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Figure 3-2. Schematic of genetic drift. Each line represents a separate "experiment" of an allele starting with a frequency of 0.10 followed over time in a population of size 100. In these computer-simulated data, frequency change is due to chance alone. Any frequency is achievable, but most new alleles quickly disappear while a few are lucky and rise to high frequency. In any population multiple alleles may be segregating, their relative frequencies drifting up or down over time, some being lost, new alleles generated from time to time by mutation. The fact that an allele has high frequency does not imply a history of adaptive natural selection having favored it. Usually, only statistical arguments can determine when that is most likely. Data simulated with Populus (Alstad 2003).

outcome can be specified. It is, however, not possible to specify what will happen in any given situation, Drift calculations are almost always approximations, but data often seem at least broadly consistent with the drift expectations—that is, as if drift were the only factor affecting allele frequencies.

Whether due just to chance or to other factors, allele frequencies can change substantially over time. If chance alone is operating, descendant copies of any selected allele will eventually either drift to a frequency of zero (be lost) or to 1.0 (at which point it is fixed, that is, replaces all other alleles at the locus in the population). The reason is simple: there is always some probability of fixation or loss, and an allele can never return from the dead or change in frequency once fixed.

The rate of drift, or probability that fixation or loss will happen in any given time period, depend on population size and structure (mating patterns, subdivisions, and so on). This is because genetic drift is a kind of sampling from one generation to the next, and the variance of a sampling process depends on the sample size. In a large population the sample is large, and the sampling variance small, so that allele frequency changes little over a generation. However, actual species may be divided into small local populations in which drift can be important and rapid. Thus, population structure as well as gene function are important determinants of evolutionary change. This may seem to be a trivial consideration because species typically seem to have very large numbers of individuals. But they may not always have that, and in any case the Earth is old enough relative to population size that there has been time for drift to have been a major, if not the major, factor in genetic change during the history of life.

There is a continual flow of substitutions (one allele replacing another in the population) as new variation arises in each generation, and some fixation or loss of variants takes place. If the population size doesn't change, there is no in or out migration, and mutation rates stay the same, a steady state will arise between fixation, loss, and mutation. An ideal steady-state population will come to have a standing level of variation that depends on the relative strengths of these factors. However, and again and most importantly, the specific variants that are present, and their frequencies, will continually change—and will vary among local populations. Different genes and different populations accumulate differences over time in a statistically regular way.

Because this is a random process, it is impossible to say which of the alleles present today will be around at some point in the distant future. However, under idealized conditions, we can estimate various aspects of the process such as how long it would take for a given number of genetic differences to accumulate in copies descended from a single individual. One can thus look backward in time to estimate how long it has been since copies of a gene we see today shared a common ancestor. With some important technical caveats, genetic variation can serve as a molecular clock of evolution (e.g., Li 1997; Nei 1987). These are purely probabilistic phemenona, and population genetic models are at best crudely approximate; therefore, time estimates have a large statistical error. This can be reduced by looking at enough data. For example, the clock can be calibrated by external information such as experimental estimates of mutation rates and the age of relevant fossils representing the common ancestor of species being considered.

If the calibrating parameter values like population size change, then the timing and/or form of the numerical results will change, but the basic idea of a dynamic flux of variation holds. Effects can be estimated by making some simplifying assumptions such as that the population is in demographic equilibrium. Looking forward, a new mutation has very little chance of surviving very long and only about a 1/N chance that its descendant copies will become fixed in the population. But looking backward, from any gene, all copies extant today must be descendants of a single ancestral copy at some point in the past. This common ancestral copy is known as the coalescent. The existence of a coalescent is implied by the assumption that all life derives from a common ancestor and that mutation is a divergent, random process that generates new branches on the tree of descent from that common origin. Even if there is no single tree of life, as discussed earlier in regard to horizontal transfer of genetic material among species, copies of the different genes present today can in principle individually be traced back to a common ancestor, and molecular clocks are used to estimate when that was. This is true even if the individual genes in an individual each go back to a different ancestral copy, in a different individual, in a different place, and at a different time.

Common ancestry is perhaps the most important organizing factor in biology and was Darwin and Wallace's major contribution. Expressed in modern genetic terms, Darwin and Wallace's theory was based on branching divergence in genes produced by mutation aided by natural selection screening on allelic variation. Genetic drift will also bring about divergence, if not so systematically as Darwin's idea of continual natural selection. Even just by genetic drift, lineages (especially if sequestered by geographic isolation) will accumulate enough genetic differences over time that their members can no longer (or do no longer) mate with members of other lineages. This mating criterion is generally used to define "species." Darwin and Wallace provided a process-based explanation for the patterns of similarity among species that were already known. Population genetics tries to emulate that process, at least in regard to the genes that are involved.

Systematic Aspects of Evolution and Biodiversity

To say that mutation, mendelian transmission, and genetic drift all involve fundamentally random elements does not mean that they appear random because of inadequate data or insufficient knowledge on science's part about the underlying truth. Chance is an inherent aspect of life. Despite this, the prevailing view in biology is basically deterministic and is concerned with the molding of biological traits by natural selection. We discussed this phenomenon conceptually in Chapter 2, but here we can see how population genetic theory deals with it.

Differential Success: What Is "Adaptation"?

Everyone has an informal idea of natural selection. Usually it centers around the idea that the fittest organisms are those that are the most successful, that is, that reproduce the most. Over time, the population will comprise an ever higher frequency of these fittest organisms as they disproportionately leave descendants. From a genetic point of view, the reason they reproduce the most is not relevant so long as the outcome is systematic over time and, because genes carry information about organisms, that information persists and proliferates. We say that as a result the successful organisms have adapted to whatever was imposing the selective screen. Of course, the environment can change and new variation is always being introduced, so that the process may never reach an end. That is one aspect of the stepwise adaptation model described in Chapter 2.

Population genetics formalizes these notions by assigning relative selective or "fitness" coefficients to each genotype being considered. For example, if Aa and aa genotypes are lethal because of the effects of the a allele, these genotypes can be assigned a fitness coefficient (often denoted by w) of 0, and 1.0 is assigned to the AA genotype because in relative terms it is the most fit genotype. The corresponding selective coefficients, denoted s, are the complements of the fitnesses, ranging from 1.0 for traits with no chance to reproduce and 0.0 for genotypes experiencing no deficit in fitness (in some treatments, s is used for the relative beneficial or harmful effect on fitness of a specific allele rather than genotype, but this is a technical detail about the way population genetic models are used).

If in such a situation the a allele has frequency pa at some time, we can compute how fast that frequency will change in the face of selection. As shown by a simple example in Figure 3-3, a favored allele increases steadily in frequency and will eventually become fixed in the population (that is, will be at a frequency of 1.0). There are many subtleties and various ways that selection may act, but this is the essence of the genetic theory of darwinian adaptive evolution.

Because selective coefficients are usually treated in relative terms, the fitness assigned to a genotype is measured not in terms of the inherent value of the organism but by comparison to the most fit genotype at a given time and in the population of inference. In the simple illustration of Figure 3-3, only one allele is ultimately

Figure 3-3. Effect of natural selection on allele frequencies. The increase over time of the frequency of an allele, A, in a population in which the aa genotype had a 10 percent disadvantage. These data are simulated by the method used in Figure 3-2, but here deterministic selection is simulated, with no factor of genetic drift. The allele's rise to high frequency in this case is due entirely to selection.

Generations (t)

Figure 3-3. Effect of natural selection on allele frequencies. The increase over time of the frequency of an allele, A, in a population in which the aa genotype had a 10 percent disadvantage. These data are simulated by the method used in Figure 3-2, but here deterministic selection is simulated, with no factor of genetic drift. The allele's rise to high frequency in this case is due entirely to selection.

successful, but the theory doesn't imply "survival of the fittest" in the literal sense that in real populations only one genotype is successful while all others fail. There are typically many genotypes with comparable fitness, and even were there a single most-fit genotype, it can become disfavored the moment a new allele arrives by mutation or gene flow (incoming migrants). Something different may occur in other populations of the same species.

This is a formally competitive model: if an allele increases in frequency we can define it as having outcompeted other alleles in its given time and place. However, this says nothing about how that is brought about in real organisms, or what "competition" means in any particular case. And of course, having done better in this sense does not mean having been good or perfect.

Selection can act in many ways, including balancing selection (sometimes called heterosis, for heterozygote advantage), that maintain rather than exhaust variation by favoring or disfavoring multiple alleles in different genotypes. In the classic example, sickle cell anemia, the AA and SS genotypes are both harmful (one causes anemia, the other susceptibility to malaria), whereas the heterozygote AS genotype is better in both regards. A stable balanced polymorphism results over time, with unchanging allele frequencies that depend on the relative fitness values of these three genotypes. Other evolutionary strategies than allelic competition can generate heterogeneity in systems we will see later on, such as in immune resistance and olfaction, and we will see why that is important.

It is not unusual for individuals with extreme values for a trait to do less well in life than those near the average, presumably because the average is in some sense the result of an adaptive history. But this is not always the case, nor does it imply that variation in any individual gene associated with the trait is maintained in this way. Each trait and each gene are different.

Empirically, there are typically many alleles at a locus all the time, continually changing in frequency. Assigning fitness in relative terms, with 1.0 given to the best available genotype, means that the theory in this form does not specify whether the population grows or shrinks in absolute size as a result of selection. Population growth can be taken into account, and although it complicates the theory somewhat it typically does not change the way that relative fitness competition is at the core of the theoretical model.

Genetic drift is omnipresent. Nonetheless, in classroom and some classical versions of population genetics (and essentially in Darwin's notions), selection coefficients are treated basically as inherent, deterministic properties of genotypes (this is what was simulated in Figure 3-3 as well). In truth, selection or fitness are probabilistic phenomena. An individual with the fittest genotype in our scheme might be struck down by lightning before reproducing. Does that mean that that individual's fitness was 0? The answer is a rather curious kind of "no" because we conceive of fitness or selection coefficients as applying to a genotype in a probabilistic sense, on average. That is, a genotype's average fitness does not mean that every individual with that genotype will have identical reproduction. In computer simulations, even if chance is built into models that include selection, we know the truth (a value of s is assigned to a genotype by the programmer). But it is much more ambiguous in reality.

What appears to be clearly selective may not be in the causal sense. Did that moth really get eaten because it did not have good camouflage and the bird saw it sitting on the tree trunk? Or because the bird noticed a leg moving, or smelled it— or chanced upon it? How can we know? These are not simple questions to answer, even in what seem like classically easy cases (Weiss 2002).

At best, the fitness of a genotype has to be estimated by observing many individuals who bear it and seeing how well they did. But if it were necessary to observe every individual event, and then determine which instances of survival, death, reproduction, or infertility "counted" specifically as being causally due to the effects of the specific genotype, rather than to other characteristics of the individuals, or to chance, we would be delving into epistemological quicksand. Usually, only when selection is consistent and rather strong can its effects be convincingly detected. However, it can be shown that the less that selection coefficients vary among existing genotypes in a population, or the more they appear to vary from one generation to the next, the more the frequency changes of the alleles will behave as if they were selectively neutral (affected by chance alone). With massive die-offs, it might seem that selection would be quite strong, and we use the evolution of antibiotic or pesticide resistances as examples. But massive die-offs in nature need not involve such selection, because they can affect individuals regardless of their genotypes. But massive die-offs, by their consequent reductions in population size, reduce the amount of variation available for selection to work with. The reason is that in a massive die-off much variation will be lost by chance.

Quantitatively, if we treat selection as a fixed property of genotypes, and apply it probabilistically, and if the absolute value of the product of population size and selective coefficient (Ns) is small, say much less than 1.0 or 2.0, then drift will predominate over selection in determining the future course of allele frequencies (e.g., Hedrick 2000). In fact, most genotypes most of the time in nature seem to be only weakly affected by selection, as discussed in Chapter 2, which essentially means that natural selection is not as discriminating or prescriptive as would be expected in the deterministic gradual adaptation described by a strictly darwinian view of life.

In general, it is difficult to appreciate the degree to which the fitness of various genotypes is empirical and contextual rather than inherent properties of the genotypes (Lewontin 2000; Schlichting and Pigliucci 1998). When genotypes are nearly neutral, their small selective coefficients are unlikely to be stable over time or across environments. Because they are formally treated as relative values of competition among peers, the coefficients depend not only on the constraints of the environment but also on the other genotypes in the population (and the genetic variation in all other genes in each individual).

After the fact, we might be able to estimate an average or net fitness for a given genotype over some time period, which could account mathematically for the observed net allele frequency change. However, this is not necessarily a good way to explain what happened to individual organisms in their individual lives over long periods of evolutionary time, much less why it happened. Yet this is important if we are to give biological meaning to a probabilistic s. For example, selection might work only through occasional episodes of intense screening or may only trim away genotypes associated with extreme phenotypes, otherwise leaving the field to drift. Except under unusually favorable circumstances, population genetic models of a given situation are basically schematic—sometimes even when the causal process seems quite clear (Weiss 2002).

With so much uncertainty in this system, or weak and perhaps changeable effects, it could require studies that were themselves on the evolutionary or whole-species scale to generate a satisfactory understanding (e.g., see Tautz 2000). This is consistent with the general contingent, step-by-step view of the evolution of complex traits. Although rarely put this way, it means that even when a trait is adaptively evolving, most of the time in most individuals most vital events are due mostly to chance (although, like every trait, every gene can be viewed as "adaptive" by definition, because it is here to be observed). And this also means tolerance of variation by the screen of selection, and that selection is correspondingly a less precise or prescriptive molder of traits.

The average or net fitness of a genotype does not say much about daily experience, but fitness does not just suddenly occur. The determinants of fitness act over the lifetime of an individual, and depend inherently on the age-specific aspects of survival and reproduction of organisms. These can be expressed in terms of the vital rate schedules, l(a) and f(a), the rates (or more properly, probabilities) of survival and reproduction, respectively, of organisms age a. Fitness is related to the product of these two, l(a)f(a), over the lifespan, and these schedules have to be estimated specifically for each genotype. This must be done in the same population at the same time, and for a long enough time and large enough sample size to obtain useful estimates. In fact, these are highly probabilistic and not necessarily stable over time, even when the gene is having some effect. Does the genotype (or a trait with which it is associated) only affect reproduction or survival early in life? Or at certain life history stages such as larval or embryonic periods? Does it affect longevity?

Fitness also depends on successful mating in sexually reproducing species, which means that each individual's fitness depends on the genotype (and hence fitness) of its mate(s)—and this is especially complicated with overlapping generations, when mates are not chosen strictly from birth cohort peers.

The formal genetic theory of evolution by natural selection was famously articulated by one of the founders of population genetics, R. A. Fisher (Fisher 1930), and has been augmented by many others (e.g., Cavalli-Sforza and Bodmer 1971;

Figure 3-4. Schematic of human age-specific survivorship and fertility l(a)f(a) schedules, showing age-related contribution to the next generation, and that the relative future contribution is greatest at puberty.The dashed line shows the proportion of remaining lifetime contribution as a function of age. Conceptually, each genotype would have its own such schedule, and that determines fitness or selection coefficients. In practice, these are usually weak inferences at best. The important point is that this is how fitness actually works on the ground and what must be estimated to truly understand its quantitative effects. It is worth keeping this in mind as we go through the diverse traits in nature and attempt to provide evolutionary explanations.

Figure 3-4. Schematic of human age-specific survivorship and fertility l(a)f(a) schedules, showing age-related contribution to the next generation, and that the relative future contribution is greatest at puberty.The dashed line shows the proportion of remaining lifetime contribution as a function of age. Conceptually, each genotype would have its own such schedule, and that determines fitness or selection coefficients. In practice, these are usually weak inferences at best. The important point is that this is how fitness actually works on the ground and what must be estimated to truly understand its quantitative effects. It is worth keeping this in mind as we go through the diverse traits in nature and attempt to provide evolutionary explanations.

Charlesworth 1994; Crow and Kimura 1971). While we stress the problems with the concept to draw attention to the temptation to apply it uncritically or too universally, we can use it conceptually to see aspects of how selection might be expected to act. For example, using a term introduced by Fisher, an individual at a given age has a reproductive value that is determined by its genotype's vital rate schedules. This has been used to demonstrate the differential potential for selection to have an effect at various ages in the organism's lifespan (e.g., Crow 1958). This concept can help us understand how selection might work.

Figure 3-4 provides a schematic of human l(a)f(a) schedules (Figure 3-4). Fertility is zero until puberty, then peaks for a while before gradually tapering off. Meanwhile, mortality rates increase from puberty onward. Overall, as shown by the dashed line, the amount of remaining reproductive potential is greatest at the beginning of adult life and declines thereafter. Events affecting young individuals can have a disproportionately great impact on reproductive success than events affecting them at later ages. So selection impacting young individuals will affect allele frequencies more rapidly than effects with later impact. Genotypes aiding in early reproduction more rapidly produce offspring than other genotypes, and their alleles outgrow their competitors over time. But late in life, differential mortality or fertility have little if any impact on the individual's total reproductive output. Even if a genotype leads somehow to an awful disease at such an age, it is not selected against in the evolutionary sense. To that extent, the alleles are selectively neutral. Thus, for example, one might in vain search for evolutionary explanations for the frequency of alleles that led to high late-onset cancer risk in humans. But an allele with high frequency that causes a serious childhood disease should have been eliminated by selection; if it isn't, one suspects some form of balancing selection has been at work.

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