Arnold & Duvall (1994) Animal Mating Systems: A Synthesis Based on Selection Theory
Arnold & Duvall (1994) use mathematical modeling and statistical analysis of classic data such as those collected by Bateman (1984) to analyse how the strength of sexual selection can be used to explain diversity in mating systems.
The previous papers (by Bateman 1948, Trivers 1972, and Emlen & Oring 1977), discussed in previous posts, had set the stage for more empirical and theoretical work attempting to explain the evolution of mating systems. Arnold & Duvall (1994) suggested that although there had been many important articles contributing to different aspects of mating system theory, including Bateman’s classic work on the relationship between fecundity and mating success, there was no formal theoretical and analytical framework that integrated all the research.
The authors reaffirm that the relationship between mating success and fecundity (based on Bateman’s original work) is a key driver of mating system evolution. One of the paper’s main themes is based on a now well-accepted idea articulated in the early 1980’s (Lande and Arnold 1983), that selection can be seen as the statistical relationship between certain traits and fitness. To integrate this analytic approach with the study of mating systems, Arnold and Duvall propose a 4 tiered hierarchical framework including the traits that influence fitness. This conceptual model illustrates the direct and indirect relationships between traits and fitness measures, and allows formal testing of the pathways that affect fitness components. Traits that have the most direct effect on fitness are assigned rank one, while more indirect agents have higher ranks (2, 3 or 4) depending on the number of presumed mediating factors that relate them with fitness (Figure 1.).
Luc noted that creating thought maps or path diagrams similar to this figure, which describe the important relationships or factors within a system, could be very useful in allowing us to visualize and understand the important questions in our own research. These conceptual diagrams often further allow one to make the statistical associations between correlated components of a system more explicit.
Arnold and Duvall explain how the ‘selection gradients’ illustrated as arrows in Figure 1 can be quantified using multiple regression of fitness on estimates of the traits presumed to be under selection. Each aforementioned selection gradient is the partial standardized regression coefficient in a multiple regression including other aspects of the phenotype. Multiple regression can therefore be used to estimate the total combined selection on all the various traits affecting fitness, including the sexual selection component that affects reproductive fitness.
The authors explain that linear regression is appropriate in the estimation of selection gradients even if the fits are nonlinear. This is now an accepted convention when trying to measure strength of selection on a trait, however Luc suggested that, notwithstanding Arnold and Duvall’s logic about the nature of evolutionary genetic change and its relationship with the well-established body of work on selection analysis, we should neverthelessalways question exactly what coefficients mean when they come from a model that might have a poor fit.
The authors further discuss how estimates of selection gradients can be used to test sexual selection theory, by integrating different aspects of mating systems such as nuptial gifts or parental care, to examine the strength of selection on males and females. They argue that their approach quantifies differences in the strength of selection (regression slopes) between males and females, which is useful for testing theory on mating systems.
They illustrate their analysis using several examples of mating systems, including one in which males provide nuptial gifts to females. In this case, models showed that there should be a small increase in female’s selection gradient (strength of sexual selection) for each multiple mating (as a result of the benefits to gaining extra gifts and therefore nutrition), and that the greater the nutritional benefit of the gift, the greater the strength of sexual selection will be.
Arnold and Duvall finally use models involving encounter rate, similar to the ideas proposed by Emlen and Oring (1977), and show that these can also be used to measure the strength of selection on fitness based traits. They do however contest Emlen and Oring’s (1977) assertion about the most useful metric for describing or determining mating systems. Whereas Emlen and Oring argue that the operational sex ratio (the average over time of the number of sexually active males to the number of females capable of insemination) is the most useful indicator of the mating system, Arnold and Duvall reason that the breeding sex ratio (the ratio of breeding males to breeding females, including the zero fecundity class for each sex) is more appropriate. This may be something to think about for some members of our lab who are looking at malaise trap samples to determine the adult operational sex ratios and mating rates of dance flies.
Ultimately the authors claim that it is the disparity in selection gradients that determines which sex competes for access to the other. While sexual selection due to competition will therefore determine a species’ mating system, it seems logical that a species mating system will also influence the level of selection in a cyclical fashion. This reminds us of Trivers (1972), who noted the cyclical relationship between mate competition and parental investment in his own analysis of what determines the sex roles.