Optimization in Evolution Research Paper

The focus here is on optimization in biological evolution; further information on the other contexts in which optimization may be important can be found in Schoemaker (1991) and references therein.

1. The Term ‘Optimization’

When a biologist makes a claim about optimization (e.g., Tyler and Gilliam 1995), it is most often a claim about natural selection among individuals within populations; such a claim generally (but not necessarily) excludes selection at the level of the population or species. More controversially, it usually excludes ‘random’ or nondirectional forces, such as genetic drift (random sampling of gametes and individuals in populations), from having any significant affect on the trait’s evolution.

A claim about optimization also always has an explicit or implicit assumption about trait inheritance, a common one being that the trait values of parents and offspring are identical or nearly so. This, along with the reproductive advantage of an optimal trait, implies that the trait will become fixed in the population, all other things being equal.

2. The Controversy Over ‘Optimization’

What does not engender controversy among evolutionary biologists is the overall theoretical conception of the process of optimization. Most evolutionary biologists agree that one can make predictions of optima for traits and that natural selection could plausibly act to cause evolution in the direction of these optima. In addition, most of these biologists agree that at least some aspects of the process of optimization occur in nature (see Travis 1989 for more details).

What does engender controversy can be better understood by describing the two most important contexts in which optimization is invoked.

2.1 Continuously-Distributed Traits And ‘Optimization’

The first context involves traits having a more-or-less continuous distribution, usually with one central peak. Many traits have such a distribution; often it is statistically indistinguishable from a normal distribution. So, for example, Van Valen and Mellin (1967) showed in their study of human babies in New York City that birth weight has such a bell-shaped distribution. Optimizing selection is invoked in such examples to explain the peaked character of the trait distribution, the hypothesis being that a central trait value performs better than any other trait value. In their study, Van Valen and Mellin showed that the probability of perinatal death is minimal at a central weight (about 3.6 kg for males and about 3.8 kg for females). Ostensibly, this is because more deviant weights are associated with specific physiological deficits that are congenitally or environmentally based, their consequence being a higher risk of death. Subsequent work has revealed that the length of the gestation period also affects the probability of perinatal death (see Schluter and Nychka 1994.)

What then explains the presence of the continuous trait distribution? After all, if there is one best birth weight, why isn’t there at most a small range of birth weights around this best weight? More generally, why do any traits undergoing trait optimization have continuous trait distributions? It is in answering this question that controversy has arisen; there are at least three different claims as to why such distributions occur.

The first claim is that the genetic ‘details’ of trait determination impede the action of optimizing natural selection. What this means is that the nature of trait determination and the Mendelian ‘breakdown’ of the trait when reproduction occurs act together to generate a continuous trait distribution in the next generation. So, for example, imagine that natural selection is such that only individuals with the optimal trait live to the start of reproduction, the result being that there is only one type of trait remaining in the population at that time. If one assumes that the optimal trait does not breed true and is, say, the result of an individual being a heterozygote at all or most of the loci affecting the trait, then newborn offspring will manifest a continuous trait distribution. This is a necessary consequence of the normal segregation of alleles during gamete production and the subsequent union of gametes to form the offspring of the next generation.

The underlying presumption of this claim about genetic details is that they are an unchangeable impediment to the action of natural selection even when the intensity of selection is strong. This could happen even if the optimal trait is not associated with being a heterozygote at many loci. One possible (but not necessary) consequence is that a stable amount of genetic variation can be maintained in a population, as a result of the balance between optimizing natural selection, which will tend to eliminate genetic variation, and the genetic details of the trait (including mutation), which can act to preserve or increase it. Such a balance has been invoked as an explanation for the high levels of genetic variation seen for some traits in some populations (see Lande 1988 and Turelli 1988 for further discussion.)

The second claim as to why continuous trait distributions occur is that natural selection is not and never will be strong enough or constant enough to eliminate or nearly eliminate nonoptimal traits from the population. However, the presumption here is that this would occur if selection were stronger; genetic details would not get in the way.

The third claim is that it is just a matter of time until the continuous distribution disappears and an optimal or near-optimal trait predominates in the population, the notion being that the current data reveal only an intermediate state of a long process. From this viewpoint, natural selection is powerful and sustained enough to cause trait optima to evolve and genetic details will not ultimately prevent this from happening, as the process of mutation will ultimately provide the appropriate kind of genetic variation to allow an optimal trait to become fixed. So, for example, a mutation that when homozygous produces an optimal trait might arise in a population in which the trait has been manifested only by heterozygotes. The truebreeding optimal trait may increase in frequency and displace the heterozygotes (see Hammerstein 1996 and Eshel and Feldman 2001 for further discussion of the dynamics and outcome of this kind of long-term evolution.)

2.2 Fixed Traits And ‘Optimization’

The second context in which optimizing selection is invoked concerns traits that are constant in a given species. For example, functional anatomists speak of the horse’s foot as having evolved for the task of running on uneven ground at high speed (e.g., see Hildebrand 1985) and behavioral ecologists speak of the dance language of honey bees (e.g., see Wilson 1971). In such instances, the trait is regarded as having a single state, which is often taken to be the result of past optimization; in other words, the trait is the way it is because it performs better than all reasonable alternatives and this superior performance has resulted in the past elimination of alternative forms of the trait. The underlying attitude is very often that optimality ‘must be,’ given the importance of the trait to the organism. From this viewpoint, the potential for understanding how the trait is optimal is limited only by the industry and ingenuity of the investigator (cf., Cain 1989). Such an ‘adaptationist’ approach is reasonable enough in theory although it is easy to see the potential for circularity in practice because discrepancies between the predictions of a model used to describe the optimal trait and the data can always be attributed to an incomplete or flawed model.

2.3 Types Of Optimality Models

All optimality models make a prediction about the trait of an individual. Beyond this common aspect, there is as much variety in the features of optimality models as there is in the traits studied. However, one can recognize two general classes of such models. The first class concerns traits for which one can determine the performance of a trait by reference only to the functioning of the trait itself. Traits still affect one another in that an optimal trait will outperform all others and thereby cause their selective elimination from the population. But the performance of any trait is the same in isolation as it is in a population. There are many optimality models of this kind in every area of evolutionary biology. For example, when constructing an optimality model of the shape of a horse’s foot, a functional anatomist will likely regard the performance of the foot as independent of the performance of any other individual’s foot in the population. Similarly, an ecologist might assume that the evolutionary consequence of a given number of offspring produced by an individual is independent of the numbers produced by other individuals.

In contrast, the second class of optimality model involves traits whose performance is inherently related to the performance of other individuals because it is dependent on the frequency or density of various traits in the population. Such dependency arises naturally for many traits, especially for those relating to the sexual production of offspring. A classic example is the evolution of the sex ratio, the relative ratio of males and females in the population. The evolutionary fate of a female producing, say, all or nearly all daughters depends very much on whether all of the other females in the population do this as well, as opposed to producing, say, equal numbers of daughters and sons. In the former instance, the population could go extinct; in the latter instance, even a female producing only daughters may survive. If the tendency to produce given numbers of males and females is autosomally inherited and sons and daughters are equally costly in terms of energy, one can show that a female-biased sex ratio will be optimal if the population is subdivided and females tend to migrate more than males (Hamilton 1967). However, in an infinite randomly-mating population such a sex ratio is not optimal; instead, a female producing equal numbers of daughters and sons will be optimal as long as equal numbers of males and females are not produced by the population as a whole. Finally, when equal numbers are produced, there is no optimal sex ratio; all sex ratios are evolutionarily equivalent. This variety of outcomes is typical for interactive traits.

Traits like the sex ratio are often analyzed with a model in which one determines the trait which when common prevents the invasion of rare mutants into the population. Such a trait is taken to be optimal in the sense that individuals possessing it outperform all other traits when the population has this configuration (this does not necessarily imply that the trait has an advantage for all other configurations.) This evolutionarily stable strategy (ESS) approach has received considerable attention since about 1980, with extensive elaboration of the theory in formal game-theoretic terms and extensive application of models to the data (see Charnov 1982, Maynard Smith 1982, and especially Hines 1987 for examples and further details.) For other traits there is no necessary choice about what type of optimality model to use and the choice depends upon the investigator’s prior assumptions about whether and how individuals interact with one another.

3. Optimization And The Debate About The Adaptationists’ Claim

To proponents of the adaptationist approach, such as Parker and Maynard Smith (1990), the danger of circularity in claims of optimality is real but of little concern if one is careful and rigorous when deriving the model and if one is scrupulous when testing it. To opponents of this approach, such as Gould and Lewontin (1979), it is inherently flawed because the hypothesis of optimality is never challenged or tested, as a failed optimality model is simply replaced with another optimality model. One alternative they suggest is to formulate predictions from nonadaptive or nonoptimal hypotheses, which can compete with the predictions of the optimality model. For example, one might claim that a trait has not evolved in response to the present environment, but instead evolved in a past environment; a plausible ancestral trait would then be used as a predictor of the trait and its predictive performance would be compared with that of an optimality model. Adherents of this ‘pluralist’ approach often claim that if the predictions of one or more of these nonoptimal competing hypotheses explain the data as well as the optimality model does, the former should be given precedence as an explanation for the trait (cf. Lewin 1980).

There are substantive differences between these viewpoints and as a result, proponents and opponents of the adaptationist approach have traded claims and counterclaims for decades; this is a central debate in evolutionary biology (see Orzack and Sober 1994, 2001). Adaptationists generally regard natural selection to be the only important influence on trait evolution, while pluralists regard natural selection to be just one of several such influences, the others being genetic drift, constraints engendered by genetic details, and phylogenetic inertia (the carryover of traits from a species’ ancestors; see Harvey and Pagel 1991 for further details). In an important sense, however, adaptationist and pluralist claims about trait evolution have a common feature—both start with a premise as to the truth or falsity of the adaptationist approach. To adaptationists, the near-certainty of optimality follows necessarily from what they view as the basic and unquestionable Darwinian dynamic of variation and selection; to pluralists, the near-certainty of nonoptimality follows necessarily from what they view as the inherent genetic and developmental complexity of the organism.

One alternative to the reliance on either of these premises is to assess the validity of the adaptationist approach via an ensemble test in which the successes and failures of specific optimality models at predicting trait values and explaining trait variation are tallied (see Orzack and Sober 1994 for further details.) One might regard the adaptationist claim to be true if, say, 90 percent of traits examined could be adequately explained by an optimality model. This ensemble test faces difficult but not insurmountable problems that relate to how traits and models are chosen to be part of the ensemble. Nonetheless, such a test has several virtues, an important one being that the truth or falsity of the adaptationist approach is not a premise; instead, either possibility is a potential conclusion of the ensemble test. To this extent, a central debate in evolutionary biology could be resolved on the basis of data, instead of being left unresolved because of the contradictory premises investigators use as a basis for their analyses.

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