The variational theory of evolution has a peculiar selfdefeating property. If evolution occurs by the differential reproduction of different variants, we expect the variant with the highest rate of reproduction eventually to take over the population and all other genotypes to disappear. But then there is no longer any variation for further evolution. The possibility of continued evolution therefore is critically dependent on renewed variation.
For a given population, there are three sources of variation: mutation, recombination, and immigration of genes. However, recombination by itself does not produce variation unless alleles are segregating already at different loci; otherwise there is nothing to recombine. Similarly, immigration cannot provide variation if the entire species is homo-zygous for the same allele. Ultimately, the source of all variation must be mutation.
Variation from mutations
Mutations are the source of variation, but the process of mutation does not itself drive evolution. The rate of change in gene frequency from the mutation process is very low because spontaneous mutation rates are low (Table 24-9). The mutation rate is defined as the probability that a copy of an allele changes to some other allelic form in one generation. Suppose that a population were completely homozygous A and mutations to a occurred at the rate of 1/100,000 Then, in the next generation, the frequency of a alleles would be only 1.0 × 1/100,000 = 0.00001 and the frequency of A alleles would be 0.99999. After yet another generation of mutation, the frequency of a would be increased by 0.99999 × 1/100,000 = 0.00009 to a new frequency of 0.000019, whereas the original allele would be reduced in frequency to 0.999981. It is obvious that the rate of increase of the new allele is extremely slow and that it gets slower every generation because there are fewer copies of the old allele still left to mutate. A general formula for the change in allele frequency under mutation is given in Box 24-3.
Point-Mutation Rates in Different Organisms.
Effect of Mutation on Allele Frequency. Let μ be the mutation rate from allele A to some other allele a (the probability that a gene copy A will become a in the DNA replication preceding meiosis). If pt is the frequency of the A allele in generation (more...)
Mutation rates are so low that mutation alone cannot account for the rapid evolution of populations and species.
If we look at the mutation process from the standpoint of the increase of a particular new allele rather than the decrease of the old form, the process is even slower. Most mutation rates that have been determined are the sum of all mutations of A to any mutant form with a detectable effect. Any specific base substitution is likely to be at least two orders of magnitude lower in frequency than the sum of all changes. So, precise reverse mutations (“back mutations”) to the original allele A are unlikely, although many mutations may produce alleles that are phenotypically similar to the original.
It is not possible to measure locus-specific mutation rates for continuously varying characters, but the rate of accumulation of genetic variance can be determined. Beginning with a completely homozygous line of Drosophila derived from a natural population, 1/1000 to 1/500 of the genetic variance in bristle number in the original population is restored each generation by spontaneous mutation.
Variation from recombination
The creation of genetic variation by recombination can be a much faster process than its creation by mutation. When just two chromosomes with “normal” survival, taken from a natural population of Drosophila, are allowed to recombine for a single generation, they produce an array of chromosomes with 25 to 75 percent as much genetic variation in survival as was present in the entire natural population from which the parent chromosomes were sampled. This outcome is simply a consequence of the very large number of different recombinant chromosomes that can be produced even if we take into account only single crossovers. If a pair of homologous chromosomes is heterozygous at n loci, then a crossover can take place in any one of the n − 1 intervals between them, and, because each recombination produces two recombinant products, there are 2(n − 1) new unique gametic types from a single generation of crossing-over, even considering only single crossovers. If the heterozygous loci are well spread out on the chromosomes, these new gametic types will be frequent and considerable variation will be generated. Asexual organisms or organisms, such as bacteria, that very seldom undergo sexual recombination do not have this source of variation, so new mutations are the only way in which a change in gene combinations can be achieved. As a result, asexual organisms may evolve more slowly under natural selection than sexual organisms.
Variation from migration
A further source of variation is migration into a population from other populations with different gene frequencies. The resulting mixed population will have an allele frequency that is somewhere intermediate between its original value and the frequency in the donor population. Suppose a population receives a group of migrants whose number is equal to, say, 10 percent of its native population size. Then the newly formed mixed population will have an allele frequency that is a 0.90:0.10 mixture between its original allele frequency and the allele frequency of the donor population. If its original allele frequency of A were, say, 0.70, whereas the donor population had an allele frequency of only, say, 0.40, the new mixed population would have a frequency of 0.70 × 0.90 + 0.40 × 0.10 = 0.67. Box 24-4 derives the general result. The change in gene frequency is proportional to the difference in frequency between the recipient population and the average of the donor populations. Unlike the mutation rate, the migration rate (m) can be large, so the change in frequency may be substantial.
Effect of Migration on Allele Frequency. If pt is the frequency of an allele in the recipient population in generation t and P is the allelic frequency in a donor population (or the average over several donor populations) and if m is the proportion of (more...)
We must understand migration as meaning any form of the introduction of genes from one population into another. So, for example, genes from Europeans have “migrated” into the population of African origin in North America steadily since the Africans were introduced as slaves. We can determine the amount of this migration by looking at the frequency of an allele that is found only in Europeans and not in Africans and comparing its frequency among blacks in North America.
We can use the formula for the change in gene frequency from migration if we modify it slightly to account for the fact that several generations of admixture have taken place. If the rate of admixture has not been too great, then (to a close order of approximation) the sum of the single-generation migration rates over several generations (let’s call this M) will be related to the total change in the recipient population after these several generations by the same expression as the one used for changes due to migration. If, as before, P is the allelic frequency in the donor population and p0 is the original frequency among the recipients, then
For example, the Duffy blood group alleleFya is absent in Africa but has a frequency of 0.42 in whites from the state of Georgia. Among blacks from Georgia, the Fya frequency is 0.046. Therefore, the total migration of genes from whites into the black population since the introduction of slaves in the eighteenth century is
When the same analysis is carried out on American blacks from Oakland (California) and Detroit, M is 0.22 and 0.26, respectively, showing either greater admixture rates in these cities than in Georgia or differential movement into these cities by American blacks who have more European ancestry. In any case, the genetic variation at the Fy locus has been increased by this admixture.
Inbreeding and assortative mating
Random mating with respect to a locus is common, but it is not universal. Two kinds of deviation from random mating must be distinguished. First, individuals may mate with each other nonrandomly because of their degree of common ancestry; that is, their degree of genetic relationship. If mating between relatives occurs more commonly than would occur by pure chance, then the population is inbreeding. If mating between relatives is less common than would occur by chance, then the population is said to be undergoing enforced outbreeding, or negative inbreeding.
Second, individuals may tend to choose each other as mates, not because of their degree of genetic relationship but because of their degree of resemblance to each other at some locus. Bias toward mating of like with like is called positive assortative mating. Mating with unlike partners is called negative assortative mating. Assortative mating is never complete.
Inbreeding and assortative mating are not the same. Close relatives resemble each other more than unrelated individuals on the average but not necessarily for any particular trait in particular individuals. So inbreeding can result in the mating of quite dissimilar individuals. On the other hand, individuals who resemble each other for some trait may do so because they are relatives, but unrelated individuals also may have specific resemblances. Brothers and sisters do not all have the same eye color, and blue-eyed people are not all related to one another.
Assortative mating for some traits is common. In humans, there is a positive assortative mating bias for skin color and height, for example. An important difference between assortative mating and inbreeding is that the former is specific to a trait, whereas the latter applies to the entire genome. Individuals may mate assortatively with respect to height but at random with respect to blood group. Cousins, on the other hand, resemble each other genetically on the average to the same degree at all loci.
For both positive assortative mating and inbreeding, the consequence to population structure is the same: there is an increase in homozygosity above the level predicted by the Hardy-Weinberg equilibrium. If two individuals are related, they have at least one common ancestor. Thus, there is some chance that an allele carried by one of them and an allele carried by the other are both descended from the identical DNA molecule. The result is that there is an extra chance of homozygosity by descent, to be added to the chance of homozygosity (p2 + q2) that arises from the random mating of unrelated individuals. The probability of homozygosity by descent is called the inbreeding coefficient (F). Figure 24-6 and Box 24-5 illustrate the calculation of the probability of homozygosity by descent. Individuals I and II are full sibs because they share both parents. We label each allele in the parents uniquely to keep track of them. Individuals I and II mate to produce individual III. If individual I is A1/A3 and the gamete that it contributes to III contains the allele A1, then we would like to calculate the probability that the gamete produced by II is also A1. The chance is 1/2 that II will receive A1 from its father, and, if it does, the chance is 1/2 that II will pass A1 on to the gamete in question. Thus, the probability that III will receive an A1 from II is 1/2 × 1/2 = 1/4 and this is the chance that III—the product of a full-sib mating—will be homozygous by descent.
Calculation of homozygosity by descent for an offspring (III) of a brother–sister (I–II) mating. The probability that II will receive A1 from its father is 1/2; if it does, the probability that II will pass A1 on to the generation producing (more...)
Effect of the Mating of Close Relatives on Homozygosity. The probability of a homozygous a/a offspring from a brother–sister mating is: We assume that the chance that both grandparents are A/a is negligible. If p is very small, then q is nearly 1.0 (more...)
Such close inbreeding can have deleterious consequences. Let’s consider a rare deleterious allelea that, when homozygous, causes a metabolic disorder. If the frequency of the allele in the population is p, then the probability that a random couple will produce a homozygous offspring is only p2 (from the Hardy-Weinberg equilibrium). Thus, if p is, say, 1/1000, the frequency of homozygotes will be 1 in 1,000,000. Now suppose that the couple are brother and sister. If one of their common parents is a heterozygote for the disease, they may both receive it and may both pass it on to their offspring. As the calculation shows, the rarer the gene, the worse the relative risk of a defective offspring from inbreeding. For more-distant relatives, the chance of homozygosity by descent is less but still substantial. For first cousins, for example, the relative risk is 1/16p compared with random mating.
Systematic inbreeding between close relatives eventually leads to complete homozygosity of the population but at different rates, depending on the degree of relationship. Which allele is fixed within a line is a matter of chance. If, in the original population from which the inbred lines are taken, allele A has frequency p and allele a has frequency q = 1 − p, then a proportion p of the homozygous lines established by inbreeding will be homozygous A/A and a proportion q of the lines will be a/a. Inbreeding takes the genetic variation present within the original population and converts it into variation between homozygous inbred lines sampled from the population (Figure 24-7).
Repeated generations of self-fertilization (or inbreeding) will eventually split a heterozygous population into a series of completely homozygous lines. The frequency of A/A lines among the homozygous lines will be equal to the frequency of allele A in the (more...)
Suppose that a population is founded by some small number of individuals who mate at random to produce the next generation. Assume that no further immigration into the population ever occurs again. (For example, the rabbits now in Australia probably have descended from a single introduction of a few animals in the nineteenth century.) In later generations, then, everyone is related to everyone else, because their family trees have common ancestors here and there in their pedigrees. Such a population is then inbred, in the sense that there is some probability of a gene’s being homozygous by descent. Because the population is, of necessity, finite in size, some of the originally introduced family lines will become extinct in every generation, just as family names disappear in a closed human population because, by chance, no male offspring are left. As original family lines disappear, the population comes to be made up of descendants of fewer and fewer of the original founder individuals, and all the members of the population become more and more likely to carry the same alleles by descent. In other words, the inbreeding coefficientF increases, and the heterozygosity decreases over time until finally F reaches 1.00 and heterozygosity reaches 0.
The rate of loss of heterozygosity per generation in such a closed, finite, randomly breeding population is inversely proportional to the total number (2N) of haploid genomes, where N is the number of diploid individuals in the population. In each generation, 1/2N of the remaining heterozygosity is lost, so
where Ht and H0 are the proportions of heterozygotes in the tth and original generations, respectively. As the number t of generations becomes very large, Ht approaches zero.
Balance between inbreeding and new variation
Any population of any species is finite in size, so all populations should eventually become homozygous and differentiated from one another as a result of inbreeding. In nature, however, new variation is always being introduced into populations by mutation and by some migration between localities. Thus, the actual variation available for natural selection is a balance between the introduction of new variation and its loss through local inbreeding. The rate of loss of heterozygosity in a closed population is 1/2N, so any effective differentiation between populations will be negated if new variation is introduced at this rate or higher.
Genetic Variation: the Raw Material of Evolution
Posted on Sunday, January 1, 2006 at 2:56 pm in Monarch Biology
For natural selection to occur there must be genetic variation in a population. To understand what this means, we need to understand the concept of phenotype. An organism’s phenotype is all of its structural and functional properties, like size, hair color and blood type. Phenotypes are the product of genotype, the genetic makeup of the organism, and its environment.
The relative importance of these two factors is the basis of the nature/nurture debate about human intelligence. Think of eye color—in humans, genes code for blue or brown eyes, creating two different phenotypes. There is little or no environmental influence; if a person grows up in Alaska or sub Saharan Africa, their eye color won’t be affected. However size is a different story. A person with very tall parents is likely to be tall, but diet can also affect height. A person’s height is therefore the result of both genes and environment, or of both nature and nurture.
If a population is genetically identical, evolution can’t occur. Even if individuals have different phenotypes due to environmental variation, these differences could not be passed onto their offspring. However, if there is a genetic variation and one genotype makes individuals more apt to pass on their genes, then this genotype will increase in frequency. The genotype can be favored in a number of ways—by increasing frequency of mating, increasing the number of surviving offspring, or by more successfully avoiding predators. It can also come from many sources, including mutations, genetic drift and influx of genes from another population. If a population becomes different enough that t can no longer mate and create viable offspring with members of another population of its species, it has become a different species.
Phenotypic Variation in Monarchs
Although at first glance all monarchs tend to look the same to humans (although you can probably tell a male from a female, a difference caused by genes in monarchs and most, but not all, other animals), they do in fact vary quite noticeably if you look closely.
One of the first things we notice is that monarchs vary in wing length and girth (some look quite fat). These differences, like human sizes, are a result of both genotype and environment. On close examination, there are also differences in wing coloration and pattern, and in stripe patterns in larvae. Recently, a Monarch Lab undergrad quantified the number of spots in different locations on monarchs’ wings, and found a surprising amount of variation. Spot number, color and size have been the subject of several excellent insect fair projects over the years. While we haven’t determined whether these differences are genetic or environmental, it’s a good bet that they are genetic; it’s hard to imagine how rearing conditions could affect the spots on a monarch’s wings. However, this could be tested.
Variation in spot size on monarch wings brings up another important evolutionary concept. If having a certain number of spots made a monarch more fit for some reason, and if spot number was caused by a monarch’s genotype, we would expect spot number to evolve. However, some traits don’t have a huge effect on an organism’s fitness, like blood type or eye color in humans. We expect that variation in these traits could last for a long time, whereas variation that makes a big difference would soon disappear as the more advantageous genotype would take over.
Investigating phenotypic variations is a great way to introduce students to evolutionary concepts. They can measure and record wing lengths or other traits such as spot characteristics, and analyze their data, looking at means, medians and mode, as well as the amount of variation. The resulting bell curve would provide discussion material for evolutionary concepts.
White Monarchs: Unusual phenotypes
Nivous monarchs are grayish white in all areas of the wings that are typically orange. They are rare in Australia, New Zealand, Indonesia, and the Americas. In Hawaii, however, the frequency of white monarchs is 10%! It is believed that the gene responsible was present in the founder population of the mid-1800’s. The genetics of this variation appear to be a simple recessive gene. Interestingly, the white form of monarchs has increased in Hawaii over the past 20 years, perhaps as a result of selective predation on orange butterflies by bulbul birds, which find the white form more difficult to see.
Monarch Larvae also have a white form that was the subject of a paper published by Monarch Lab researchers and also observed by Monarch Larvae Monitoring Project volunteer, Sherry Skipper-Spurgeon. These larvae lack the yellow pigment found in most monarch larvae, and looked like caterpillar zebras. WE did study the genetics of this variation, and found that the trait is due to a single recessive gene. If this trait caused higher fitness among its bearers, it would be expected to increase in frequency. However, the fact that this is rare suggests that it is disadvantageous.