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Abstract While female mate choice is well established, mutual choice may play a larger role in mate selection than currently recognized. Assortative mating is a common form of nonrandom mating in animals that can result from mutual choice. However, few studies address assortative patterns beyond the social pair, potentially overlooking assortativity in the mating pair and in the social environment that shapes reproductive decisions. We asked whether North American barn swallows (Hirundo rustica erythrogaster) breeding in a large colony form pairs, mate (through both within-pair and extra-pair fertilizations), and interact assortatively by ventral plumage color, wing length, and age. Social interactions were tracked using proximity loggers, which recorded close contact between tagged individuals when birds were mating and laying eggs. Barn swallows paired and mated assortatively by their ventral plumage color; however, the assortative patterns in mating pairs were not as strong as they were in social pairs. Barn swallows also interacted assortatively, associating more often with individuals of both sexes who had similar phenotypes relative to the other birds in the colony. Finally, older males and females with darker ventral plumage achieved the highest reproductive success. Investigation of assortative behavior beyond the level of the social pair provides a more complete understanding of mate choice and suggests a mechanism that may maintain the large variation in ventral plumage color in North American barn swallows. 

Abstract Extra-pair mating is common in avian species and can modulate the strength of sexual selection. Mate searching behavior of female birds may be an important predictor of mating opportunities and extra-pair mating, yet important knowledge is lacking as we have little data on fine-scale movement of females during the peak fertilization period. Accordingly, much is still unknown about whether and how female phenotypes contribute to extra-pair mating. Here, we examined how female space use and female plumage color are associated with extra-pair mating outcomes in wild barn swallows (Hirundo rustica erythrogaster). We tracked 10 females breeding in Colorado, USA with GPS backpack tags for two hours each morning during their fertile period following an experimental nest failure. We then used low-coverage whole-genome sequencing to determine offspring paternity and to quantify extra-pair mating in the removed clutch and the replacement clutch. Plumage and movement did not correlate with changes in paternity between successive clutches, but movement did correlate with paternity in the replacement clutch. Females that spent more time away from the nest had a higher proportion and number of extra-pair offspring in the clutch laid immediately after the tracking period. These results suggest that differences in female space use contribute to differences in extra-pair fertilizations. In contrast to the historic emphasis on male traits, our study highlights female movement behavior as an important variable associated with mating outcomes in natural populations. 

Undirected, binary network data consist of indicators of symmetric relations between pairs of actors. Regression models of such data allow for the estimation of effects of exogenous covariates on the network and for prediction of unobserved data. Ideally, estimators of the regression parameters should account for the inherent dependencies among relations in the network that involve the same actor. To account for such dependencies, researchers have developed a host of latent variable network models; however, estimation of many latent variable network models is computationally onerous and which model is best to base inference upon may not be clear. We propose the probit exchangeable (PX) model for undirected binary network data that is based on an assumption of exchangeability, which is common to many of the latent variable network models in the literature. The PX model can represent the first two moments of any exchangeable network model. We leverage the EM algorithm to obtain an approximate maximum likelihood estimator of the PX model that is extremely computationally efficient. Using simulation studies, we demonstrate the improvement in estimation of regression coefficients of the proposed model over existing latent variable network models. In an analysis of purchases of politically aligned books, we demonstrate political polarization in purchase behavior and show that the proposed estimator significantly reduces runtime relative to estimators of latent variable network models, while maintaining predictive performance. 

Summary Relational arrays represent measures of association between pairs of actors, often in varied contexts or over time. Trade flows between countries, financial transactions between individuals, contact frequencies between school children in classrooms and dynamic protein-protein interactions are all examples of relational arrays. Elements of a relational array are often modelled as a linear function of observable covariates. Uncertainty estimates for regression coefficient estimators, and ideally the coefficient estimators themselves, must account for dependence between elements of the array, e.g., relations involving the same actor. Existing estimators of standard errors that recognize such relational dependence rely on estimating extremely complex, heterogeneous structure across actors. This paper develops a new class of parsimonious coefficient and standard error estimators for regressions of relational arrays. We leverage an exchangeability assumption to derive standard error estimators that pool information across actors, and are substantially more accurate than existing estimators in a variety of settings. This exchangeability assumption is pervasive in network and array models in the statistics literature, but not previously considered when adjusting for dependence in a regression setting with relational data. We demonstrate improvements in inference theoretically, via a simulation study, and by analysis of a dataset involving international trade.