Abstract
An organism's life history is closely interlinked with its allocation of energy between growth and reproduction at different life stages. Theoretical models have established that diminishing returns from reproductive investment promote strategies with simultaneous investment into growth and reproduction (indeterminate growth) over strategies with distinct phases of growth and reproduction (determinate growth). We extend this traditional, binary classification by showing that allocation‐dependent fecundity and mortality rates allow for a large diversity of optimal allocation schedules. By analyzing a model of organisms that allocate energy between growth and reproduction, we find twelve types of optimal allocation schedules, differing qualitatively in how reproductive allocation increases with body mass. These twelve optimal allocation schedules include types with different combinations of continuous and discontinuous increase in reproduction allocation, in which phases of continuous increase can be decelerating or accelerating. We furthermore investigate how this variation influences growth curves and the expected maximum life span and body size. Our study thus reveals new links between eco‐physiological constraints and life‐history evolution and underscores how allocation‐dependent fitness components may underlie biological diversity.
Highlights
Simple life-history models often predict that it is optimal to allocate all surplus energy to growth early in life, before switching to allocate all energy to reproduction
The slope of a decelerating fitness-return curve affects the shape of gradually increasing optimal reproductive- allocation schedules, such that more deceleration causes a transition from an accelerating to a decelerating gradual increase
The shape of the fitness-return curve for low levels of reproductive investment affects the shape of optimal reproductive-allocation schedules at low ages or masses
Summary
Simple life-history models often predict that it is optimal to allocate all surplus energy to growth early in life, before switching to allocate all energy to reproduction. This allocation pattern is often referred to as a “bang-bang control” and leads to determinate growth. Simultaneous investment into growth and reproduction, leading to indeterminate growth, is common in nature. Much theoretical research on reproductive allocation has investigated mechanisms and conditions, which can promote evolution of indeterminate growth, for example, stochastic environments (King & Roughgarden, 1982), diminishing returns of reproductive investments (Sibly, Calow, & Nichols, 1985; Taylor, Gourley, Lawrence, & Kaplan, 1974), or structural constraints (Kozłowski & Ziólko, 1988). Whereas bang-bang control strategies can be characterized by the ages or sizes at which the switch from growth to reproduction occurs, it is less clear how to characterize and understand allocation schedules that cause reproductive investment to
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