Dynamic networks of fighting and mating in a wild cricket population

Reproductive success is often highly skewed in animal populations. Yet the processes leading to this are not always clear. Similarly, connections in animal social networks are often non-randomly distributed, with some individuals with many connections and others with few, yet whether there are simple explanations for this pattern has not been determined. Numerous social interactions involve dyads embedded within a wider network. As a result, it may be possible to model which individuals accumulate social interaction through a more general understanding of the social network’s structure, and how this structure changes over time. We analysed fighting and mating interactions across the breeding season in a population of wild field crickets under surveillance from a network of video cameras. We fitted stochastic actor-oriented models to determine the dynamic process by which networks of cricket fighting and mating interactions form, and how they co-influence each other. We found crickets tended to fight those in close spatial proximity to them, and those possessing a mutual connection in the fighting network, and heavier crickets fought more often. We also found that crickets who mate with many others tended to fight less in the following time period. This demonstrates that a mixture of spatial constraints, characteristics of individuals and characteristics of the immediate social environment are key for determining social interactions. The mating interaction network required very few parameters to understand its growth and so structure; only homophily by mating success was required to simulate the skew of mating interactions seen in this population. This demonstrates that relatively simple, but dynamic processes can give highly skewed distributions of mating success.

network required very few parameters to understand its growth and so structure; only 3 1 homophily by mating success was required to simulate the skew of mating We used stochastic actor-orientated models (SAOMs) to model the dynamic Unless otherwise stated, we used the same method and rationale as outlined in Bellow we explain the modelling process for each of the networks. fighting a cricket can simply attack another or leave the area when they both meet. The initial SAOM for fighting behaviour contained rate parameters for each time- period and the effects of "density" (the tendency for individuals to be connected to all 1 9 5 others in the network, typically negative as networks are generally sparse) and 1 9 6 "triadic closure" (the tendency for individuals to form connections with those they 1 9 7 share a mutual connection with, typically positive as individuals interact with those 1 9 8 they share a mutual connection with). We tested this for satisfactory goodness-of-fit 1 9 9 (GOF) with three network statistics: degree distribution (the frequencies of the  indicating a satisfactory fit had been achieved. We therefore began adding terms of 2 1 0 interest. After adding a term, we ran the model until it achieved convergence, and 2 1 1 assessed the GOF. If the GOF had worsened we removed the newly-added term(s) 2 1 2 before continuing, otherwise it/they were retained. tendency for members of one sex to fight more often than members of the other sex,  2016a,b). The latter term models the tendency for crickets to predominantly fight 2 1 9 members of the same sex as themselves, which we expected to be a strong effect 2 2 0 as fights between males and females are exceptionally rare. We next added a 2 2 1 changing dyadic covariate of distance, which was the Euclidean distance between 2 2 2 each pair of crickets at the start of the time-period. This models the extent to which 2 2 3 crickets nearer each other are more likely to interact than those further away. As a 2 2 4 SAOM models the transitions between networks, rather than the structure of the four transitions. We then added the constant covariate of individual mass (g), and its between the mass of each individual and its potential associates. We expected 2 2 9 heavier crickets to fight more often (Dixon and Cade 1986), and crickets to avoid 2 3 0 fighting much heavier individuals (Arnott and Elwood 2009). We next added two 2 3 1 effects for weather: the total amount of rainfall (cm) and the intensity of solar 2 3 2 radiation (Watts/m 2 ) in each time-period. These were predicted to increase and 2 3 3 decrease the frequency of social interactions respectively, as they have concurrent 2 3 4 effects on movement around burrows (Fisher et al. 2015). Each individual is scored 2 3 5 as being exposed to the same amount of rainfall and solar radiation in each time-2 3 6 period. Each term did not worsen the GOF of the model (not shown) and so were 2 3 7 retained. This is the final model for the fighting network dynamics. converged, we began adding terms. The GOF for the mating network was not initially  the GOF tests for degree distribution, geodesic distribution and the triad census 2 5 6 respectively), so we began adding terms of interest.

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We first added the changing dyadic covariate of distance for both networks, 2 5 8 calculated in the same way as previously of the fighting network. We next added the 2 5 9 effect of mass for both networks, and the interaction between the mass of two 2 6 0 potential associates for the mating network. The latter effect was not added for the  (Table 1), and we wished to avoid over-parameterising the model. We to not be important, as individuals of all sizes may prefer larger, presumably more 1 0 those of greatly different weight to them (the interaction between the mass of an 3 0 0 individual and the mass of its potential fighting partner was not important). The 3 0 1 weather variables did not influence the fighting network.  Networks plotted using the R package "network" (Butts 2008). In the SAOM for the mating and fighting networks, all the significant effects from the 3 2 1 previous analysis of the fighting network were in the same direction as before, 3 2 2 although the effects of sex, distance and mass were not significant (Table 3). This  For the mating network, the density effect was strongly negative as for the networks. The effect of degree assortativity was positive, indicating that promiscuous 3 3 0 males mated with promiscuous females. Otherwise no effects were significant, but 3 3 1 since there is a lack of power in this analysis we will mention the following effects 3 3 2 that were close to significance (|estimate / standard error| >1). Increasing distance    absolute t-statistic is greater than two. Such effects (aside from the rate parameters) network are calculated rather than estimated, so convergence scores are not given  when the absolute t-statistic is greater than two. Such effects (aside from the rate fighting network were fixed rather than freely estimated, hence their statistics other 3 7 2 than the estimate are not provided (see Table 1). Overall, using two SAOMs we could recapture the skew in social interactions that network. This demonstrated that a relatively simple process, the assortment of interactions in another context. We now deal with each of our results in more detail. The effect of spatial distance was negative, as expected. In many species 4 0 2 individuals will associate more with those close to them, so controlling for spatial 4 0 3 proximity when attempting to detect genuinely socially driven associations is aggressively, and then the size difference influences the outcome.

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Finally, we found no link between the weather variables and frequency of 4 1 9 fighting behaviour. We consider it unlikely that rain and solar radiation do not 4 2 0 influence cricket social interactions, as crickets' activity levels on a given day are suspect that the eight-day periods we selected were too coarse a scale to detect with this approach in some systems. After adding the term of degree assortativity, we were successful in simulating the degree assortativity is as important in other mating systems as it is in the crickets.

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Lifetime reproductive success is correlated with number of mating partners in 4 3 8 this species (Rodríguez-Muñoz et al. 2010). Therefore, assortment by promiscuity between closely related species (Tyler et al. 2015), so may play a role here.

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Only degree assortativity was needed to get a satisfactory GOF for the mating 4 5 1 network, perhaps suggesting that the mating system is quite simple and beyond 4 5 2 these few terms only stochasticity plays an additional role in determining its within the effect of degree assortativity, such as the trait(s) crickets are using for 4 5 7 mate choice and the processes that generate variation in these traits that cannot be partner in an eight-day period, as we used binary networks. Therefore, there is likely 4 6 1 variation in preference among mating partners that we are ignoring, which could 4 6 2 influence fitness as frequency of copulation is likely related to share of paternity  We found that spatial distance did not significantly influence the mating We thank Paul Hopwood, Alex Thornton and Andrew Jackson for comments that 5 0 6 improved this manuscript. We also thank Luke Meadows and Carlos Rodríguez del 5 0 7 Valle for assistance with data collection. Funding for this study was provided by the Natural Environment Research Council can't always get what you want: size assortative mating by mutual mate choice as a 5 3 0 resolution of sexual conflict. BMC Evol. Biol. 9:129. BioMed Central Ltd. Ecol. 20:3045-3055. Actor-oriented models for co-evolving social networks and individual behaviors. Int. J. 5 4 7 Behav. Dev. 31:397-404.