Stage-Structured Evolutionary Demography: Linking Life Histories, Population Genetics, and Ecological Dynamics

Abstract

Demographic processes and ecological interactions are central to understanding evolution and vice versa. We present a novel framework that combines basic Mendelian genetics with the powerful demographic approach of matrix population models. The ecological components of the model may be stage classified or age classified, linear or nonlinear, time invariant or time varying, and deterministic or stochastic. Genotypes may affect, in fully pleiotropic fashion, any mixture of demographic traits (viability, fertility, development) at any points in the life cycle. The dynamics of the stage # genotype structure of the population are given by a nonlinear population projection matrix. We show how to construct this matrix and use it to derive sufficient conditions for a protected genetic polymorphism for the case of linear, time-independent demography. These conditions demonstrate that genotype-specific population growth rates (l) do not determine the outcome of selection. Except in restrictive special cases, heterozygote superiority in l is neither necessary nor sufficient for a genetic polymorphism. As a consequence, the population growth rate does not always increase, and populations can be driven to extinction due to evolutionary suicide. We demonstrate the construction and analysis of the model using data on a color polymorphism in the common buzzard (Buteo buteo). The model exhibits a stable genetic polymorphism and declining growth rate, consistent with field data and previous models.

Selection in two-sex stage-structured populations: Genetics, demography, and polymorphism

“…We also find that an allele with a higher survival for both males and females but a lower (female) fertility can successfully invade a resident population by taking advantage of the residents’ higher fertility during invasion. Once a polymorphism containing this allele is reached, however, its low fertility can push the population from a positive to a negative growth rate (see de Vries and Caswell (2019b)). Similarly, an allele with a faster maturation rate for both sexes at the cost of lower fertility can lead to evolutionary suicide if survival in the adult stage is much higher than in the juvenile stage (unpublished results).…”

“…As we will show, heterozygote advantage in λ fails as a criterion for genotype coexistence except in special cases (cf. de Vries and Caswell, 2019b). The reason is that the matrix (13) from which λi is calculated allocates all of the reproduction of genotype i to genotype i, whereas in reality each genotype contributes offspring to other genotypes, depending on the population structure.…”

“…Demographic ergodicity guarantees that the homozygous population will converge to a stable stage distribution and grow exponentially; we assume this degree of ergodicity provided the initial population has a nonzero number of females. As in de Vries and Caswell (2019b), we write an equation for the proportional population vector, so that the boundary state is an equilibrium state even if the original population is shrinking or growing, p~(t+1)=A~[trueboldp~(t)]p~(t)A~[trueboldp~(t)]p~(t),where ‖‖⋅ is the 1-norm. Equilibrium solutions of (14), denoted by trueboldpˆ, satisfy pˆ=A~[trueboldpˆ]pˆA~[trueboldpˆ]pˆ…”

“…In one-sex population genetic models, the gamete pool is constructed from the female population vector. In the case of structured one-sex population genetics models, it is (implicitly) assumed that each (st)age contributes to the gamete pool proportional to its relative abundance in the population (Coulson et al, 2011, de Vries and Caswell, 2019b). The construction of such a one-sex model requires two assumptions: (1) the male and female population vectors are proportional, and (2) male mating success is independent of (st)age and genotype.…”

The formal demography of kinship II: Multistate models, parity, and sibship

“…The multistate model classifies individuals jointly by age and some other characteristic, referred to generically as “stage.” In Section 5, the stage variable will be parity. The model is constructed using the vec-permutation matrix approach introduced by Hunter and Caswell (2005) and described in detail in Caswell et al (2018); it has been applied, inter alia, to frailty (Caswell, 2014; Hartemink, Missov, and Caswell, 2017), latent heterogeneity (Hartemink and Caswell, 2018; Jenouvrier et al, 2018; van Daalen and Caswell, 2020), maternal age effects (Hernández et al, 2019), socioeconomic inequality (Caswell, 2019b), epidemiology (Klepac and Caswell, 2011), and genetics (de Vries and Caswell, 2019).…”