What life cycle graphs can tell about the evolution of life histories

Abstract

We analyze long-term evolutionary dynamics in a large class of life history models. The model family is characterized by discrete-time population dynamics and a finite number of individual states such that the life cycle can be described in terms of a population projection matrix. We allow an arbitrary number of demographic parameters to be subject to density-dependent population regulation and two or more demographic parameters to be subject to evolutionary change. Our aim is to identify structural features of life cycles and modes of population regulation that correspond to specific evolutionary dynamics. Our derivations are based on a fitness proxy that is an algebraically simple function of loops within the life cycle. This allows us to phrase the results in terms of properties of such loops which are readily interpreted biologically. The following results could be obtained. existence of optimisation principles in models with an arbitrary number of evolving traits. These models are then classified with respect to their appropriate optimisation principle. Second, under the assumption of just two evolving traits we identify structural features of the life cycle that determine whether equilibria of the monomorphic adaptive dynamics (evolutionarily singular points) correspond to fitness minima or maxima. Third, for one class of frequency-dependent models, where optimisation is not possible, we present sufficient conditions that allow classifying singular points in terms of the curvature of the trade-off curve. Throughout the article we illustrate the utility of our framework with a variety of examples.

Necessary and sufficient conditions for $$R_{0}$$ to be a sum of contributions of fertility loops

“…These authors show that the outcome of an evolutionary invasion analysis of a life history problem in which the life cycle can be partitioned into a phase affected by the resident community through an environmental feedback loop and a phase in which life history transitions are affected by mutations can be predicted from an optimization procedure given the transition between the two phases can be described by a matrix of rank one. This idea is treated from a more general perspective in Section 3.3 in Rueffler et al (2012).…”

When Do Optimisation Arguments Make Evolutionary Sense?

“…We start with the plethora of sufficient conditions for the existence of an optimisation principle derived by Rueffler et al [43]. Two immediate trivial cases are Proposition 3.20.…”

“…Presently two manuscripts are floating around, by Roger Bowers [5] and by Claus Rueffler and co-workers [43], that relate life cycle structure to properties of the associated invasion fitness function. Both manuscripts deal with finite state individuals in constant environments, i.e., community dynamical equilibria.…”

“…Moreover, it is not clear yet whether possibly any further special cases are still out in the wild. Hence we give only one simple example and refer to [43] for the details.…”

“…Q for this life cycle equals −1 + (t 22 + t 33 + t 21 t 32 f 13 + t 32 f 23 ) − (t 22 t 33 ), with the bracketed terms corresponding to the first and second sums in (3.7). From [43].…”