Adaptive changes in harvested populations: plasticity and evolution of age and size at maturation

Abstract

We investigate harvest-induced adaptive changes in age and size at maturation by modelling both plastic variation and evolutionary trajectories. Harvesting mature individuals displaces the reaction norm for age and size at maturation toward older ages and larger sizes and rotates it clockwise, whereas harvesting immature individuals has the reverse qualitative effect. If both immature and mature individuals are harvested, the net effect has approximately the same trend as when harvesting immature individuals only. This stems from the sensitivity of the evolutionary response, which depends on the maturity state of harvested individuals, but also on the type of harvest mortality (negatively or positively density dependent, density independent) and the value of three life-history parameters (natural mortality, growth rate and the trade-off between growth and reproduction). Evolutionary changes in the maturation reaction norm have strong repercussions for the mean size and the density of harvested individuals that, in most cases, result in the reduction of biomass-a response that population dynamical models would overlook. These results highlight the importance of accounting for evolutionary trends in the long-term management of exploited living resources and give qualitative insights into how to minimize the detrimental consequences of harvest-induced evolutionary changes in maturation reaction norms.

Function-valued adaptive dynamics and the calculus of variations

“…9 recovering an earlier result obtained by Dieckmann et al (2004). The calculus of variations allows us to prove that the singular strategy (31) is evolutionarily stable.…”

“…While previous work focused on the canonical equation of function-valued adaptive dynamics (Dieckmann et al, 2004;Ernande et al, 2004;Heino et al, 2004), the general result derived here shows that an evolutionarily singular strategy has to satisfy Euler's equation with environmental feedback. The resultant two alternative approaches to function-valued adaptive dynamics constructively complement each other:…”

“…For coherence's sake, all examples in this article address the evolution of metabolic investment strategies, by extending a model introduced by Dieckmann et al (2004).…”

“…By contrast, adaptive dynamics theory (Metz et al, 1992Dieckmann and Law, 1996;Geritz et al, 1997Geritz et al, , 1998 has been devised as a general framework to analyze the phenotypic evolutionary dynamics of populations under environmental feedback. It is only very recently that adaptive dynamics theory has been extended to function-valued strategies (Dieckmann et al, 2004), and applied to maturation reaction norms (Ernande et al, 2004) and resource utilization strategies (Heino et al, 2004).…”

“…According to Dieckmann et al (2004), the following equation, referred to as the canonical equation of function-valued adaptive dynamics, describes the rate of expected evolutionary change, d dt s, in a function-valued strategy s, d dt s(a) = 1 2 µ sns σ 2 s (a , a)G s (a )da ,…”