A diffusion‐based approach to stochastic individual growth and energy budget, with consequences to life‐history optimization and population dynamics

Abstract

Using diffusion processes, I model stochastic individual growth, given exogenous hazards and starvation risk. By maximizing survival to final size, optimal life histories (e.g. switching size for habitat/dietary shift) are determined by two ratios: mean growth rate over growth variance (diffusion coefficient) and mortality rate over mean growth rate; all are size dependent. For example, switching size decreases with either ratio, if both are positive. I provide examples and compare with previous work on risk‐sensitive foraging and the energy–predation trade‐off. I then decompose individual size into reversibly and irreversibly growing components, e.g. reserves and structure. I provide a general expression for optimal structural growth, when reserves grow stochastically. I conclude that increased growth variance of reserves delays structural growth (raises threshold size for its commencement) but may eventually lead to larger structures. The effect depends on whether the structural trait is related to foraging or defence. Implications for population dynamics are discussed.

The relation between maternal phenotype and offspring size, explained by overhead material costs of reproduction

“…This upper threshold depends on the structural size already constructed (i.e., on z(t)), therefore, it defines a curve in the z-y coordinate space. Following my previous work (Filin, 2009), I hereafter refer to this curve as the singular arc, denoted by _ yðzÞ. The singular arc represents the optimal strategy for investment in (irreversible) structural growth, or an optimal rule for dividing total body mass between reversible reserves, y, and irreversible structure, z, as the organism grows (Filin, 2009).…”

“…Following much recent modeling of individual growth (Kooijman et al, 1999;Kooijman, 2010;Müller and Nisbet, 2000;Filin, 2009Filin, , 2010, I divide the total body mass of an individual into a reversibly changing component (hereafter, reserves; denoted by y) and an irreversibly growing component (hereafter, structure; z). Therefore, organismal size is defined by a pair of values (y,z).…”

Target size and optimal life history when individual growth and energy budget are stochastic

“…In this study, I extended my previous work (Filin, 2009) and considered optimal 254 stopping conditions for structural growth, when individuals must grow to some given finite 255 target size, and when reproduction is included in the optimization objective. I found that even 256 when the optimization objective is maximizing survival to target size (as in Filin, 2009; i.e., 257 no reproduction) it is optimal to abandon structural growth altogether close to the target size, 258 and to proceed only by accumulating reserves.…”

“…I found that even 256 when the optimization objective is maximizing survival to target size (as in Filin, 2009; i.e., 257 no reproduction) it is optimal to abandon structural growth altogether close to the target size, 258 and to proceed only by accumulating reserves. 259…”

“…This is also the optimization objective in Filin (2009 However, in that study I did not consider the possible effect of a finite target size on the 133 optimal structural growth curve z * (θ) (in effect, θ 2 is taken to be infinite in Filin, 2009). …”