Deterioration, death and the evolution of reproductive restraint in late life

Abstract

Explaining why organisms schedule reproduction over their lifetimes in the various ways that they do is an enduring challenge in biology. An influential theoretical prediction states that organisms should increasingly invest in reproduction as they approach the end of their life. An apparent mismatch of empirical data with this prediction has been attributed to age-related constraints on the ability to reproduce. Here we present a general framework for the evolution of age-related reproductive trajectories. Instead of characterizing an organism by its age, we characterize it by its physiological condition. We develop a common currency that if maximized at each time guarantees the whole life history is optimal. This currency integrates reproduction, mortality and changes in condition. We predict that under broad conditions it will be optimal for organisms to invest less in reproduction as they age, thus challenging traditional interpretations of age-related traits and renewing debate about the extent to which observed life histories are shaped by constraint versus adaptation. Our analysis gives a striking illustration of the differences between an age-based and a condition-based approach to life-history theory. It also provides a unified account of not only standard life-history models but of related models involving the allocation of limited resources.

Figure 1.

A graphical determination of the optimal reproductive rate r* when instantaneous mortality m is constant. According to expression (3.2), we seek to maximize [r − mV(x)]/D(r). This is maximized by the r value of the point at which the tangent to the curve D(r) from the point (m V(x),0) and the curve touch. Note that at this point there is the highest net reproductive gain rate (r* − mV; horizontal curly bracket) per damage accumulation (vertical curly bracket). Two cases are shown: mV(x) = 0 and mV(x) = 0.2. Curly brackets refer to the latter case.

Figure 2.

The effect of different combinations of (a) mortality and damage functions on (b) optimal reproduction and (c) reproductive value, in a situation where instantaneous mortality depends on reproductive rate r but not on damage level x. Functions f(r) = r² (a; thin line) and g(r) = 0.1 + r² (a; bold line) are used as mortality and damage functions in three combinations to produce the results of case 1 (solid line) case 2 (dashed) and case 3 (dotted) in (b) and (c). Case 1: m(r) = f(r), D(r) = g(r); case 2: m(r) = g(r), D(r) = f(r); case 3: m(r) = D(r) = f(r).

Figure 3.

Effect of different (a) mortality functions on (b) optimal reproduction and (c) reproductive value, in a situation where instantaneous mortality depends on damage level x but not on reproductive rate r. Mortality functions are: m(x) = 0.1 (solid line); m(x) = 0.1 + r² (dashed); m(x) = e^5x−2.5/(1 + e^5x−2.5) (stippled). Damage function: D(r) = r².