Courtney L. Fitzpatrick

Not Just a Theory—The Utility of Mathematical Models in Evolutionary Biology

Models have made numerous contributions to evolutionary biology, but misunderstandings persist regarding their purpose. By formally testing the logic of verbal hypotheses, proof-of-concept models clarify thinking, uncover hidden assumptions, and spur new directions of study. thumbnail image credit: modified from the Biodiversity Heritage Library

A Mathematical Model Gives Insights into the Effects of Vitamin B-6 Deficiency on 1-Carbon and Glutathione Metabolism

We experimented with a mathematical model for 1-carbon metabolism and glutathione (GSH) synthesis to investigate the effects of vitamin B-6 deficiency on the reaction velocities and metabolite concentrations in this metabolic network. The mathematical model enabled us to independently alter the activities of each of the 5 vitamin B-6-dependent enzymes and thus determine which inhibitions were responsible for the experimentally observed consequences of a vitamin B-6 deficiency. The effect of vitamin B-6 deficiency on serine and glycine concentrations in tissues and plasma was almost entirely due to its effects on the activity of glycine decarboxylase. The effect of vitamin B-6 restriction on GSH concentrations appeared to be indirect, arising from the fact that vitamin B-6 restriction increases oxidative stress, which, in turn, affects several enzymes in 1-carbon metabolism as well as the GSH transporter. Vitamin B-6 restriction causes an abnormally high and prolonged homocysteine response to a methionine load test. This effect appeared to be mediated solely by its effects on cystathionine beta-synthase. Reduction of the enzymatic activity of serine hydroxymethyltransferase (SHMT) had negligible effects on most metabolite concentrations and reaction velocities. Reduction or total elimination of cytoplasmic SHMT had a surprisingly moderate effect on metabolite concentrations and reaction velocities. This corresponds to the experimental findings that a reduction in the enzymatic activity of SHMT has little effect on 1-carbon metabolism. Our simulations showed that the primary function of SHMT was to increase the rate by which the glycine-serine balance was reequilibrated after a perturbation.

Seasonality, sociality, and reproduction: Long-term stressors of ring-tailed lemurs (Lemur catta).

Fecal glucocorticoid (fGC) concentrations are reliable, non-invasive indices of physiological stress that provide insight into an animals energetic and social demands. To better characterize the long-term stressors in adult members of a female-dominant, seasonally breeding species - the ring-tailed lemur (Lemur catta) - we first validated fecal samples against serum samples and then examined the relationship between fGC concentrations and seasonal, social, demographic, genetic, and reproductive variables. Between 1999 and 2006, we collected 1386 fecal samples from 32 adult, semi-free-ranging animals of both sexes. In males and non-pregnant, non-lactating females, fGC concentrations were significantly elevated during the breeding season, specifically during periods surrounding known conceptions. Moreover, group composition (e.g., multi-male versus one-male) significantly predicted the fGC concentrations of males and females in all reproductive states. In particular, the social instability introduced by intra-male competition likely created a stressor for all animals. We found no relationship, however, between fGC and the sex, age, or heterozygosity of animals. In reproducing females, fGC concentrations were significantly greater during lactation than during the pre-breeding period. During pregnancy, fGC concentrations were elevated in mid-ranking dams, relative to dominant or subordinate dams, and significantly greater during the third trimester than during the first or second trimesters. Thus, in the absence of nutritional stressors, social dominance was a relatively poor predictor of fGC in this female-dominant species. Instead, the animals were maximally challenged by their social circumstances and reproductive events-males by competition for mating opportunities and females by late-term gestation and lactation.

Sources of variance in a female fertility signal: exaggerated estrous swellings in a natural population of baboons

Signals of fertility in female animals are of increasing interest to evolutionary biologists, a development that coincides with increasing interest in male mate choice and the potential for female traits to evolve under sexual selection. We characterized variation in size of an exaggerated female fertility signal in baboons and investigated the sources of that variance. The number of sexual cycles that a female had experienced after her most recent pregnancy (“cycles since resumption”) was the strongest predictor of swelling size. Furthermore, the relationship between cycles since resumption and swelling size was most evident during rainy periods and was not evident during times of drought. Finally, we found significant differences in swelling size between individual females; these differences endured across cycles (i.e., were not explained by variation within individuals) and persisted in spite of ecological effects. This study is the first to provide conclusive evidence of significant variation in swelling size between female primates (controlling for cycles since resumption) and to demonstrate that ecological constraints influence variation in this signal of fertility.

Embracing multiple definitions of learning

Definitions of learning vary widely across disciplines, driven largely by different approaches used to assess its occurrence. These definitions can be better reconciled with each other if each is recognized as coherent with a common conceptualization of learning, while appreciating the practical utility of different learning definitions in different contexts.

Male mate choice, male quality, and the potential for sexual selection on female traits under polygyny.

Observations of male mate choice are increasingly common, even in species with traditional sex roles. In addition, female traits that bear the hallmarks of secondary sexual characters are increasingly reported. These concurrent empirical trends have led to the repeated inference that, even under polygyny, male mate choice is a mechanism of sexual selection on female traits. It is often either assumed or argued that in these cases females are competing for males of superior “quality”; females might experience sexual selection under polygyny if they compete for mates that provide either direct or indirect benefits. However, the theoretical foundation of this testable hypothesis remains largely uninvestigated. We develop a population genetic model to probe the logic of this hypothesis and demonstrate that, contrary to common inferences, male mate choice, variation in male quality (in the form of a direct fecundity benefit to females), and female ornamentation can coexist in a population without any sexual selection on female ornamentation taking place at all. Furthermore, even in a “best case scenario” where high quality males with a preference for ornamented females are able to mate disproportionately more often with them, the evolution of female traits by sexual selection may be relatively weak. We discuss the implication of these findings for ongoing empirical and theoretical research on the evolution of sexual‐signaling in females.

Theory Meets Empiry: A Citation Network Analysis

According to a recent survey, ecologists and evolutionary biologists feel that theoretical and empirical research should coexist in a tight feedback loop but believe that the two domains actually interact very little. We evaluate this perception using a citation network analysis for two data sets, representing the literature on sexual selection and speciation. Overall, 54%-60% of citations come from a papers own category, whereas 17%-23% are citations across categories. These cross-citations tend to focus on highly cited papers, and we observe a positive correlation between the numbers of citations a study receives within and across categories. We find evidence that reviews can function as integrators between the two literatures, argue that theoretical models are analogous to specific empirical study systems, and complement our analyses by studying a cocitation network. We conclude that theoretical and empirical research are more tightly connected than generally thought but that avenues exist to further increase this integration.