, we did not limit included variables to those for which a
significant relationship had been previously identified (for example, song complexity [
test whether their inclusion in a path analysis would result in a identification of a significant
relationship. Due to the expansive number of potential explanatory variables, those included
here are not an exhaustive list, but provide a range of factors to test in the SEM framework.
We did not include binary traits (e.g. song duetting, ), or variables that have additional
confounding effects. For example, although species midpoint breeding latitude may correlate
with EPP , the variation in latitude effects between hemispheres, and non-linear
relationships between latitude and other factors (e.g. range size, ) could make interpretation of the
results challenging at best [
]. SEM analyses can also be compromised if the causal variables
are too highly correlated (multicollinearity ). We examined whether our analyses were
susceptible to multicollinearity through a pairwise plot of the included variables S1 File).
We transformed our data to satisfy the requirements of SEM. Both range size and altitude
range were log-transformed to obtain approximately normal distributions. To minimize
differences in variances for the model components, we divided EPP rates and male feeding scores
by 10. To correct for the statistical non-independence of species, the raw values for each factor
were transformed by calculating phylogenetic independent contrasts (PIC ).
Transformations were performed using phylogenetic data from  constructed using the backbone
phylogeny of , implemented in the R package ape . Both raw data with no correction for
the relationships between species, and the transformed data were then passed to the SEM
]. We chose not to implement dedicated packages for calculating phylogenetic path
analyses as they frequently estimate the λ parameter for calculating correlation structure. The
λ parameter is notably problematic, and its inclusion would add another layer of uncertainty
to this study.
The SEM framework allows for testing the contribution of a large number of variables while
simultaneously accounting for potential correlations between them. Each unique combination
4 / 14
Fig 1. Graphical depictions of the six models tested in this study. All models include a connection between the six variables tested included here, but
differed in the number of connections between variables. All models were fit with PIC and non-PIC transformed data.
of connections between variables constitutes a single model to fit to the data, with all models
defined a priori. In this study, we defined six different models (Fig 1). Each included a direct
link between the eight variables tested here (male feeding, testes size, body size, range in clutch
size, longevity, range size, altitudinal range and song complexity) and rates of EPP. The models
differed in the number of regressions between the eight explanatory variables. We chose
connections between variables based primarily on previously identified relationships, for example
between body size and longevity , but we did not specify whether any of these correlations
were positive or negative a priori. None of the models included a link between body size and
testes size as the testes size data from [
] were corrected for body size. We chose six models to
evaluate the effect of network complexity on model fit and parameter estimation.
5 / 14
We solved each model using the R package lavaan  using maximum-likelihood
estimation. To compare the relative fit of each model, we calculated AIC scores  to penalize the
likelihood of each model by the respective number of parameters. We calculated three
additional measures of fit for each model: χ2 (a general goodness-of-fit measure), root-mean square
error of approximation (rmsea, which estimates the lack of fit between a tested model and the
data given optimized parameters), and the comparative fit index (cfi, which compares the
performance of each tested model to a `baseline' model which assumes a zero correlation between
all of the observed variables).
The SEM analysis using PIC-transformed data recovered multiple significant relationships
throughout the network (Fig 2, S1 File). Simpler models were generally favored, with models 3
and 6 estimated to be equally likely in explaining the data (Table 2). Despite a ΔAIC of 50.23 in
estimated model fit, the parameter estimates were similar across all models. Testes size, range
size, longevity, and male provisioning were all estimated to have large direct correlations with
rates of EPP (p<0.05). Additionally, using only the best fitting model, two of the eight variables
were estimated to have indirect correlations with rates of EPP. Body size had a negative
indirect correlation with rates of EPP via longevity (Fig 2, regression weight −0.298). Longevity
also had a similar negative indirect correlation with on rates of EPP via range size (estimated
regression weight −0.227), despite not being estimated to be significant at the .05 level
(p = 0.058). None of the remaining 51 estimated indirect correlations between the eight
Fig 2. Graphical depiction of which of the six models were estimated to best explain the data when using PIC-transformed data (model 6, left)
and non-PIC-transformed data (model 5, right). For clarity of display, the values for only those regressions estimated to be significant at the .05 level
are shown. Regressions shown in gray are present in the model but not significant at the .05 level. All direct and indirect parameter estimates are
provided in the supplementary material. Although the use of arrows in SEM figures suggests the directional effect of one variable on another, SEM
analyses cannot identify cause and effect between variables.
6 / 14
Top: Estimates of model fit for the six tested models sorted by ΔAIC, followed statistics for evaluating model performance. df is the degrees of freedom in each model, cfi
is the comparative fit index, rmsea is the root-mean square approximation of error. In SEM, an insignificant pvalue for the chi-square test indicates good model
performance. Bottom: standardized estimates of the direct correlations between the eight tested variables on EPP rates. Asterisks denote those parameters estimated to
be significant at the 0.05 level.
variables and EPP were significant at the .05 level, with the largest absolute regression weight
being 0.13 (S1 File).
In the SEM analysis using non-PIC-transformed data, there was little differentiation in the
fit of the six models to the data, with all of the models covered by a ΔAIC of 3.56 (Table 2). As
a result, each model could be considered equally likely in explaining the data. In similar
fashion to the analysis using PIC-transformed data, each model had nearly identical parameter
estimates, but in contrast to that analysis, only male provisioning was estimated to be
significant at the .05 level (Table 2, S1 File). The estimated regression weights for testes size and
range size were only slightly smaller than the PIC analysis, but the estimates for the correlation
with longevity were considerably smaller (Table 2). None of the 19 indirect correlations
between the eight variables on EPP from the best fitting model were estimated to be significant
(S1 File). The largest absolute standardized indirect correlation was 0.11 (between body size
and rates of EPP via male feeding). Transforming the data using PIC before using SEM had a
dramatic effect on estimated model fit. The analysis of non-PIC-transformed data shows better
performance fit in terms of all four measures (χ2, pvalue, cfi and rmsea). Nevertheless, the
parameter estimates from the two sets of models are broadly comparable with the notable
7 / 14
Variables do not have an r2 value if it was not on the left-hand side of a regression equation. This is depicted graphically as a variable not having an arrow pointing at it,
see Fig 1.
exception of longevity. Transforming the data increased the regression weight of longevity by
0.36 on average (ranging between 0.32 and 0.41, Table 2). The r2 values for the endogenous
model variables for both transformed and transformed data are presented in Table 3.
Identifying interactions between variables in biological systems is challenging due to the
number of potential explanatory factors and their ability to covary. In this study we used SEM to
estimate the correlation between eight variables on rates of EPP while simultaneously
estimating the extent to which they co-vary each other. When phylogenetic independent contrasts
were performed prior to SEM analysis, testes size, range size, and species longevity were
estimated to be significant predictors of rates of EPP. Although the estimates were similar for
testes size and range size in the analysis where no PIC was performed, only male care was
estimated to be a significant predictor of EPP. Both analyses showed a strong negative
relationship between male care and rates of EPP.
An important consideration when interpreting the results of SEM analyses is that it is not
possible to distinguish cause and effect. This is because there is no manipulation of an
independent variable, and variables can be considered `independent' and `dependent' at the same
time for different parts of the same model. Therefore, although SEM models are almost
ubiquitously depicted with arrows, suggesting the directional influence of one variable on another,
these only reflect a priori expectations about how variables may interact. Instead, SEM analyses
fit parameters to the observed data to determine which variables of the model appear to be
Interpretation of the results from this study also requires consideration of two important
methodological points: controlling for statistical non-independence of species before
performing SEM, and how well each of the models are estimated to explain the data. The
long-established idea that species do not represent statistically independent data points  means that
statistical transformation to account for shared ancestry should be performed prior to the data
being passed to the models [
]; however, it is not always performed . If species traits are
not evolving under Brownian Motion, then PIC transformation may not be the most
appropriate method for transforming the data . Although PIC allows the SEM models to account
8 / 14
for shared ancestry among species, the fit estimates of models based on PIC transformed data
were all poor, while non-PIC transformed data yielded better-fitting models. Thus, although
PIC-transformation might be appropriate, the parameter estimates may not accurately
describe the data. It is unclear why the appropriate data transformation resulted in such a
pronounced drop in estimated model performance. Interpretation of the results must therefore
incorporate consideration of both the data used and whether the parameter estimates appear
to accurately describe the data.
Numerous studies have provided evidence that, in species where males provide less parental
care, rates of EPP are higher [6, 16, 52±54]. In this study we also recover a strong negative
relationship between male care and rates of EPP, with the estimated regression weight only
marginally smaller when non-PIC transformed data are used. Greater parental care by males
reduces the amount of time available to seek extra-pair copulations, with low EPP rates
increasing the chance that males are raising their own young . However, this hypothesis
implies that, even though females may actively pursue extra-pair matings, rates of EPP are
differentially controlled by male strategies. If instead males are responding to the strategies of
females, then the amount of care provided by males could be in response to a perceived idea of
how many chicks in a brood they have sired [56±58], even if feeding efforts increase when the
female has mated with more than one male [
]. Different studies have suggested that
males (of the study species) cannot recognize, or at least do not discriminate against, unrelated
], so we can't determine which hypothesis best explains the observed
relationship; the results simply provide strong evidence that rates of EPP are related to male care. One
potential issue is that there may be biasÐout of 18 species for which data were available, only
two lacked any form of mate guarding (Vireo solitarius and Agelaius phoenicus, [
52, 63, 64
Mate guarding by males likely means a greater investment in their social brood, potentially
reducing EPP. Thus, care must be taken in interpreting the results in case our data do not
equally represent all possibilities of potentially confounding variables.
Our results suggest a positive relationship between testes size and rates of EPP (Fig 2),
although the magnitude of the correlation differs between analyses. Only the analysis using
PIC-transformed data recovers a significant regressions (p<0.05); however, the estimated
regression weights between the two analyses differ by only 0.04 on average (Table 2). A
comparison of the regression weights is important because, although p-value significance can be a
useful yardstick for interpretation of results, there is a growing consensus that research should
be moving away from the strict rigidity of only considering results significant at the 0.05 level
]. In this case, the inference of a positive relationship between testes size and rates of
EPP does have biological merit. It could be driven by breeding synchrony, as the species in this
study are predominantly temperate breeders which breed more synchronously . A large
number of males breeding at the same time increases the potential for sperm competition
which can lead to an increase in testes size [
]. This hypothesis is complicated by a lack of a
definitive correlation between breeding synchrony and rates of EPP (reviewed by [
Furthermore, temperate passerine species have larger testes than those from the tropics , so
the prevalence of temperate species in this study may influence the relationship between EPP
and testes size in an unknown manner.
As with testes size, the estimated positive relationship between EPP and range size is almost
identical between the two analyses (Table 2), but biological interpretation of the relationship is
more challenging. Increasing range size correlates with increasing local abundance [
it could represent increasing breeding density. However, there is no strong evidence for a
relationship between breeding density and rates of EPP [8, 69]. Furthermore, increasing breeding
density should increase testes size [
], and our results suggest a negative relationship (Fig 2).
9 / 14
One hypothesis, therefore, is that the greater dispersal ability of species with larger ranges [
facilitates movement between nest sites and subsequently increases extra-pair copulations.
Determining whether species longevity is a significant predictor of EPP based on our results
is somewhat equivocal as a large, a significant regression weight was only estimated in the
analysis using PIC-transformed data. The data transformation is likely affecting longevity due to
its strong correlation with body size (Fig 2), which has strong phylogenetic signal [
Correcting for the strong non-independence of body size could therefore affect the estimated
correlation between longevity and EPP in turn. At the same time, the low estimated model fit for
the models using PIC-transformed data means that the parameter estimates may not
accurately describe the data. Nevertheless, there is also a theoretical basis for predicting that longer
lived species should exhibit higher rates of EPP; males can benefit by investing less in a single
brood if there is both a chance that some of the chicks were sired by another individual, and he
has a chance to breed again in a subsequent year (reviewed by [
]). Our results are consistent
with this idea, but this hypothesis relies on the male having knowledge about his level of
paternity (discussed previously), and would mean that this is principally a male-driven strategy.
Instead, if high rates of EPP were a species-level adaptation to reduced longevity then this may
better incorporate female-based strategies to seeking extra-pair copulations.
Our application of SEM to these EPP data demonstrate its utility as a statistical tool for
identifying ecological correlates; however, there is scope for improvement. First, we need to
seek biological explanations for those trends that are currently unexplainedÐprincipally the
relationship between species range size and rates of EPP. The second focus should be on
increasing sample size, as analyses like SEM can be sensitive to low sample sizes [
suspect this problem is further compounded in these analyses by the predominance of temperate
species in the data (which reflects that the majority of research quantifying rates of EPP has
been performed at European and North American research institutions).
Future research can also aim to incorporate intra-specific variation in EPP as it can vary
]. For example, rates of EPP in the Reed bunting (Emberiza schoeniclus) can
vary between 54% and 88% of broods in different populations [
]. Variation can be due to, for
example: habitat [
], genetic similarity to partner [
], age of individuals , and breeding
]. Incorporating intraspecific variation into analyses as presented here is non-trivial
as the other model variables may also vary between populations. Therefore, simply changing
the EPP value used in the model would not be biologically meaningful. Perhaps the best
approach for future research would be, where possible, to analyze data at the population level
which could account for these potential differences.
Our results nevertheless demonstrate that SEM can be applied to highly complicated
biological networks through identification of novel (range size) and established (male
provisioning) correlates of EPP, while accounting for covariation between variables (e.g. body size and
longevity, ). Furthermore, as SEM considers multiple variables simultaneously, the relative
influence of these different variables can be estimated. These characteristics of SEM mean it
has the potential to address questions on a range of topics, including: carbon cycling [
relationships between organismal traits [
], and predator-prey interactions [
]. It is with
increasing data availability, however, that the widespread utility of SEM will undoubtedly
S1 File. Supplementary tables.
10 / 14
S2 File. A markdown file showing how the analyses were performed.
S3 File. An R file containing the specification of the six models plus an additional function used in the analyses.
S4 File. Data used in this study.
The authors wish to thank D. Wise, J. Bates, V. Gomez & J. Capurucho for comments and
discussion on this work.
Conceptualization: Nicholas M. A. Crouch.
Data curation: Nicholas M. A. Crouch.
Formal analysis: Nicholas M. A. Crouch. Writing ± original draft: Nicholas M. A. Crouch, Roberta J. Mason-Gamer. Writing ± review & editing: Nicholas M. A. Crouch, Roberta J. Mason-Gamer.
11 / 14
12 / 14
13 / 14
Webster MS , Pruett-Jones S , Westneat DF , Arnold SJ . Measuring the effects of pairing success, extrapair copulations and mate quality on the opportunity for sexual selection . Evolution . 1995 ; 49 : 1147 ± 1157 . https://doi.org/10.1111/j.1558- 5646 . 1995 .tb04441. x PMID: 28568519
2. Avise JC , Jones AG , Walker D , DeWoody JA. Genetic mating systems and reproductive natural histories of fishes: lessons for ecology and evolution . Annual Review of Genetics . 2002 ; 36 : 19 ± 45 . https:// doi.org/10.1146/annurev.genet. 36 .030602.090831 PMID: 12429685
3. Mobley KB , Jones AG . Environmental, demographic, and genetic mating system variation among five geographically distinct dusky pipefish (Syngnathus floridae) populations . Molecular Ecology . 2009 ; 18 ( 7 ): 1476 ± 1490 . https://doi.org/10.1111/j. 1365 - 294X . 2009 . 04104 . x PMID : 19368649
4. Cornwallis CK , West SA , Davis KE , Griffin AS . Promiscuity and the evolutionary transition to complex societies . Nature . 2010 ; 466 : 969 ± 972 . https://doi.org/10.1038/nature09335 PMID: 20725039
5. Sardell RJ , Arcese P , Keller LF , Reid JM . Are there indirect fitness benefits of female extra-pair reproduction? Lifetime reproductive success of within-pair and extra-pair offspring . The American Naturalist . 2012 ; 179 ( 6 ): 779 ± 793 . https://doi.org/10.1086/665665 PMID: 22617265
6. Bonier F , Eikenaar C , Martin PR , Moore IT . Extrapair paternity rates vary with latitude and elevation in Emberizid sparrows . The American Naturalist . 2014 ; 183 ( 1 ): 54 ± 61 . https://doi.org/10.1086/674130 PMID: 24334735
Current Ornithology . 1990 ; 7 : 331 ± 369 .
8. Griffith SC , Owens IPF , Thuman KA . Extra pair paternity in birds: a review of interspecific variation and adaptive function . Molecular Ecology . 2002 ; 11 ( 11 ): 2195 ± 2212 . https://doi.org/10.1046/j. 1365 - 294X . 2002 . 01613 . x PMID : 12406233
Westneat DF , Stewart IRK . Extra-pair paternity in birds: causes, correlates, and conflict . Annual Review of Ecology , Evolution, and Systematics . 2003 ; 34 : 365 ± 396 . https://doi.org/10.1146/annurev.ecolsys.
10. Neudorf DLH . Extrapair paternity in birds: understanding variation among species . The Auk . 2004 ; 121 ( 2 ): 302 ± 307 . https://doi.org/10.2307/4090394
11. Trivers RL . Parental investment and sexual selection . In: Campbell B, editor. Sexual selection and the descent of man. Aldine Publishing Company, Chicago; 1972 . p. 136 ± 179 .
12. Foerster K , Delhey K , Johnsen A , Lifjeld JT , Kempenaers B . Females increase offspring heterozygosity and fitness through extra-pair matings . Nature . 2003 ; 422 : 714 ± 717 . https://doi.org/10.1038/ nature01969
13. Eliassen S , Kokko H . Current analyses do not resolve whether extra-pair paternity is male or female driven . Behavioral Ecology and Sociobiology . 2008 ; 62 : 1795 ± 1804 . https://doi.org/10.1007/s00265- 008-0608-2
14. Gohli J , Anmarkrud JA , Johnsen A , Kleven O , Borge T , Lifjeld JT . Female promiscuity is positively associated with neutral and selected genetic diversity in passerine birds . Evolution . 2013 ; 67 ( 5 ): 1406 ± 1419 . PMID: 23617917
15. Haggerty TM , Morton ES , Fleischer RC . Genetic monogamy in Carolina wrens (Thryothorus ludovicianus) . The Auk . 2001 ; 118 : 215 ±219 https://doi.org/10.1642/ 0004 - 8038 ( 2001 ) 118 %5B0215: GMICWT% 5D2.0.CO;2
16. Petrie M , Kempenaers B . Extra-pair paternity in birds: explaining variation between species and populations . Trends in Ecology & Evolution . 1998 ; 13 : 52 ± 58 . https://doi.org/10.1016/S0169- 5347 ( 97 ) 01232 - 9
17. Double M , Cockburn A . Pre-dawn infidelity: females control extra-pair mating in superb fairy-wrens . Proceedings of the Royal Society of London B: Biological Sciences . 2000 ; 267 : 465 ± 470 . https://doi.org/10. 1098/rspb. 2000 .1023
18. AkcËay E , Roughgarden J . Extra-pair paternity in birds: review of the genetic benefits . Evolutionary Ecology Research . 2007 ; 9 : 855 ± 868 .
19. Forstmeier W , Kempenaers B , Meyer A , Leisler B. A novel song parameter correlates with extra-pair paternity and reflects male longevity . Proceedings of the Royal Society of London B: Biological Sciences . 2002 ; 269 : 1479 ±1485 https://doi.org/10.1098/rspb. 2002 .2039
20. Ball AD , van Dijk RE , Lloyd P , PogaÂny AÂ , Dawson DA , Dorus S , Bowie RCK , Burke T , SzeÂkely T. Levels of extra-pair paternity are associated with parental care in penduline tits (Remizidae) . Ibis . 2017 ; 159 ( 2 ): 449 ±455 https://doi.org/10.1111/ibi.12446
21. Møller AP , Birkhead TR . The evolution of plumage brightness in birds is related to extrapair paternity . Evolution . 1994 ; 48 ( 4 ): 1089 ±1100 https://doi.org/10.2307/2410369 PMID: 28564455
22. Arnold KE , Owens IPF . Extra-pair paternity and egg dumping in birds: Life history, parental care and the risk of retaliation . Proceedings of the Royal Society of London B: Biological Sciences . 2004 ; 269 ( 1497 ): 1263 ±1269 https://doi.org/10.1098/rspb. 2002 .2013
23. Pitcher TE , Dunn PO , Whittingham LA . Sperm competition and the evolution of testes size in birds . Journal of Evolutionary Biology . 2005 ; 18 : 557 ± 567 . https://doi.org/10.1111/j.1420- 9101 . 2004 . 00874 . x PMID : 15842485
24. Møller AP , Briskie JV . Extra-pair paternity, sperm competition and the evolution of testis size in birds . Behavioral Ecology and Sociobiology . 1995 ; 36 ( 5 ): 357 ± 365 . https://doi.org/10.1007/BF00167797
25. Møller A , Jennions MD . How much variance can be explained by ecologists and evolutionary biologists? Oecologia . 2002 ; 132 ( 4 ): 492 ± 500 . https://doi.org/10.1007/s00442-002 -0952-2 PMID: 28547634
26. Mitchell RJ. Testing evolutionary and ecological hypotheses using path analysis and structural equation modelling . Functional Ecology . 1992 ; 6 ( 2 ): 123 ± 129 . https://doi.org/10.2307/2389745
27. Lesku JA , Amlaner CJ , Lima SL . A phylogenetic analysis of sleep architecture in mammals: the integration of anatomy, physiology, and ecology . The American Naturalist . 2006 ; 168 ( 4 ): 441 ± 443 . https://doi. org/10.1086/506973 PMID: 17004217
Wang IJ , Glor RE , Losos JB . Quantifying the roles of ecology and geography in spatial genetic divergence . Ecology Letters . 2013 ; 16 : 175 ± 182 . https://doi.org/10.1111/ele.12025 PMID: 23137142
29. Garamszegi LZ , Møller AP . Extrapair paternity and the evolution of bird song . Behavioral Ecology . 2004 ; 15 ( 3 ): 508 ± 519 . https://doi.org/10.1093/beheco/arh041
30. Dunning JB . CRC Handbook of Avian Body Masses, Second Edition . CRC Press, New York; 2007 .
31. de Magalhãs JP , Costa J. A database of vertebrate longevity records and their relation to other life-history traits . Journal of Evolutionary Biology . 2009 ; 22 : 1770 ± 1774 . https://doi.org/10.1111/j.1420- 9101 . 2009 . 01783 .x
32. Tacutu R , Craig T , Budosvsky A , Wuttke D , Lehmann G , Taranukha D , et al. Human ageing genomic resources: integrated databases and tools for the biology and genetics of ageing . Nucleic Acids Research . 2013 ; 41 : D1027±D1033 . https://doi.org/10.1093/nar/gks1155 PMID: 23193293
33. Møller AP , Cuervo JJ . The evolution of paternity and paternal care in birds . Behavioral Ecology . 1999 ; 11 ( 5 ): 472 ± 485 .
34. BirdLife International and NatureServe. Bird species distribution maps of the world; 2012 .
Hijmans RJ , Cameron SE , Parra JL , Jones PG , Jarvis A. Very high resolution interpolated climate surfaces for global land areas . International Journal of Climatology . 2005 ; 25 : 1965 ± 1978 . https://doi.org/ 10.1002/joc.1276
Del Hoyo J , Elliott A , Sargatal J . Handbook of the Birds of the World . vol. 6 : 15 . Lynx Edicions , Barcelona; 2008 .
Araya-Salas M , Smith-Vidaurre G. warbleR: an R package to streamline analysis of animal acoustic signals . Methods in Ecology and Evolution . 2016 ; 8 ( 2 ): 184 ± 191 . https://doi.org/10.1111/2041-210X. 12624
R Core Team. R: A Language and Environment for Statistical computing; 2013 . Available from: http:// www.R-project. org.
Audacity Team. Audacity (R): Free audio editor and recorder; 2014 . Available from: http://audacity.
Behavioral Ecology and Sociobiology. 2008 ; 62 ( 6 ): 983 ± 988 . https://doi.org/10.1007/s00265-007-0524-x
Behaviour . 1995 ; 132 ( 9 ): 675 ± 690 . https://doi.org/10.1163/156853995X00081
Orme CDL , Davies RG , Olson VA , Thomas GH , Ding TS , Rasmussen PC , et al. Global Patterns of Geographic Range Size in Birds. PLoS Biology . 2006 ; 4 ( 7 ). https://doi.org/10.1371/journal.pbio. 0040208 PMID: 16774453
Tarka P. An overview of structural equation modeling: its beginnings, historical development, usefulness and controversies in the social sciences Quality & Quantity . 2017 ;
Felsenstein J. Phylogenies and the comparative method . The American Naturalist . 1985 ; 125 :1± 15 .
Nature . 2012 ; 491 ( 7424 ): 444 ± 448 . https://doi.org/10.1038/nature11631 PMID: 23123857
Hackett SJ , Kimball RT , Reddy S , Bowie RCK , Braun EL , Braun MJ , et al. A Phylogenomic Study of Birds Reveals Their Evolutionary History. Science . 2008 ; 320 ( 5884 ): 1763 ± 1768 . https://doi.org/10.
1126/science.1157704 PMID: 18583609
Paradis E , Claude J , Strimmer K. APE : analyses of phylogenetics and evolution in R language . Bioinformatics . 2004 ; 20 ( 2 ): 289 ± 290 . https://doi.org/10.1093/bioinformatics/btg412 PMID: 14734327
Healy K , Guillerme T , Finlay S , Kane A , Kelly SBA , McClean D , et al. Ecology and mode-of-life explain lifespan variation in birds and mammals . Proceedings of the Royal Society of London B: Biological Sciences . 2014 ; 281 ( 1784 ). https://doi.org/10.1098/rspb. 2014 .0298
Rosseel Y. An R Package for Structural Equation Modeling . Journal of Statistical Software . 2012 ; 48 ( 2 ):1± 36 . https://doi.org/10.18637/jss.v048.i02
1974 ; 19 ( 6 ): 716 ± 723 . https://doi.org/10.1109/TAC. 1974 .1100705
Revell LJ . Phylogenetic signal and linear regression on species data . Methods in Ecology and Evolution . 2010 ; 1 ( 4 ): 319 ± 329 . https://doi.org/10.1111/j.2041- 210X . 2010 . 00044 .x
1993 ; 142 ( 1 ): 118 ± 140 . https://doi.org/10.1086/285531 PMID: 19425972
Dixon A , Ross D , Omalley SLC , Burke T. Paternal investment inversely related to degree of extra-pair paternity in the reed bunting . Nature . 1994 ; 371 : 698 ± 700 . https://doi.org/10.1038/371698a0
Perlut NG , Kelly LM , Zalik NJ , Strong AM . Male savannah sparrows provide less parental care with increasing paternity loss . Northeastern Naturalist . 2012 ; 19 : 335 ± 344 . https://doi.org/10.1656/045.019.
Arnqvist G , Kirkpatrick M. The evolution of infidelity in socially monogamous passerines: the strength of direct and indirect selection on extrapair copulation behavior in females . The American Naturalist . 2005 ; 165 ( suppl .) :S26±S37 . https://doi.org/10.1086/429350 PMID: 15795859
Houston AI . Parental effort and paternity . Animal Behaviour . 1995 ; 50 : 1635 ± 1644 . https://doi.org/10.
2002 ; 357 : 341 ± 350 . https://doi.org/10.1098/rstb. 2001 .0931
MatysiokovaÂ B , RemesÏ V. Faithful females receive more help: the extent of male parental care during incubation in relation to extra-pair paternity in songbirds . Journal of Evolutionary Biology . 2013 ; 26 ( 1 ): 155 ± 162 . https://doi.org/10.1111/jeb.12039 PMID: 23176707
GarcÂõa-Vig oÂn E , Veiga JP , Cordero PJ . Male feeding rate and extrapair paternity in the facultatively polygynous spotless starling . Animal Behaviour . 2009 ; 78 : 1335 ± 1341 . https://doi.org/10.1016/j.
anbehav. 2009 . 08 .017
60. Du B , Guan MM , Ren QM , Chen GL . Cuckolded male ground tits increase parental care for the brood . Animal Behaviour . 2015 ; 110 : 61 ± 67 . https://doi.org/10.1016/j.anbehav. 2015 . 09 .023
61. Kempenaers B , Sheldon BC . Why do male birds not discriminate between their own and extra-pair offspring? Animal Behaviour . 1996 ; 51 : 1165 ± 1173 . https://doi.org/10.1006/anbe. 1996 .0118
62. Riehl C , Strong MJ . Social living without kin discrimination: experimental evidence from a communally breeding bird . Behavioral Ecology and Sociobiology . 2015 ; 69 : 1293 ± 1299 . https://doi.org/10.1007/ s00265-015-1942-9
63. Møller AP , Birkhead TR . Frequent copulations and mate guarding as alternative paternity guards in birds: a comparative study . Behaviour . 1991 ; 118 : 170 ± 186 . https://doi.org/10.1163/156853991X00274
64. Morton ES , Stutchbury BJM , Howlett JS , Piper WH . Genetic monogamy in blue-headed vireos and a comparison with a sympatric vireo with extrapair paternity . Behavioral Ecology . 1998 ; 9 ( 5 ): 515 ± 524 . https://doi.org/10.1093/beheco/9.5. 515
65. Vidgen B , Yasseri T. P-values: misunderstood and misused . Frontiers in Physics. 2016 ; 4 ( 6 ).
Wasserstein RL , Lazar NA . The ASA's statement on p-values: context, process, and purpose . The American Statistician . 2016 ; 70 ( 2 ): 129 ± 133 . https://doi.org/10.1080/00031305. 2016 .1154108
67. Bock CE , Ricklefs RE . Range size and local abundance of some North American songbirds: a positive correlation . The American Naturalist . 1983 ; 122 ( 2 ): 295 ± 299 . https://doi.org/10.1086/284136
68. Gaston KJ , Blackburn TM , Gregory RD . Abundance-range size relationships of breeding and wintering birds in Britain: a comparative analysis . Ecography . 1997 ; 20 ( 6 ): 569 ± 579 . https://doi.org/10.1111/j. 1600- 0587 . 1997 .tb00425.x
Behavioral Ecology and Sociobiology. 1997 ; 41 ( 4 ): 205 ± 215 . https://doi.org/10.1007/s002650050381
70. Laube I , Korntheuer H , Schwager M , Trautmann S , Rahbek C , BoÈhning-Gaese K. Towards a more mechanistic understanding of traits and range sizes . Global Ecology and Biogeography . 2012 ; 22 ( 2 ): 233 ± 241 . https://doi.org/10.1111/j.1466- 8238 . 2012 . 00798 .x
71. Phillimore AB , Owens IPF , Orme CDL , Owens IPF . Ecology predicts large scale diversification in birds . The American Naturalist . 2006 ; 168 ( 2 ): 220 ± 229 .
72. MacCallum RC , Browne MW , Sugawara HM . Power analysis and determination of sample size for covariance structure modeling . Psychological Methods . 1996 ; 1 ( 2 ): 130 ± 149 . https://doi.org/10.1037/ 1082 - 989X . 1 .2. 130
73. Charmantier A , Blondel J , Perret P , Lambrechts MM . Do extra-pair paternities provide genetic benefits for female blue tits Parus caeruleus ? Journal of Avian Biology . 2004 ; 35 : 524 ±532 https://doi.org/10. 1111/j.0908- 8857 . 2004 . 03296 .x
74. Freeman-Gallant CR , Wheelwright NT , Meiklejohn KE , Sollecito SV . Genetic similarity, extrapair paternity, and offspring quality in Savannah sparrows (Passerculus sandwichensis) . Behavioral Ecology . 2006 ; 17 ( 6 ): 952 ± 958 . https://doi.org/10.1093/beheco/arl031
Wagner RH , Schug MD , Morton ES . Condition-dependent control of paternity by female Purple Martins: Implications for coloniality . Behavioral Ecology and Sociobiology . 1996 ; 38 ( 6 ): 379 ±389 https://doi.org/ 10.1007/s002650050255
76. Thusius KJ , Dunn PO , Peterson KA , Whittingham LA . Extrapair paternity is influenced by breeding synchrony and density in the common yellowthroat Behavioral Ecology . 2001 ; 12 ( 5 ): 633 ±639 https://doi. org/10.1093/beheco/12.5. 633
77. Jonsson M , Wardle DA . Structural equation modelling reveals plant-community drivers of carbon storage in boreal forest ecosystems . Biology Letters . 2010 ; 6 ( 1 ): 116 ± 119 . https://doi.org/10.1098/rsbl. 2009 .0613 PMID: 19755530
78. GoÂmez JM , VerduÂ. Mutualism with plants drives primate diversification . Systematic Biology . 2012 ; 61 ( 4 ): 567 ± 577 . https://doi.org/10.1093/sysbio/syr127 PMID: 22228798
79. McGhee KE , Pintor LM , Bell AM . Reciprocal Behavioral Plasticity and Behavioral Types during Predator-Prey Interactions . The American Naturalist . 2013 ; 182 ( 6 ): 704 ± 717 . https://doi.org/10.1086/673526 PMID: 24231533