The core of lifehistory theory

When Charles Darwin travelled with the H.M.S. Beagle to Tierra del Fuego and the Falkland Islands in 1834, he was surprised to find, on counting the eggs of a large white Doris (a sea slug), how extraordinarily numerous they were. The slugs produce their eggs as a long ribbon, rolled up in a cone, and adhered to the rock. The inquisitive naturalist, extrapolating from a part of the structure, estimated the total number of eggs in one spire to be at least 600000. Yet the animal itself was certainly not very common. Although he often searched under the stones, he could find only seven individuals. He then added in a footnote (Darwin 1845):

No fallacy is more common with naturalists than that the numbers of an individual species depend on its powers of propagation.

If the abundance of a species does not depend on the number of offspring, why are there such large differences between species in reproductive styles? That such differences exist is obvious. The mathematical biologist A.J. Lotka distinguished between the 'lavish type' and the 'economical type' (Lotka 1924). Many marine animals, including Darwin's slug, obviously belong to the first type, whereas humans, with their low birth rate and long lifespan, are an example of the second type. Also within relatively homogeneous groups of organisms large differences between species may exist. For example, in birds clutch size varies from one egg in petrels and condors up to 20 eggs in pheasants and partridges. Likewise, among lizards the number of eggs laid in a season varies per species from 2 to 20. An even more extreme variation may be observed among plant species. This diversity in reproductive output across species is usually positively correlated with juvenile mortality rate and negatively with longevity, so each species with stationary population size strikes a balance between mortality and natality; however, the weights on each side of the balance vary enormously between species.

An answer to the question of why the power of propagation differs so much between species comes from life-history theory. Characteristic for this area of population ecology is the recognition that the various life-history traits, also called vital rates, such as juvenile mortality, age at maturity, adult body size, clutch size, and longevity, cannot be isolated from each other. The theory considers all these traits jointly, including the interrelationships among them. An important concept is the presence of trade-offs. A trade-off is a negative correlation between two life-history traits in such a way that an increase of one trait (e.g. clutch size) imposes a cost to another (e.g. chick mortality). However, the term trade-off is also used in a broader sense to indicate any negative correlation between two traits, whether they are causally related or not. Given the trade-off structure among life-history traits, the theory attempts to explain patterns across species by assuming that the life history as a whole is subjected to natural selection and is optimized with respect to the environmental conditions to which the organism is exposed, subject to lineage-specific constraints. Life-history theory has developed into a major field of population ecology and the subject is summarized in several textbooks, such as those by Stearns (1992) and Roff (2002).

Life histories can be described using the formalism of demography, the science of age-structured populations and their dynamics. The aim of demographic analysis is to develop models in which life-history traits, such as mortality and fertility, are linked to population size and age structure. In human demography such models are used to forecast future population growth and composition, given fertility and mortality schedules. In ecology, the same models are used to estimate the optimal life history, given a trade-off structure among the vital rates and a criterion for optimality, which is usually taken as the population growth rate. In other words, it is assumed that survival and fertility of a species are optimized in such a way that, accounting for constraints from trade-offs, population growth rate is at a maximum. In addition to trade-offs, vital rates are also constrained by lineage-specific effects, which arise from the body plan and the physiological limits posed by the phylogenetic history of the group to which the species belongs, which, for example, prevents a bird from producing as many eggs as a mussel.

As an example of how arguments are developed in life-history theory, we consider a relatively simple model outlined by Roff (2002), who considers a hypothetical animal in a constant environment with a simplified life history about which the following two assumptions are made. First, mortality rate, indicated by 8, is constant. This implies that throughout life a constant fraction of a birth cohort is removed and the survival of the cohort is described by a negative exponential. Such a survival curve is often seen in species for which mortality mainly comes from external sources, such as from predators. Second, fertility is constant within one life cycle, but there are different options, depending on the age at which reproduction starts. If reproduction starts later, fertility is higher; a linear relationship is assumed between fertility and the age at maturity. Such a relationship is often seen in organisms in which reproductive capacity increases with body size. By postponing reproduction, the animal can reach a larger body size and consequently acheive greater fertility.

These assumptions are displayed graphically in Fig. 5.1. Three possible fertility scenarios are plotted: one that starts at age 5 and maintains a reproductive output of 15 per time unit (the total number of eggs laid by a female surviving to age 20 would be 225), one that starts at age 10 and produces 40 eggs per time unit (total number of eggs produced from age 10 to 20 would be 400), and one that starts at age 15 and produces 65 eggs per time unit (total output 325 eggs). If all animals survive to age 20, the best of these three scenarios would be the second; however, a still-better scenario is to start at age 11, since this would provide a total reproductive output of 405 eggs (= (20 — 11) x 45). However, reproductive output must be corrected for the fewer and fewer animals remaining to produce eggs and so the actual optimum will be lower than 11. How much? A quantitative valuation can be given by considering a common criterion for optimality, net reproductive rate, R0, which is given by

R0 = l(x)m(x)dx ■J a where m(x) is fertility (number of offspring produced per time unit by individuals aged x), l(x) is survival from birth to age x (as a fraction),

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