Measure dynamics on a one-dimensional continuous trait space: theoretical foundations for adaptive dynamics

The measure dynamics approach to modelling single-species coevolution with a one-dimensional trait space is developed and compared to more traditional methods of adaptive dynamics and the Maximum Principle. It is assumed that individual fitness results from pairwise interactions together with a background fitness that depends only on total population size. When fitness functions are quadratic in the real variables parameterizing the one-dimensional traits of interacting individuals, the following results are derived. It is shown that among monomorphisms (i.e. measures supported on a single trait value), the continuously stable strategy (CSS) characterize those that are Lyapunov stable and attract all initial measures supported in an interval containing this trait value. In the cases where adaptive dynamics predicts evolutionary branching, convergence to a dimorphism is established. Extensions of these results to general fitness functions and/or multi-dimensional trait space are discussed.     

CSS, NIS and dynamic stability for two-species behavioral models with continuous trait spaces

Static continuously stable strategy (CSS) and neighborhood invader strategy (NIS) conditions are developed for two-species models of frequency-dependent behavioral evolution when individuals have traits in continuous strategy spaces. These are intuitive stability conditions that predict the eventual outcome of evolution from a dynamic perspective. It is shown how the CSS is related to convergence stability for the canonical equation of adaptive dynamics and the NIS to convergence to a monomorphism for the replicator equation of evolutionary game theory. The CSS and NIS are also shown to be special cases of neighborhood p^*- superiority for p^* equal to one half and zero, respectively. The theory is illustrated when each species has a one-dimensional trait space.     

An exact form of the breeder's equation for the evolution of a quantitative trait under natural selection

Starting with the Price equation, I show that the total evolutionary change in mean phenotype that occurs in the presence of fitness variation can be partitioned exactly into five components representing logically distinct processes. One component is the linear response to selection, as represented by the breeder's equation of quantitative genetics, but with heritability defined as the linear regression coefficient of mean offspring phenotype on parent phenotype. The other components are identified as constitutive transmission bias, two types of induced transmission bias, and a spurious response to selection caused by a covariance between parental fitness and offspring phenotype that cannot be predicted from parental phenotypes. The partitioning can be accomplished in two ways, one with heritability measured before (in the absence of) selection, and the other with heritability measured after (in the presence of) selection. Measuring heritability after selection, though unconventional, yields a representation for the linear response to selection that is most consistent with Darwinian evolution by natural selection because the response to selection is determined by the reproductive features of the selected group, not of the parent population as a whole. The analysis of an explicitly Mendelian model shows that the relative contributions of the five terms to the total evolutionary change depends on the level of organization (gene, individual, or mated pair) at which the parent population is divided into phenotypes, with each frame of reference providing unique insight. It is shown that all five components of phenotypic evolution will generally have nonzero values as a result of various combinations of the normal features of Mendelian populations, including biparental sex, allelic dominance, inbreeding, epistasis, linkage disequilibrium, and environmental covariances between traits. Additive genetic variance can be a poor predictor of the adaptive response to selection in these models. The narrow-sense heritability sigma2A/sigma2P should be viewed as an approximation to the offspring-parent linear regression rather than the other way around.     

Plant species with the trait of continuous flowering do not hold core roles in a Neotropical lowland plant‐pollinating insect network

Plant–animal interaction science repeatedly finds that plant species differ by orders of magnitude in the number of interactions they support. The identification of plant species that play key structural roles in plant–animal networks is a global conservation priority; however, in hyperdiverse systems such as tropical forests, empirical datasets are scarce. Plant species with longer reproductive seasons are posited to support more interactions compared to plant species with shorter reproductive seasons but this hypothesis has not been evaluated for plant species with the longest reproductive season possible at the individual plant level, the continuous reproductive phenology. Resource predictability is also associated with promoting specialization, and therefore, continuous reproduction may instead favor specialist interactions. Here, we use quantitative pollinating insect–plant networks constructed from countryside habitat of the Tropical Wet forest Life Zone and modularity analysis to test whether plant species that share the trait of continuous flowering hold core roles in mutualistic networks. With a few exceptions, most plant species sampled within our network were assigned to the role of peripheral. All but one network had significantly high modularity scores and each continuous flowering plant species was in a different module. Our work reveals that the continuous flowering plant species differed in some networks in their topological role, and that more evidence was found for the phenology to support specialized subsets of interactions. Our findings suggest that the conservation of Neotropical pollinating insect communities may require planting species from each module rather than identifying and conserving network hubs.