Phenotypic evolution in stochastic environments: The contribution of frequency‐ and density‐dependent selection

Abstract

Understanding how environmental variation affects phenotypic evolution requires models based on ecologically realistic assumptions that include variation in population size and specific mechanisms by which environmental fluctuations affect selection. Here we generalize quantitative genetic theory for environmentally induced stochastic selection to include general forms of frequency‐ and density‐dependent selection. We show how the relevant fitness measure under stochastic selection relates to Fisher's fundamental theorem of natural selection, and present a general class of models in which density regulation acts through total use of resources rather than just population size. In this model, there is a constant adaptive topography for expected evolution, and the function maximized in the long run is the expected factor restricting population growth. This allows us to generalize several previous results and to explain why apparently “K‐selected” species with slow life histories often have low carrying capacities. Our joint analysis of density‐ and frequency‐dependent selection reveals more clearly the relationship between population dynamics and phenotypic evolution, enabling a broader range of eco‐evolutionary analyses of some of the most interesting problems in evolution in the face of environmental variation.

Ancestral ecological regime shapes reaction to food limitation in the Least Killifish,Heterandria formosa

“…However, demonstrating that selection at higher density confers a greater ability to cope with low food levels is a step forward in moving the study of density-dependent selection toward a more biological and less phenomenological focus (cf. Engen et al 2020). Survival was reduced at the lower food level, particularly in fish from Trout Pond, and positively associated with size at birth and potentially maternal size.…”

“…However, demonstrating that selection at higher density confers a greater ability to cope with low food levels is a step forward in moving the study of density-dependent selection toward a more biological and less phenomenological focus (cf. Engen et al 2020).…”

“…Understanding how selection acts differently in different density regimes is not a mere exercise in detail. The responses to density-dependent selection and their consequences for subsequent population dynamics depend on the demographic details of selection, for example regarding the age classes primarily affected (Charlesworth 1994; Engen and Saether 2016; Mueller et al 2000), and on which traits respond to which selection pressures (Engen et al 2020; Tung et al 2019).…”

An Evolutionary and Ecological Community Model for Distribution of Phenotypes and Abundances among Competing Species

“…Since the ψ are symmetric, and to get realistic models, the factor γ(z i ) should be related to the intrinsic growth rate r(z i ), implying a trade-off so that individuals with large intrinsic growth rate are also strongly affected by density. At an evolutionary time scale, this will generate a balance between rand K-selection (Lande et al 2009;Engen et al 2013Engen et al , 2020. In other words, individuals that have genotypes favouring high growth rates will be most negatively affected by other individuals, either of the same or of competing of species.…”

“…We assume that the noise parameters are not genetically determined and hence not subject to selection. Including such variation, as done by Lande (2007), Saether and Engen (2015) and Engen et al (2020), would make the model slightly more complex and less transparent.…”