Life-history invariants

7.2.5 Life-history invariants

The objective of most life-history research in fish is to test hypotheses of adaptive and non-adaptive variation to explain the extraordinary life-history variability expressed within and among species. An alternative approach has been to determine whether there is a constancy, or invariance, among life-history traits that may reflect adaptive life- history processes of a very broad and general nature. This search for constancy amidst diversity was very much evident when quantitative studies of patterns of growth, maturation and longevity in fish first appeared in the late 1950s. Alm (1959), for

Life Histories

157

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example, sought patterns among growth rate, age Another invariant that appears to have some con- and size at maturity from experiments he had con- sistency among taxa is L a /L • , which Jensen (1997) ducted on Swedish populations of brown trout. suggests is 0.66 for fish, implying that all fish Using data primarily from commercially impor- mature at a length that is approximately two- tant marine species, Beverton and Holt (1959) thirds of their maximum. investigated general associations among growth

Despite its comparatively lengthy history, the pattern, as shown by the von Bertalanffy growth application and understanding of life-history in- coefficient (K) and asymptotic length (L • ), age (a) variants is very much in its infancy. Most of the re-

and length at maturity (L a ), natural mortality (M) search to date has comprised a search for pattern and lifespan (proportional to M - 1 ). In addition to among combinations of life-history metrics. Use- Beverton’s (1992) excellent historical perspective ful as this has been, the challenge now is to formu- of the search for invariants in fish, Charnov (1993) late and test hypotheses that would identify the provides the most comprehensive treatment of processes responsible for the observed patterns. life-history invariants to date.

Mangel’s (1996) study on life-history invariants in

The practical objective underlying much of the brown trout and Arctic char is an excellent exam- early search for life-history invariants in fish was ple of an attempt to do just that. to identify generalizations which could then be used to estimate natural mortality rate in com- mercially exploited fishes (Beverton 1992). For

7.3 OFFSPRING SIZE AND

example, based on an analysis of 175 fish stocks

NUMBER STRATEGIES

(Pauly 1980; Charnov 1993), the invariant M/K for

7.3.1 Theoretical context

teleosts is approximately 1.7, although Charnov (1993) suggests a range of possible values extend- Why do some fish, ranging phylogenetically from ing from 1.6 < M/K < 2.1. If one had an estimate of the sea lamprey (Petromyzon marinus, Cepha- the von Bertalanffy growth coefficient, K, for a laspidomorpha) through the Atlantic sturgeon given stock, a comparatively easy metric to esti- (Acipenser oxyrhynchus, Acipenseriformes) and mate (see Jobling, Chapter 5, this volume), one the Atlantic cod (Gadus morhua, Gadiformes) to could then use the invariant M/K = 1.7 to estimate the sunfish (Mola mola, Tetraodontiformes), natural mortality for the same stock.

produce hundreds of thousands, often millions, of

Life-history invariants are thus ratios of para- very small eggs (<1.5 mm diameter), while other meters and/or variables that have the same units fish, including myxinids, chondrichthyans, many of measure so that the ratios are dimensionless. salmoniforms and mouth-brooding siluriforms Among the most commonly examined life-history produce comparatively few, relatively large eggs invariants in fish are those between (i) mortality (>4 mm diameter)? and growth rate, M/K, (ii) length at maturity and

The evolutionary implications of the trade-off asymptotic length, L a /L • , (iii) age at maturity and between offspring number and offspring size in lifespan, (aM) - 1 , (iv) age and length at maturity, fish were first considered by the Swedish fish biol- aL a and (v) asymptotic length and growth rate, L • K ogist Gunnar Svärdson (1949). He suggested that (Beverton and Holt 1959; Pauly 1980; Roff 1984; there must be an upper limit to fecundity and that Beverton 1992; Charnov 1993; Vøllestad and this upper limit depends on the influence of egg L’Abée-Lund 1994; Mangel 1996; Jensen 1997; size on offspring survival and parental reproduc- Froese and Binohlan 2000; Reynolds et al. 2001).

tive success. Otherwise, he argued, directional

In addition to their practical utility, invariants selection – or, as he put it, a tendency to increase have the potential to provide insight into life- egg number every generation – would favour con- history evolution. For example, the invariant M/K tinually increased numbers of eggs per female. implies that fast-growing fish experience higher Svärdson (1949) remarked that, ‘From a theoretical natural mortality rates than slow-growing fish. point of view it is rather easy to conclude that there

Life Histories

must be a selection pressure for decreasing egg vival curve (the solid curves in Fig. 7.1a). In other numbers, but it is not so extremely evident how words, the optimum corresponds to the egg size at this selection works.’

which the instantaneous rate of gain in fitness per The theoretical underpinning of most research unit increase in offspring size is at its maximum. investigating the adaptive significance of offspring As this instantaneous rate of gain increases, along size and number variability is a graphical model with the slope of the line drawn from the origin, op- proposed by Smith and Fretwell (1974), who asked timal egg size decreases (Winkler and Wallin 1987). how a parent should distribute a fixed amount of Smith and Fretwell’s (1974) model has formed the energy or resources to an indeterminate number of basis of many theoretical treatments of the evolu- young. Optimal egg size is defined graphically tion of egg size, including those examining the by the point on the fitness function at which a effects of parental care (Sargent et al. 1987), food straight line drawn from the origin (the dashed abundance (Hutchings 1991, 1997) and lifetime lines in Fig. 7.1a) is tangential to the offspring sur- reproductive effort (Winkler and Wallin 1987).

(a)

(b)

1 High food

Medium food

High food

Low food

Medium food Low food

Juvenile survival

Juvenile survival

Small

Large High Medium Low

Large

Small

High/medium/low Egg size

Egg size (c)

Parental fitness

Parental fitness

High food

High food

Medium food Low

Medium food

Low food Small

Low food

Low

High/medium/low Large High Medium Low

Large

Small

Egg size Egg size Fig. 7.1 Functions relating juvenile survival (a and b) and parental fitness (fecundity ¥ egg-size-specific survival

probabilities, the latter for c and d taken from panels a and b, respectively) to egg size in environments differing in food abundance. Solid triangles below the abscissas indicate egg-size optima. (Source: from Hutchings 1997, with kind permission of Kluwer Academic Publishers.)

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Strong empirical support for Smith and Fretwell’s (1974) model was recently obtained from a study of Atlantic salmon egg size and maternal fitness (Einum and Fleming 2000).