Structure of sexual networks determines the operation PNAS PLUS of

Grant C. McDonalda,1 and Tommaso Pizzaria

aEdward Grey Institute, Department of Zoology, University of Oxford, Oxford OX1 3PS, United Kingdom

Edited by Scott V. Edwards, Harvard University, Cambridge, MA, and approved November 27, 2017 (received for review June 12, 2017) Sexual selection is a fundamental evolutionary process but remains that increasing average may strengthen sexual selection on debated, particularly in the complexity of polyandrous populations males, by allowing a subset of males to increase their reproductive where females mate with multiple males. This lack of resolution is success by mating with more females (20–23). For example, poly- partly because studies have largely ignored the structure of the andry has been suggested to drive the of exaggerated sexual network, that is, the pattern of mate sharing. Here, we sexual ornaments with which males attract partners across (24, 25) quantify what we call mating assortment with network analysis to and even within of socially monogamous (refs. 23 and specify explicitly the indirect as well as direct relationships between 26; see ref. 27). In contrast, other studies, often of more polyandrous partners. We first review empirical studies, showing that mating species, have suggested that increasing average polyandry may in fact assortment varies considerably in nature, due largely to basic weaken sexual selection (10, 28). These studies predict that poly- properties of the sexual network (size and density) and partly to andry should reduce variance in male mating success and limit the nonrandom patterns of mate sharing. We then use simulations to potential strength of precopulatory sexual selection because the re- show how variation in mating assortment interacts with population- level polyandry to determine the strength of sexual selection on productive benefits of mating with additional females are reduced males. Controlling for average polyandry, positive mating assort- when paternity is shared among multiple males. Thus, polyandry ment, arising when more polygynous males tend to mate with more may weaken the relationship between male mating success and re- polyandrous females, drastically decreases the intensity of pre- productive success (i.e., the Bateman gradient), and thus erode copulatory sexual selection on male mating success (Bateman precopulatory sexual selection on male mating success (4, 10, 11, 16). gradient) and the covariance between male mating success and Behavioral studies investigating the relationship between postcopulatory paternity share. Average polyandry independently precopulatory male mating success and postcopulatory paternity weakened some measures of sexual selection and crucially also share have yielded similarly inconsistent results (14). A positive impacted sexual selection indirectly by constraining mating assort- relationship between a male’s mating success and his paternity ment through the saturation of the mating network. Mating share, which would be expected to reinforce sexual selection on assortment therefore represents a key—albeit overlooked—modu- male mating success (14), has been found in several species, lator of the strength of sexual selection. Our results show that including junglefowl, Gallus gallus, , Poecila reticulata, jointly considering sexual network structure and average polyandry and fruit flies, melanogaster (10, 29–32). In other taxa, more precisely describes the strength of sexual selection. however, this relationship may be negative (33–35), indicating that precopulatory and postcopulatory episodes represent alter- Bateman gradient | | opportunity for selection | SCIC | native pathways to male , thereby creating competition opportunities for alternative male mating tactics. Finally, in other species, episodes of precopulatory and postcopulatory arwin suggested that male reproductive success is typically sexual selection are largely independent (17, 36, 37). Dlimited by competitive access to fertilization opportunities and that sexual selection drives the evolution of traits conferring Significance an advantage in intrasexual competition (1). Darwin’s view of sexual selection on males was limited to competition over mating opportunities. The realization that, across many sexually repro- Sexual selection is a powerful evolutionary force, but debate ducing taxa, females often mate with multiple males so that their persists over its strength and quantification. We argue that current approaches ignore the structure of the sexual network. ejaculates overlap at the time of fertilization (polyandry) (e.g., We capture this network structure with a metric we call refs. 2 and 3), has revolutionized our understanding of sexual “mating assortment” that precisely and exhaustively captures selection (4, 5). Polyandry extends sexual selection on males the indirect as well as direct relationship between a male’s after mating (postcopulatory), via (6) and and that of his sexual partners. We show that cryptic female choice (7, 8), by generating variation in the pro- mating assortment is highly variable in nature and use simu- portion of a female’s eggs fertilized by her sexual partners (pa- lations to reveal that such variation plays a key—but so far ternity share). Polyandry therefore adds complexity to the unappreciated—role in determining the strength of sexual se- architecture of male reproductive success through variance in lection on males. Our results provide a clear and quantitative paternity share and covariance with precopulatory success: that method for studying sexual selection in the many mating sys- is, the number of females mated (mating success) and their fe- tems in which both and polyandry co-occur. cundity (9–14). This complexity directly affects the overall EVOLUTION strength of sexual selection and the way different selective epi- Author contributions: G.C.M. and T.P. conceived the study; G.C.M. and T.P. designed re- sodes target male traits (9, 10, 14–18). Integrating episodes of search; G.C.M. performed research; G.C.M. led the empirical review; G.C.M. analyzed precopulatory and postcopulatory sexual selection represents a data; and G.C.M. and T.P. wrote the paper. fundamental challenge for understanding the evolution of sexu- The authors declare no conflict of interest. ally selected traits and reproductive strategies (14, 18, 19). This article is a PNAS Direct Submission. A rapidly growing body of research has focused on the link be- Published under the PNAS license. tween polyandry and the operation of sexual selection on males. This 1To whom correspondence should be addressed. Email: [email protected]. effort, however, has produced contradicting results. Some studies, This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. often of species displaying low levels of polyandry, have suggested 1073/pnas.1710450115/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1710450115 PNAS | Published online December 14, 2017 | E53–E61 Downloaded by guest on September 24, 2021 A potential reason underpinning these inconsistencies is that broad range of species (Table 1 and Materials and Methods). these studies have largely focused on the average level of poly- Mating assortment in these networks vary considerably, from andry in a population or group, ignoring the details of how positive to negative (Fig. 1B and Table 1). In most networks, the polyandry varies among females and is distributed across males observed SCIC did not differ significantly from the null distri- within a group. We call this quantitative structure of variation in bution of values generated from randomizations. This indicates polyandry among females and across males “mating assortment.” that mating assortment can vary substantially even when mating The crucial point is whether highly polygynous males tend to mate between males and females occurs at random, given simple with more monogamous females (negative assortment) or with properties of the network such as network size (i.e., the number more polyandrous females (positive assortment). By describing of male and female nodes), mating density (number of mating the relationship between the polygyny of males and the polyandry pairs/total number of possible mating pairs), and the variation in of their sexual partners, mating assortment modulates the re- male and female mating success (Fig. 1B). Randomizations of lationship between male mating success (precopulatory) and the smaller networks, that is, those with fewer males and females, had intensity of sperm competition (postcopulatory), and thus can play less continuous null distributions of SCIC values as a consequence a crucial role in determining variation in male reproductive suc- of the limited number of possible permutations (SI Appendix,Fig. cess and the strength of precopulatory and postcopulatory sexual S1). Confirming previous theoretical predictions (43), our results selection (32, 38–46). Consider, for example, a population where show that for small networks both empirical estimates of SCIC males that mate with many females also tend to mate with the and their respective null distributions tended to reach more ex- most polyandrous females. This may result in those males with treme values (Fig. 2A and SI Appendix,Fig.S2). As networks greatest mating success (i.e., most polygynous) suffering the become larger, empirical SCIC values, and their randomized null highest intensity of sperm competition. Consider now the opposite distributions, become less variable and absolute deviations from scenario, where males with higher mating success experience less zero tend to decrease (Fig. 2 and SI Appendix, Fig. S2). This is sperm competition because the females with whom they mate are because, in larger networks, SCIC estimates are impacted less by less polyandryous. In the former scenario, positive mating as- small random deviations in mating patterns, whereas, in small sortment between male polygyny and female polyandry weakens networks, relatively minor changes in the organization of matings the relationship between the mating success of a male and his between males and females can result in large changes in SCIC reproductive success (Bateman gradient), thus reducing pre- values (43). The size of networks varied across taxonomic groups, copulatory sexual selection on male mating success. In the latter such that tended to be represented by smaller groups, scenario, negative mating assortment increases the reproductive by the largest networks, and birds by intermediate-sized returns that a male derives by mating with additional females, thus networks (Figs. 1A and 2B and Table 1). strengthening precopulatory sexual selection (39, 41–43). Importantly, while the majority of empirical SCIC values could be Here, we demonstrate that quantifying patterns of mating parsimoniously explained as random, given the observed variation in assortment is fundamental to assessing the impact of polyandry individual male and female mating success, network size, and mating on male sexual selection. We first review the empirical literature density, in a minority of cases, SCIC values are more extreme than to characterize variation in patterns of mating assortment across expected by chance (Fig. 1B). This suggests that mating assortment taxa. We then clarify how mating assortment and population- may in some cases arise through nonrandom mechanisms, for ex- level polyandry interact to mold the operation of sexual selection ample, nonrandom spatial variation in mating rates or phenotypic on males. To do so, we adopt a network-based approach that preferences between individual partners. We next use a theoretical represents sexually reproducing populations as a network of in- simulation approach to explore how such variation in SCIC values dividuals (nodes) connected by links (copulations) (40, 41, 47– affects sexual selection under different levels of average polyandry. 49). A unique property of network analysis is its ability to capture both direct and indirect relations between interacting entities Simulations. The average level of polyandry of a population had two (39, 50–53). By its very nature, mating assortment requires distinct effects. First, increasing average polyandry tended to con- quantification of indirect as well as direct measures of sexual sistently reduce the absolute maximum value of all measures of partnership. Only by considering indirect interactions can we sexual selection (Fig. 3). Second, increasing average polyandry capture the true interplay between the polygyny of a male and resulted in a progressive contraction in the range of random SCIC the polyandry of his partners. We use a recently developed sexual variation, such that, at high polyandry, simulations were less likely to network metric of mating assortment, the sperm competition reach strongly positive or negative SCIC values due to a progressive intensity correlation (SCIC) (43), and simple simulations to saturation of the network (i.e., increasing mating density; Fig. 3 and generate basic qualitative predictions. Crucially, our approach SI Appendix,Fig.S3). dissects the effect of patterns on sexual se- Independently of average polyandry, increasingly positive levels lection independently of changes in population-level polyandry. of mating assortment (SCIC) reduced total variation in male We show that (i) estimates of mating assortment vary widely reproductive success (i.e., IT;Fig.3A and Table 2), and led to a across empirical studies of different organisms, (ii) variation in more negative covariance between male mating success and pa- mating assortment directly affects the strength of sexual selec- ternity share (i.e., COVMP;Fig.3B and Table 2, using the Pear- tion, and (iii) the effect of mating assortment on sexual selection son’s correlation coefficient between M and P also yielded is partly determined by how it interacts with average polyandry. qualitatively similar results; SI Appendix,Fig.S4). Consequently, We conclude that focusing exclusively on the average level of increasing SCIC also weakened precopulatory sexual selection, polyandry, without considering its interaction with mating as- measured as male Bateman gradients (i.e., βM). Instead, the ef- sortment, does not accurately capture the impact of polyandry on fects of average polyandry on COVMP and βM when controlling for sexual selection. Our explicit quantification of mating assortment SCIC, were much weaker and close to zero (Fig. 3 B and C and provides a more integrative framework for understanding the Table 2). The weak effect of average polyandry on COVMP and impact of polyandry on sexual selection, and the evolution of, βM is driven by a contraction in the range of absolute SCIC values: and variation in, sexually selected traits in nature. at low average polyandry, mating networks are relatively sparse, allowing for more negative assortments, while at higher average Results polyandry, networks become increasingly saturated producing Empirical Patterns of Mating Assortment. We built sexual networks less extreme negative assortments (SI Appendix, Fig. S3). Aver- (Fig. 1A) and calculated SCIC from empirical studies of freely age polyandry and SCIC had similarly negative impacts on the mating groups in both natural and laboratory populations of a maximum potential selection differential on precopulatory traits

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Fig. 1. Mating assortment (SCIC) varies considerably across empirical populations. (A) Visualizations of the 52 empirical sexual networks obtained from the literature. Nodes represent males and females and the links connect mating pairs. White nodes represent females, and colored nodes represent males. Colors designate the taxonomic group of the species of each sexual network (red, ; yellow, birds; green, mammals; pink, molluscs; tan, ).(B) Points show the observed values of sperm competition intensity correlation (SCIC) for 52 empirical sexual networks obtained from the literature. Colors designate the taxonomic group of the species of each sexual network (red, arthropods; yellow, birds; green, mammals; pink, molluscs; tan, reptiles). Estimatesare ordered Top to Bottom by taxonomic group. Error bars represent the 95% range of SCIC values based on 1,000 randomizations of each empirical network. SCIC estimates significantly different from simulated null distributions are highlighted with asterisks (***P < 0.001, **P < 0.01, *P < 0.05). The estimate of network ID 5 remained significant after correcting for false-discovery rate using the Benjamini–Hochberg procedure. Numbers on Right of the plot represent total group size (n males + n females). Estimates were obtained from the following studies [sexual network number (reference)]: 1 (17), 2–4 (84), 5 (45), 6–7 (46), 8–15 (85), 16 (86), 17–18 (87), 19–38 (32), 39–40 (88), 41 (89), 42 (90), 43 (91), 44 (92), 45–47 (93), 48 (94), 49–50 (95), 51 (96), and 52 (97).

(i.e., Jones’ index; Fig. 3D and Table 2). The strong reductive with corresponding mating densities. All of these complementary effect of average polyandry on the Jones’ index was driven largely simulations produced qualitatively similar results (SI Appendix,Figs. by the reduction in the standardized variation in male mating S7–S10), confirming that the roles of mating assortment and av- success with increasing polyandry (i.e., opportunity for sexual se- erage polyandry in male sexual selection are broadly robust to lection, Is; Materials and Methods and SI Appendix, Fig. S5), variation in SCIC variance, female fecundity, and population size. whereas the effect of SCIC on all measures remained strong after controlling for variation in male mating success (SI Appendix, Fig. Discussion S6). Finally, increasing average polyandry interacted with SCIC In polyandrous populations, males must compete for fertilization

such that, at higher mating densities, the effect of SCIC on all both before and after mating. Polyandry is thus expected to be a EVOLUTION measures was reduced. High levels of polyandry therefore reduced strong modulator of the strength of precopulatory and post- the impact of mating assortment on patterns of selection. copulatory sexual selection on males (4, 9–12, 15, 17, 36). Never- We confirmed the generality of these results using complemen- theless, understanding sexual selection in polyandrous populations tary simulations, where (i) SCIC was variance-standardized rather and the interplay between precopulatory and postcopulatory epi- than mean-standardized (i.e., where T and M were standardized to sodes of selection has remained incomplete because we lack a have a mean of zero and SD of 1; equal to the correlation co- quantitative metric for the relationship between male mating efficient between T and M, 43), (ii) females produce only one success and the polyandry of female partners (38–43). We have ovum, and (iii) using larger populations (100 males and 100 fe- utilized a method to link the polygyny of males and the poly- males) with the same range average of polyandry and, separately, andry of their partners (mating assortment) based on a network

McDonald and Pizzari PNAS | Published online December 14, 2017 | E55 Downloaded by guest on September 24, 2021 approach that provides the requisite quantification of both direct number of highly successful, preferred males. In contrast, low-quality and indirect effects. females may not be able to discriminate, leading to high polyandry Here, we present a survey of mating assortment across em- linked to the low polygyny of the less successful males. Positive as- pirical studies of freely mating groups of different organisms. To sortment may arise when trade-offs result in a negative relationship measure mating assortment, we used a recently proposed mea- between a male’s ability to mate guard and his mating success. For sure called the SCIC (43). Our survey shows that SCIC is highly example, in many species characterized by low-level polyandry, those variable and ranges from positive to negative across species and polygynous males who travel to mate with other females, may populations. Assortative mating patterns may arise through both themselves lose paternity to polygynous competitors (57). As we have stochastic processes in randomly mating populations and as demonstrated, positive assortment erodes the benefits of male mat- emergent properties of nonrandom mating due to individual ing success and negates precopulatory sexual selection on males (41, strategies and ecological factors (32, 43–46, 54, 55). We used 58). Similarly, local variation in environmental conditions, group size, randomizations to generate null expectations of SCIC arising in a densities, or phenotypic variation may drive local variation in poly- group as a simple consequence of random mating given a certain andry and the intensity of sperm competition and ultimately network structure (group size, average polyandry, and variation population-level patterns of SCIC (14, 59–62). For example, local in individual mating success). We show that much of the varia- variation in density may result in some highly polygynandrous groups tion in mating assortment is consistent with such null expecta- and other less dense, more monogamous groups, and positive mating tions and can be explained by such simple properties of the assortment may arise at the population level (60, 61). Therefore, network (e.g. strongly negative SCIC is driven by the skew in both random and nonrandom mechanisms are likely to generate male mating success). Importantly, however, our randomizations range of mating structures in natural populations. suggest that, even under conditions of random mating, stochastic We used simulations to disentangle the effect of average poly- variation in mating assortment can generate nondirectional andry and mating assortment on the operation of sexual selection. in estimates of sexual selection, particularly when groups Our simulations confirm previous suggestions that average poly- are small, as is often the case in detailed studies of mating be- andry has a direct effect on sexual selection on males, largely by haviors. However, we also show that, in some cases, SCIC values negating the strength of precopulatory sexual selection (10, 12). may be more extreme than null expectations, suggesting poten- Importantly, these simulations also reveal a critical role of mating tial for nonrandom patterns of assortative mating where the most assortment independent of polyandry: for any given level of poly- successful (i.e., highly polygynous) males mate with the most (or andry, a negatively assorted mating network, with high polygyny least) polyandrous females, more than expected by chance. linked to low polyandry, reinforces selection on male mating suc- Several behavioral mechanisms may drive nonrandom mating cess (i.e., Bateman gradients). Steeper Bateman gradients arise as assortment. For example, in Soay sheep (Ovis aries), dominant rams a consequence of an increased positive covariance between male with high mating success (M) can exclude subdominant males from mating success (M) and paternity share (P,i.e.,COVMP), which in mating with high-quality females, resulting in many less successful turn contributes to the covariance between mating success and males (with low M) mating with a shared subset of relatively few male reproductive success (T, i.e., COVMT). Average polyandry is females (56). This is predicted to generate strongly negative patterns often predicted to reduce sexual selection on male M by dimin- of mating assortment (most polygynous males paired with least ishing the correlation between M and P (16). Our results stress that polyandrous females). Generally, positive covariances between male these effects may be obscured or reversed by differences in mating mating success and mate guarding ability may drive negative as- assortment across populations and therefore have key implica- sortment (44). Females may also actively drive assortative patterns. tions for studies of sexual selection across groups and populations For example, if mate discrimination and resistance to mating are that vary in mating assortment (39). Importantly, while this is of costly, only high-quality females may be able to mate with a small most interest to populations with nonrandom mating assortment,

Table 1. Levels of mating assortment (SCIC) and average polyandry estimated from empirical studies across different taxa Mean Mean No. of Taxonomic Mean SCIC Mean group polyandry mating estimates Refs. group (range) size (range) (±SE) density (±SE) (studies) Species (alphabetical) (chronological)

Arthropod −0.143 57.375 (21–161) 3.824 (0.295) 0.174 (0.025) 16 (6) Aquarius remigis 17, 45, 46, 84–86 (−0.717 to 0.182) Gryllus campestris, Laupala cerasina, Rhynchophorus ferrugineus, Serracutisoma proximum −0.206 20.682 (12–22) 5.16 (0.378) 0.544 (0.036) 22 (2) Gallinago media, 32, 87 (−0.616 to 0.127) Gallus gallus −0.294 12.667 (7–18) 2.01 (0.303) 0.34 (0.027) 12 (8) Alouatta caraya, Canis 88–95 (−1.163 to 0.375) familiaris, Cryptoprocta ferox, catta, Macaca fascicularis, Mandrillus sphinx, Saimiri oestedi, Mollusc −0.511 (—)53(—) 2.111 (—) 0.06 (—) 1 (1) Sepia apama 96 −0.134 (—)59(—) 1.8 (—) 0.053 (—) 1 (1) Agkistrodon contortrix 97

Mating assortment (Sperm competition intensity correlation; SCIC) calculated from 52 empirical sexual networks provided in 18 studies, grouped by along with the population/group size, average polyandry, average mating density, species name and reference.

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Fig. 2. The relationship between empirical estimates of SCIC and mating density and the number of competing males. (A) Each point represents the relationship between the number of competing males and observed values of sperm competition intensity correlation (SCIC) for 52 empirical sexual networks obtained from the literature. The shading of points indicates mating density (number of mating pairs/number of possible mating pairs). Black vertical lines provide 95% range of simulated SCIC values based on 1,000 randomizations of each empirical network. Colored lines and shaded areas show the mean and 95% range of null expectations for SCIC from randomly mating populations with differing number of competing males at three mating densities (tan/solid, ∼0.25; pink/dashed, ∼0.5; blue/dotted, ∼0.75). Null expectations are generated from 100 randomly mating populations for each group size and density combination, where each population has an equal ratio. (B) The relationship between the absolute magnitude of SCIC values and the number of competing males for 52 empirical sexual networks obtained from the literature. Colors designate the taxonomic group of the species of each sexual network (red, arthropods; yellow, birds; green, mammals; pink, molluscs; tan, reptiles).

variation in assortment may obscure the effects of average poly- Thus, for any given level of average polyandry and variation in andry on sexual selection even in randomly mating populations male mating success (opportunity for sexual selection; Is), mating where mating assortment is determined by stochastic processes. assortment is a key additional parameter of mating systems that

A I T B CovMP 2.0

1.5 0.0

1.0 −0.5 0.5 Polyandry 0.0 −1.0 2 CDStandardized M Jones' Index 4 3 6 8

Coefficient value Coefficient 2 1.0

1 0.5 0

0.0 EVOLUTION −1 −1.5 −1.0 −0.5 0.0 0.5 1.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 Mating assortment (SCIC)

Fig. 3. Mating assortment (SCIC) and average population polyandry combine to modulate the potential for sexual selection. Results for mating assortment simulations. Each point represents one simulated population. Plots show the relationship between mating assortment, measured as the sperm competition

intensity correlations (SCIC), and four population level measures including (A) the opportunity for selection (IT), (B) standardized covariance between male β ’ mating success and paternity share (COVMP), (C) standardized male Bateman gradients ( M), and the (D) maximum precopulatory selection differential (Jones index). Colors show the average polyandry of populations. Polyandry levels of 2, 4, 6, and 8 correspond to mating densities (total number mating pairs/total number of possible mating pairs) of 0.2, 0.4, 0.6, and 0.8, respectively.

McDonald and Pizzari PNAS | Published online December 14, 2017 | E57 Downloaded by guest on September 24, 2021 Table 2. The effect of mating assortment (SCIC) and average polyandry on measures of sexual selection

Parameter IT COVMP βM Jones’ index

SCIC −0.560 (0.003) −0.084 (0.001) −0.409 (0.002) −0.111 (0.001) Average polyandry −0.701 (0.016) 0.012 (0.001) 0.010 (0.003) −0.108 (0.004) SCIC*Average polyandry 0.071 (0.004) 0.072 (0.001) 0.032 (0.002) 0.055 (0.001)

Linear mixed model results for the effects of population-level average polyandry and sperm competition

intensity correlation (SCIC) on the opportunity for selection (IT), the standardized covariance between mating β success and paternity share (COVMP), mean-standardized Bateman gradients ( M), and the maximum precopu- latory selection differential (Jones’ index). Fixed effects are scaled to have a mean of zero and SD of 1 and so are comparable within models. Effects are shown with SEs in brackets; all main effects and interactions were significant at the <0.001 level.

can shape sexual selection on males. Moreover, our simulations scope for . For example, if highly polygynous males indicate that the role of mating assortment is indirectly modu- are constrained in their ejaculate expenditure and thereby un- lated by the average polyandry of a population. As average able to fertilize all of the ova of their female partners (76), polyandry increases, the mating network becomes increasingly negative mating assortment may accentuate variation in female saturated, limiting the range of possible mating assortment and . Supporting this prediction, in feral fowl (Gallus thus reducing the scope for SCIC to influence variation in male domesticus), dominant old males provide fewer and lower-quality reproductive success. ejaculates to female partners but are able to exclude other male More broadly, our results shed light on the utility of the Bate- competitors from mating, compromising the fertility of females man gradient as an indicator of sexual selection on males. A recent in the group (77). study identified the Bateman gradient as a relatively poor indicator Taken together, these empirical and simulation results provide of sexual selection on males (63) and advocated the Jones’ index as predictions about sexual selection in polyandrous populations. a better indicator of the strength of sexual selection (63). Our As networks become increasingly more saturated, we expect results suggest that the Bateman gradient and the Jones’ index average polyandry to become a key driver of sexual selection provide complementary information. Bateman gradients are typi- through its direct effect on variance in male reproductive success cally standardized by dividing both T and M by their respective and indirect effects via mating assortment. All else being equal, means (64–68). The slope of a mean standardized Bateman gra- small populations and groups might be more vulnerable to sat- dient of 1 can be interpreted as follows: “a 100% increase in rel- uration, because a certain level of average polyandry is more ative mating success results in a 100% increment in relative likely to saturate the network than in larger populations. In reproductive success” (64, 66, 68). In contrast, the Jones’ index, larger populations, on the other hand, mating densities will likely which represents the maximum potential selection differential on a be relatively low because the absolute number of possible mating trait predicting male mating success (63, 65), is equivalent to a pairs increases multiplicatively with the number of males and variance-standardized Bateman gradient (i.e., M is standardized by females. Larger populations may therefore offer more opportu- subtracting its mean and dividing by its SD). The Jones’ index thus nities for different mating structures and more potential for measures selection on M in units of SDs (64, 66, 68, 69). By nonrandom patterns of mating assortment. These results there- measuring the strength of selection on mating success in isolation fore generate helpful null expectations concerning the influence from changes in variation in male mating success, the mean- of mating assortment and average polyandry on sexual selection. standardized Bateman gradient reveals that increasing the aver- These expectations should help reconcile previous empirical age polyandry of a population alone does not necessarily change studies suggesting diverse effects of polyandry on male Bateman the functional relationship between male M and T.Instead,our gradients and the covariance between precopulatory and post- results demonstrate that mating assortment is a key modulator of copulatory episodes of sexual selection (14). For example, pre- this relationship. In comparison, the Jones’ index reveals how the dictions that increasing average polyandry should strengthen reduced variation in male M, associated with high mating densities sexual selection on males often arise from studies of species (high polyandry), combines with increasing SCIC to accentuate displaying low levels of polyandry, such as socially monogamous the reduction in the potential strength of precopulatory selection birds (20–23). Our results suggest that an increase might in on male traits. These results should be useful in interpreting and principle be observed in some measures of sexual selection (e.g., reconciling the findings of previous studies that used either vari- IT) when modest increments in average polyandry (i.e., from low ance- (10, 70) or mean-standardized Bateman gradients (65, 71). to intermediate) are associated with negative SCIC (i.e., more Taken together, both measures (i.e., Bateman gradient and Jones’ polygynous males are better able to prevent female polyandry). index) provide a fuller understanding of how polyandry shapes Further increments in average polyandry in these populations sexual selection on males and consideration of SCIC clarifies the may increasingly saturate the network, ultimately increasing the complementarity of Bateman gradients and the Jones’ index. polyandry of most females, and resulting in a less negative SCIC. Our simulations are necessarily a deliberate simplification of Indications that average polyandry may weaken sexual selection nature, where male reproductive success is often determined by on males often come from studies of highly polyandrous pop- the complex interaction of multiple factors, and polyandry can ulations (10, 28). As we show, high polyandry constrains varia- dynamically feed back into male strategies (72, 73). For example, tion in SCIC, and increments in average polyandry under such our simulations do not incorporate variation in male fertilization conditions are likely to weaken sexual selection and further limit efficiency or sperm limitation, which may affect paternity dis- the relative role of SCIC. Future empirical work should seek to tributions for any given pattern of assortative mating (15, 74, 75). explore these predictions. Nor did we consider that male ejaculate expenditure and female Mating assortment patterns may also contribute to explain polyandry can dynamically affect each other (19), and will variation in ornament exaggeration and . All modulate male differential investment in precopulatory versus else being equal, we might expect that, for a given level of av- postcopulatory competition. Importantly, mating assortment erage polyandry, populations that are consistently negatively may interact with such postcopulatory processes to mediate the assorted might evolve more exaggerated male ornaments than

E58 | www.pnas.org/cgi/doi/10.1073/pnas.1710450115 McDonald and Pizzari Downloaded by guest on September 24, 2021 positively assorted populations. One should be cautious, however, responds to a density of 0.5 (i.e., 50% of all possible pairs of males and females PNAS PLUS about predicting evolutionary responses based on contemporary mate). However, in a population of 16 males and 16 females, average patterns of mating assortment because mating assortment is likely polyandry of 4 corresponds to a mating density of 0.25. to change dynamically across multiple breeding seasons and gen- erations. Future studies should investigate socioecological pa- Empirical Review. To obtain measures of SCIC from empirical studies in the literature, we conducted multiple searches on Web of Science (wok.mimas. rameters underpinning these temporal dynamics and characterize ac.uk). We were interested in studies that published data of behavioral their impact on sexual selection. Doing so will help us understand observations, providing information on which males copulated with which the way assortative mating patterns influence contemporary evo- females so we could construct the relevant sexual networks. Because our lutionary change and ultimately patterns of exaggeration of pre- focus was on sperm competition, whenever information allowed it, we copulatory and postcopulatory traits. A crucial next step will be to considered females that mated with multiple males within a period that— understand how patterns of mating assortment relate to variation given the reproductive biology of the species—could result in sperm com- in male reproductive success and patterns of sexual selection in petition (SI Appendix, Table S1). If a study contained multiple datasets (i.e., nature. A particularly interesting focus will be to understand how multiple discreet social units and/or multiple breeding seasons), we consid- different sperm competition mechanisms (e.g., fair versus loaded ered each separate individual dataset in our analysis. Our first search used the TOPIC field and contained the following search raffles; ref. 75) and variation in male traits generate deviations terms (“Bateman* gradient*”)OR(“Bateman* slope*”)OR(“Bateman* from the qualitative expectations set out here and whether mating principle*”)OR(“opportunit* for selection”)OR(“opportunit* for sexual patterns themselves have stronger role in different systems. selection”) on February 14, 2017. This resulted in 440 records. We chose Future work should also seek to understand how local differ- these search terms as studies calculating Bateman gradients and variation in ences in environmental conditions, population densities, group mating success were thought likely to have data on individual mating pat- size, and phenotypic variation may drive local variation in poly- terns. Of these, we excluded records based on the title and/or abstract that andry and the intensity of sperm competition (59–61), and how indicated the study would not provide appropriate data. A small number of these in turn translate into mating assortment at the population papers were not available to the authors. Other studies were excluded if level. Recent studies have argued that a key goal in sexual selec- they omitted the required information in the manuscript, supporting ma- terial, or on associated data repository websites (e.g., Dryad). Furthermore, tion research is to understand how the social and environmental we excluded datasets with trivial group sizes of up to only two males and/or variation within and across populations shape covariances be- females, or where males and females were not allowed to freely interact tween precopulatory and postcopulatory episodes of sexual se- and copulate (i.e., enforced sequential ) and where there was no lection (14). Our results highlight that understanding how such variation in male mating success. Similarly, we excluded those studies in socioecological variation shapes assortative mating patterns in which mating success was only inferred from molecular parentage. This is nature will form an important component of this goal. As fine- because any mating patterns based on molecular parentage exclude males grain data on mating behavior become more readily available, an that mate but never sire any offspring (especially so in species with low important aspect of this pursuit will be to investigate and compare fecundity). Thus, the observed mating patterns may likely represent the the link between social and sexual organization across taxa, from result of sperm competitive processes rather than male sperm competitive environments per se (43, 70). This resulted in only two papers that provided invertebrates to primates (61, 62, 78). Information on patterns of raw male and female behavioral pairings that fit our criteria. mating assortment and underpinning social drivers may also help Our second search followed the same procedure as above using the search evolutionary and epidemiological studies of societies (e.g., terms (sexual network* OR social network*) AND (sexual selection OR refs. 79 and 80). mating system). This search returned 58 records, of which three papers In conclusion, the present study helps to clarify ongoing de- provided data that fit our criteria. Our third search contained the terms bate on the role of polyandry in sexual selection (16, 38–40, 44– (mating* or copulat*) AND (behavio*) AND (observ*), restricting our search 46). We demonstrate that mating assortment varies widely across to the journals Animal Behavior, , and Behavioral Ecology populations and that such variation, together with population- and Sociobiology. This returned 697 records of which six studies provided level average polyandry, dictates the potential for sexual selec- appropriate datasets. tion on males (9, 16, 38). Collectively, our results reveal that We complemented these searches with additional datasets obtained via references in other papers, any datasets already known to the authors from mating assortment constitutes a potentially key facet of mating previous searches and through ad hoc searches in relation to mating patterns systems, which modifies the postcopulatory competitive land- and sexual behavior via Google. We excluded one study in which all females scape and can drive variation in the operation of sexual selection were monogamous with the exception of one female who remated with across populations. another male only after her current mate was killed by the study. A second study in which most females were monogamous was eliminated because it Materials and Methods was hard to distinguish between copulations and attempts. This Calculating SCIC, Polyandry, and Mating Density. SCIC measures the relation- selection process generated 52 datasets across 18 studies (SI Appendix, Table ship between a male’s mating success (M) and the mating success of his S1). The final data do not therefore reflect an exhaustive review of mating partners [i.e., his partners’ polyandry (43)]. To estimate SCIC, we first calcu- patterns across the animal kingdom, being limited by (i) taxonomic , late each male’s “sperm competition intensity” (SCI) as the harmonic mean (ii) a tendency to rely on genetic parentage assignment as a proxy for mating success of each female mated with a given male [i.e., the average mating success rather than behavioral observations, and (iii) limited avail- – polyandry of this male’s partners (16, 43, 44); note that this index includes ability of raw data of male female combinations. the focal male within the polyandry of his partners]. The SCIC is then mea- For each dataset, we then estimated SCIC as above, average polyandry, sured as the least-squares regression of male SCI against male mating success and mating density. We include mating density as a comparable measure of (M) [where both parameters are standardized at the population level by the levels of polyandry and polygyny in a group as empirical networks vary their respective means (43)]. Negative values of SCIC describe a tendency for in both the number of males and females. Importantly, populations are males with high mating success to mate with females with few mating likely to show nonzero values of SCIC by chance (43). We therefore in- partners. Positive values describe a positive correlation between a male’s vestigated the extent to which empirical estimates of SCIC may be driven by EVOLUTION mating success and the mating success of his female partners. Only those nonrandom patterns of assortative mating using randomizations of each individuals that copulated are included in network measures. empirical network to generate null expectations for SCIC for each network. We calculated average polyandry as the mean number of unique mating Specifically, we generated a null distribution of mating structures (SCIC)for partners across copulating females. The mating density of networks was each empirical mating network using an approach that randomly shuffles calculated as the total number mating pairs divided by total number of copulating pairs of males and females in the network, maintaining the possible mating pairs. For any given population, increasing polyandry will mating density of the network, and therefore average polyandry, constant always result in an increase in density. However, similar levels of polyandry within each population (81). Furthermore, this approach also holds constant will result in differing mating densities across populations with different the variation in male and female mating success [i.e., the opportunity for ð = σ2 = 2Þ numbers of males and females (i.e., network size). For example, in a pop- sexual selection Is M M for both males and females (65)]. This approach ulation with eight males and eight females, an average polyandry of 4 cor- thus allows us to assess whether observed values of SCIC were more or less

McDonald and Pizzari PNAS | Published online December 14, 2017 | E59 Downloaded by guest on September 24, 2021 than would be expected by chance under random mating, given the ob- probability of fertilizing an ovum proportional to the number of males served variation in male and female mating success, network size, and av- mating with that female [e.g., if four males mated with a female, each male erage polyandry. If observed SCIC values are not more extreme than can be has 25% chance of fertilizing each ovum (19)]. expected by chance given these constraints, this would suggest that an ex- For each male in each population, we then calculated his reproductive planation beyond these more basic properties of the network need not be success (T) as the number of ova fertilized, his mating success (M)asthe invoked when accounting for observed SCIC values. Using this randomiza- number of unique females he mated with, and his paternity share (P)as tion approach, we generated 1,000 randomized versions of each of the the proportion of his partners’ ova that he fertilized. We then measured the 52 networks, resulting in 52,000 randomized networks. Importantly, while relationship between a male’s mating success (M) and the mating success of this approach allows us to ask whether empirical values of SCIC are more or his partners (i.e., his partners’ polyandry) using the SCIC (43). less extreme than may be expected in a randomly mating population with a We assessed the effects of SCIC on sexual selection on males, using linear given basic structure, we are not able consider the individual details of each mixed models across all simulated populations (totaling 9,558 populations). dataset. These details may include, for example, whether all individuals Response variables in models were (i) the standardized variation in re- overlapped in time. Therefore, in some cases, randomizations may generate = σ2 =2 pairings not possible in nature. With this is mind, our approach can establish productive success (opportunity for selection; IT T T ); (ii) the standard- whether given mating patterns are particularly extreme given key aspects of ized covariance between male mating success and male paternity share the empirical sexual network, and inspection of methodologies in each (COVMP), which represents the contribution of the covariance between M published study suggests that such improbable pairings may only represent a and P to variation in male reproductive success; (iii) standardized male minority of the data collected. Bateman gradients calculated as the slope of male reproductive success All randomizations and analyses were carried out using R statistical on male mating success where both are standardized by their respective

software (82). means (βM; also denoted βss); and (iv) the maximum potential precopulatory selection differential (i.e., the Jones’ index) (9, 65). The Jones’ index quan- Simulations. To assess the effects of mating assortment on sexual selection, we tifies the maximum potential strength of precopulatory sexual selection first generated artificial populations with 10 males and 10 females. For each (through M) on a male trait as the product of standardized Bateman gra- population, we fixed the average polyandry so that females mated with two, dient and theqffiffiffiffiffiffiffiffiffiffiffiffiffiffi opportunity for sexual selection on male mating success (i.e., four, six, or eight males on average. To achieve this, we randomly selected pffiffiffi β I = β σ2 =M2) and has recently been identified as useful proxy mea- male and female pairs to copulate with each other, ensuring a set number of M s M M male–female pairs copulated. In all cases, each pair copulated once, and all surepffiffiffi for precopulatory sexual selection on phenotypic traits (63). Note that individuals had at least one mating partner. Because populations were fixed Is is equal to the coefficient of variation in male mating success (CVM) to 10 males and 10 females, these four levels of polyandry correspond to and so the Jones’ index is equal to the variance-standardized Bateman mating densities (total number mating pairs/total number of possible mat- βσ gradient ( M), whereqffiffiffiffiffiffiffiffiffiffiffiffiffiffiM is standardized to have a mean of 0 and SD of 1 (i.e., ing pairs) of 0.2, 0.4, 0.6, and 0.8, respectively. In total, we generated βσ = β CV = β σ2 =M2). Fixed effects in all models included SCIC,the 100 populations for each level of average polyandry (i.e., average pop- M M M M M ulation polyandry, 2, 4, 6, and 8; totaling 400 populations). We then gen- average polyandry of the population, and their interaction. The identity of erated a range of mating structures by conducting randomizations of each the original random mating population was included as a random effect. of our 400 simulated populations so that we either increased or decreased Statistical significance of interaction terms was assessed using likelihood the correlation between a male’s mating success and the mating success of ratio tests to compare a model with the interaction to a model with only his female partners. This was achieved by randomly selecting two copulating main effects. Statistical significance of main effects was assessed using pairs within a population and swapping mating partners between these likelihood ratio tests to compare a model with both main effects to model

mating pairs. We did this in a stepwise fashion for each population by with the focal main effect removed. The opportunity for selection (IT) was making one pairwise swap at a time, retaining each newly assorted pop- log-transformed to meet model assumptions. We scaled explanatory vari- ulation for analysis. We repeated this process for each population in two ables by subtracting the mean and dividing it by its SD to facilitate com- directions, either by continuously increasing positive assortment one swap at parisons between the effect of average polyandry and SCIC within models. a time or by continuously increasing negative assortment one swap at a All simulations and statistical analyses were carried out using R statistical time, until we could no longer increase or decrease the correlation between software (82) and mixed-effects models using lme4 (83). Data used in this male and female mating success (i.e., no swap could be made that increased study are provided as Datasets S1 and S2. or decreased mating assortment after 25,000 attempts). This approach holds both average polyandry and variation in male and female mating success ACKNOWLEDGMENTS. We are very grateful to those who collected and [i.e., the opportunity for sexual selection (Is)] constant across each random- published the empirical data presented in this work. This work was funded ization of a given population. This process resulted in a broad spectrum of by a Biotechnology and Biological Sciences Research Council (BBSRC) mating patterns for each level of average polyandry (SI Appendix, Fig. S3). Collaborative Awards in Science and Engineering Scholarship in collabora- We then simulated sperm competition for every population, where each tion with Aviagen (to G.C.M.), and a LINK grant from the BBSRC in collabo- female produced 100 ova and all males that mate with a female have a ration with Aviagen (to T.P.).

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