Research Article: Generalized structural equations improve sexual-selection analyses

Date Published: August 15, 2017

Publisher: Public Library of Science

Author(s): Sonia Lombardi, Giacomo Santini, Giovanni Maria Marchetti, Stefano Focardi, Ludek Bartos.


Sexual selection is an intense evolutionary force, which operates through competition for the access to breeding resources. There are many cases where male copulatory success is highly asymmetric, and few males are able to sire most females. Two main hypotheses were proposed to explain this asymmetry: “female choice” and “male dominance”. The literature reports contrasting results. This variability may reflect actual differences among studied populations, but it may also be generated by methodological differences and statistical shortcomings in data analysis. A review of the statistical methods used so far in lek studies, shows a prevalence of Linear Models (LM) and Generalized Linear Models (GLM) which may be affected by problems in inferring cause-effect relationships; multi-collinearity among explanatory variables and erroneous handling of non-normal and non-continuous distributions of the response variable. In lek breeding, selective pressure is maximal, because large numbers of males and females congregate in small arenas. We used a dataset on lekking fallow deer (Dama dama), to contrast the methods and procedures employed so far, and we propose a novel approach based on Generalized Structural Equations Models (GSEMs). GSEMs combine the power and flexibility of both SEM and GLM in a unified modeling framework. We showed that LMs fail to identify several important predictors of male copulatory success and yields very imprecise parameter estimates. Minor variations in data transformation yield wide changes in results and the method appears unreliable. GLMs improved the analysis, but GSEMs provided better results, because the use of latent variables decreases the impact of measurement errors. Using GSEMs, we were able to test contrasting hypotheses and calculate both direct and indirect effects, and we reached a high precision of the estimates, which implies a high predictive ability. In synthesis, we recommend the use of GSEMs in studies on lekking behaviour, and we provide guidelines to implement these models.

Partial Text

Sexual selection is a fundamental evolutionary force that operates either through (i) direct competition between males or (ii) female mate choice which leads to the evolution of forms of exaggerated and useless ornaments in males (e.g. the peacock’s tail). The ornaments are supposed to display male genetic quality or the absence of sexually transmissible diseases [1]. Albeit a long record of studies since Darwin’s time have addressed this problem, many questions about sexual selection remain open, and this continues to be a major research theme. For the present contribution, the main question is how to investigate the factors affecting male copulatory success in lek mating. In lekking species, the two sexes interact mainly during the rut [2, 3] when males defend small display territories inside an arena or lek. For males, lekking is a high cost—high benefits strategy, in which the risk of injuries and even death is high, but a few dominant males may monopolize most of the copulations [4, 5]. On the other hand, females are supposed to benefit from visiting a lek, since they can choose among several potential partners [6, 7].

The distribution of CopS is showed in Fig 2. Most of the bucks (68.6%) had no copulations. The number of copulations per individual ranged from 0 to 43, and the distribution has high kurtosis (32.33) and skewness (4.99). The distribution of CopS is best fitted by a negative binomial distribution (χ2 = 0.28, P = 0.595), which is much better supported than alternative models (ZINB, ΔAIC = 33.39; ZIP, ΔAIC = 152.47; Poisson, ΔAIC = 535.02). Data transformation changes the discrete CopS distribution into a continuous one, which remains, however, non-normally distributed (Shapiro-Wilk Test: log(CopS+1), W = 0.648, P<0.001; log(CopS+0.5), W = 0.659, P<0.001; log(CopS+0.1), W = 0.662, P<0.001; CopS0.5, W = 0.635, P<0.001). The data collected at Castelporziano on the mating behaviour of fallow bucks represents a typical example of the many studies performed on the leks of this species [11, 12, 34, 23] and other species of vertebrates [9, 12, 29]. These behavioural studies are important not only to identify the proximate causes of mate selection, but also for determining the intensity of sexual selection and understanding the evolution of exaggerated traits in males.   Source:


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