Coarsegrained Temporal Heterogeneity

Just as a population can move through space via the dispersal of its constituent individuals, a population can also move through time via acts of reproduction to create generation after generation. The environment can change as a population moves through time such that different generations experience different environments, and because fitness is a genotype-by-environment interaction, the fitnesses associated with particular genotypes can also change across the generations.

Gene pools do not change instantaneously in response to a changed environment but rather at a rate proportional to the magnitude of the average excesses of the gametes. As a result, whenever there is a significant environmental change over time, there is usually a time lag before the gamete frequencies can fully adjust. These time lags in turn are strongly influenced by the genetic architecture. We saw in Chapter 11 that there was a rapid increase in S alleles at the j-Hb locus after the introduction of the Malaysian agricultural complex, but there was hardly any initial response at all in the C allele frequency. As discussed in Chapter 11 this difference in the relative time lags to the altered environment was due to the initial allele frequencies, population structure, and details of genetic architecture. In this particular case, the critical feature of the genetic architecture emerges from the fact the S allele behaves as a dominant allele for malarial resistance, whereas the C allele behaves as a recessive allele. These features of genetic architecture, when coupled with initial rare allele frequencies and random mating, lead to orders-of-magnitude differences in the initial adaptive response to the novel environment associated with the Malaysian agricultural complex. Recall also that genetic architecture includes the nature of the genotype-to-phenotype relationship, which itself can be directly altered by an environmental change. Thus, we already saw in Chapter 8 that the S allele is a recessive allele for viability in the nonmalarial environment but an overdominant allele in the malarial environment. Evolution in coarse-grained temporal heterogeneity can become complex and difficult to predict because the adaptive response depends upon a potentially changing genetic architecture, population structure, and historical factors (e.g., the initial composition of the gene pool).

The ever-present time lags in evolutionary response to temporal changes in the environment also mean that the current genetic state of a population is not always well adapted to the current environment. A past environment can continue to affect the genetic composition of a population for long periods of time. We also see this with the S allele. Most African Americans are no longer subject to death via malaria nor have they been for centuries, yet the S allele still persists in high frequency, although its frequency has been reduced (Table 12.1). Thus, the key to understanding the current high frequency of the S alleles in African Americans lies in an understanding of the past environments experienced by this population and not just the current environment.

Time lag effects can be particularly strong for coarse-grained cyclical temporal variation. For example, the twin-spotted ladybug beetle, Adalia bipunctata, has at least two generations per year in Germany (Timofeef-Ressovsky 1940). One generation hibernates over winter as adults and comes out in the spring. The second generation lives over the summer and into the autumn. There is also a genetically based color polymorphism in this species, with red and black forms. Populations of these beetles were monitored near Berlin, Germany, to reveal that the black forms survive better in the summer than the red forms, but the red forms survive hibernation much better than the black forms. This seasonal reversal of viabilities results in an annual cycle such that the red forms constitute

63.4% of the population in April (the beetles emerging from hibernation), whereas the black forms predominate by autumn, being some 58.7% of the population in October. Note that the red form is most common in the spring, just as the environmental conditions favoring the black forms are beginning. By autumn, the black forms predominate, yet it is the red form that is better adapted to the hibernation phase that will soon commence. Thus, the time lags inherent in any evolutionary response can yield seemingly maladaptive consequences.

Insight into the evolutionary implications of coarse-grained seasonal selection can be obtained through a simple one-locus, two-allele model (Hoekstra 1975). In most models in population genetics, the basic temporal unit is a point in the life cycle at one generation to the corresponding point in the next generation. However, for a cyclical selection model, Hoekstra chose as his basic unit one complete cycle of the environmental changes, which corresponds to more than one generation in the coarse-grained case. The special case of a cycle of two environments and two generations (such as with the ladybug beetles) is shown in Table 14.3. Notice that the frequencies of the genotypes after one complete cycle are of the same form as the standard single-generation models if we use the cycle fitnesses wAA, wAa, and waa. However, these cycle fitnesses are not the standard single-generation fitnesses but rather are nonlinear functions of the fitnesses that occur in both environments in the cycle as weighted by the zygotic genotype frequencies at the beginning of the cycle. Hence, much biological complexity is buried in these seemingly simple equations. Fortunately, we already have the tools to reveal that complexity. Note that the cycle fitnesses are all of the form Wi = p2rni2 + 2pqrni 1 + q2rni0, where we let i = 2 correspond to AA, i = 1 to Aa, and i = 0 to aa. This mathematical form is identical to that of the model of competitive selection of Cockerham et al. (1972) given in Table 13.6. Thus, although these two models

Table 14.3. Hoekstra's (1975) Model of Coarse-Grained Cyclical Selection at One Locus with Two Alleles (A and a) over Two-Environment Cycle with Each Environment Experienced by Different Generation

Genotype

Zygotic frequency at beginning of cycle Fitness in environment 1

Genotype frequency after selection

Zygotic frequency at second generation Fitness in environment 2

Genotype frequency after one cycle where

AA P2

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