Equations or Organisms? A Comment on Berrigan and Charnov

Abstract

In Forum article, Berrigan and Charnov (1994) point out that recent work on life-history traits, and on age and size at maturity in particular, illustrates the power of the natural selection approach as tool for generating quantitative and testable predictions. In their paper, they discuss a that involves the surprisingly different responses of age and size at maturity to changes in temperature versus food in ectotherms. A decrease in temperature and decrease in food quality both lead to decreased growth rate, but decreased temperature usually results in delayed maturity at larger size, while decreased food quality results in delayed maturation at smaller size. Perhaps we should not be surprised that decreased temperature and decreased food quality elicit different (optimal) responses, even if they both decrease the rate of growth. They are, after all, quite different changes in the environment. As Berrigan and Charnov state, the to temperature is remarkably difficult to predict. The likely reason for this difficulty is that we simply do not know how temperature affects the fitness implications of size (and of growing to certain size). Judging from the generality of the temperature response, one suspects some basic mechanism, but this presently remains elusive (Atkinson 1994). Berrigan and Charnov approach the apparent discrepancy between the responses to temperature and to food quality with the Von Bertalanffy equation. This model describes growth as decelerating, asymptotic function of age. They assume that selection acts only on the age of maturity, x, and that temperature and food quality only affect the growth rate, k. Within these constraints, Berrigan and Charnov search for relationships between the model's parameters that could generate the observed response to temperature. In group of Von Bertalanffy models from the literature they find that the required correlations are too restrictive to give general explanation for the delayed maturity at larger size seen at lower temperatures. Berrigan and Charnov's own hypothesis is based on the Von Bertalanffy equation for length. It describes length at age x, lx, as lx = A(I Be kx), where A is the asymptotic length, B is (A lo)/A, and k is the growth coefficient. Fitness is defined as the net reproductive rate, Ro. The only benefit of delayed maturity is increased fecundity caused by linear relationship between size at maturity and fecundity. The only cost to delayed maturity is increased mortality due to constant juvenile mortality rate. This model predicts delayed maturation at smaller size if the growth coefficient decreases without affecting the asymptotic size (Berrigan and Charnov's Fig. 1.I). It may predict delayed maturation at larger size if the decrease of the growth coefficient is accompanied by an increase in the asymptotic size, as is illustrated by Berrigan and Charnov's Fig 1.II (curves a, b and c in Fig. 1). Berrigan and Charnov claim that these two cases may account for the differences in ectotherm responses to changes in temperature versus food quality. Is this explanation of the puzzle helpful? The crucial point is that the negative correlation between A and k in Berrigan and Charnov's model has the effect of steepening the size-age curve in the middle part of the graph for their lower values of k, i.e. at lower temperatures. Note that in the region of maturation organisms of equal sizes experience faster growth at lower temperatures (curves a, b and c in Fig. 1). Since fitness increases linearly with size and the juvenile mortality rate is constant, it is not surprising that this leads to an optimum with delayed maturity at larger size. Other models that steepen the middle part of the graph could (but not necessarily do) also predict higher age and size at maturity, regardless of the asymptotic size. Moreover, the reaction norm of Berrigan and Char-