Reproductive value

Natural selection favors those individuals that make the greatest proportionate contribution to the future of the population to which they belong. All life history components affect this contribution, ultimately through their effects on fecundity and survival. It is necessary, though, to combine these effects into a single currency so that different life histories may be judged and compared. A number of measures of fitness have been used. All the better ones have made use of both fecundity and survival schedules, but they have done so in different ways, and there has often been marked disagreement as to which of them is the most appropriate. The intrinsic rate of natural increase, r, and the basic reproductive rate, R0 (see above) have had their advocates, as has 'reproductive value' (Fisher, 1930; Williams, 1966), especially reproductive value at birth (Kozlowski, 1993; de Jong, 1994). For an exploration of the basic patterns in life histories, however, the similarities between these various measures are far more important than the minor differences between them. We concentrate here on reproductive value.

Reproductive value is described in some detail in Box 4.1. For most purposes though, these details can be ignored as long as it is remembered that: (i) reproductive value at a given age or stage is the sum of the current reproductive output and the residual (i.e. future) reproductive value (RRV); (ii) RRV combines expected future

100 80 60 40 20 0


Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months

□ Parent corm (PC) □ Daughter corm (DC) □ Fruit ■ Roots (R) □ Inflorescence stalk (IS)

reproductive value described in words

Figure 4.17 Percentage allocation of the crucial resource nitrogen to different structures throughout the annual cycle of the perennial plant Sparaxis grandiflora in South Africa, where it sets fruit in the southern hemisphere spring (September-December). The plant grows each year from a corm, which it replaces over the growing season, but note the development of reproductive parts at the expense of roots and leaves toward the end of the growing season. The plant parts themselves are illustrated to the right for a plant in early spring. (After Ruiters & McKenzie, 1994.)

Box 4.1 Reproductive value

The reproductive value of an individual of age x (RVx) is the currency by which the worth of a life history in the hands of natural selection may be judged. It is defined in terms of the life-table statistics discussed earlier. Specifically:

where mx is the birth rate of the individual in age-class x; lx is the probability that the individual will survive to age x; R is the net reproductive rate of the whole population per unit time (the time unit here being the age interval); and S means 'the sum of'.

To understand this equation, it is easiest to split RVx into its two components:

Here, mx, the individual's birth rate at its current age, can be thought of as its contemporary reproductive output. What remains is then the residual reproductive value (Williams, 1966): the sum of the 'expectations of reproduction' at all subsequent ages, modified in each case by Rx-y for reasons described below. The 'expectation of reproduction' for age class y is (lyllx ■ (my)), i.e. it is the birth rate of the individual should it reach that age (my), discounted by the probability of it doing so given that it has already reached stage x (lyllx).

Reproductive value takes on its simplest form where the overall population size remains approximately constant. In such cases, R = 1 and can be ignored. The reproductive value of an individual is then simply its total lifetime expectation of reproductive output (from its current age class and from all subsequent age classes).

However, when the population consistently increases or decreases, this must be taken into account. If the population increases, then R > 1 and Rx-y < 1 (because x < y). Hence, the terms in the equation are reduced by Rx-y the larger the value of y (the further into the future we go), signifying that future (i.e. 'residual') reproduction adds relatively little to RVx, because the proportionate contribution to a growing population made by a given reproductive output in the future is relatively small - whereas the offspring from present or early reproduction themselves have an early opportunity to contribute to the growing population. Conversely, if the population decreases, then R < 1 and Rx-y > 1, and the terms in the equation are successively increased, reflecting the greater proportionate contribution of future reproduction.

In any life history, the reproductive values at different ages are intimately connected, in the sense that when natural selection acts to maximize reproductive value at one age, it constrains the values of the life table parameters - and thus reproductive value itself - for subsequent ages. Hence, strictly speaking, natural selection acts ultimately to maximize reproductive value at birth, RV0 (Kozlowski, 1993). (Note that there is no contradiction between this and the fact that reproductive value is typically low at birth (Figure 4.18). Natural selection can discriminate only between those options available at that stage.)

x survival and expected future fecundity; (iii) this is done in a way that takes account of the contribution of an individual to future generations, relative to the contributions of others; and (iv) the life history favored by natural selection from amongst those available in the population will be the one for which the sum of contemporary output and RRV is highest.

The way in which reproductive value changes with age in two contrasting populations is illustrated in Figure 4.18. It is low for young individuals when each of them has only a low probability of surviving to reproductive maturity; but for those that do survive, it then increases steadily as the age of first reproduction is approached, as it becomes more and more certain that surviving individuals will reach reproductive maturity. Reproductive value is then low again for old individuals, since their reproductive output is likely to have declined, and their expectation of future reproduction is even lower. The detailed rise and fall, of course, varies with the detailed age- or stage-specific birth or mortality schedules of the species concerned.

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  • nancy
    How to calculate reproductive value v(x)?
    12 months ago
  • Isabelle
    What is the reproductive values?
    2 months ago

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