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## Section 5 Evolution in Small Populations

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**Section 5**Evolution in Small Populations The central problems are losses of genetic diversity in small populations and changes in the distribution of this diversity among populations. Losses of genetic diversity can result in reduced evolutionary flexibility and decline in fitness. Changes in distribution of diversity can destroy local adaptations and break up co-adapted gene complexes (outbreeding depression).**Both of these problems can lead to a poorer**“match” of the organism to its environment, reducing individual fitness and increasing the probability of population or species extinction. Therefore, conservation biologists should be concerned with maintaining, as much as possible, natural levels of genetic variation and natural patterns of genetic diversity so that evolutionary and ecological processes can continue!**Four factors that can reduce genetic variation**and are a function of population size: Founder Effect Population Bottleneck Genetic Drift Inbreeding The severity of these factors is dependent upon the Genetically Effective Population Size (Ne) and not the absolute number of individuals or census size (Nc).**Population size is defined in terms of the**equivalent size of a standardized population called the “Idealized Population”. We begin by assuming an infinitely large, randomly mating base population, from which we take a sample of N adults to form the “Ideal Population”. The idealized population is maintained as a randomly mating, closed population in succeeding generations in which alleles may be lost by chance and allele frequencies may vary due to sampling variation.**Conditions of the Idealized Population:**No migration Generations are distinct & do not overlap Number of breeding individuals is the same in all generations All individuals are potential breeders All individuals are hermaphroditic Union of gametes is random, including the possibility of selfing. No selection at any stage of life-cycle No mutation Number of offspring per adult averages 1 and has a variance of 1**The Effective Population Size (Ne) is the size of**an idealized population that would lose genetic diversity, or become inbred, at the same rate as the actual population. In practice, the effective size of real populations is usually much smaller than the number of breeding individuals because real populations deviate in structure from the idealized population by having unequal sex-ratios, high variances in family size, variable numbers of successive generations, and in having overlapping generations.**Sex Ratio effective population size:**Ne = (4Nm X Nf)/(Nm + Nf) Example: A census population of 500 individuals would have an Ne of 500 (with respect to sex ratio) if all individuals bred and there was a 1:1 sex ratio such as: Ne = (4 X 250 X 250)/(250 + 250) = 500**However, if in this population of 500 with 250**females and 250 males, only 114 and 63 females and males, respectively, bred, then Ne would be: Ne = (4 X 114 X 63)/(114 + 63) = 28,728/117 = 162.31 This relationship can produce some surprising results. For example, one male breeding with four females results in an Ne of 3.2, not much different than one male breeding with 9 females (Ne = 3.6)**Effective population size is also strongly affected**by the distribution of progeny among females (family size) and is estimated as: Ne = (4N)/(2 + 2) Where 2 is the variance in family size among females. Higher variances result in smaller effective population sizes.**Effects of variance in number of progeny among**females on Ne. 2 Nc Ne Ne/Nc 0 100 200 2.00 1 100 133 1.33 2 100 100 1.00 5 100 57 0.57 10 100 33 0.33**If males can mate with more than one female, the**variation in family size (Vk) for males and females must be incorporated since Vk is likely to be different for males and females. Ne = 8Nc/(Vkm + Vkf + 4) Large population fluctuations also reduce Ne because every time a population crashes to small size, it experiences a demographic bottleneck. The harmonic mean of population size in each generation provides an estimate of Ne as follows:**1/Ne = 1/t(1/N1 + 1/N2 + 1/N3 + . . . . . + 1/Nt)**Where t is the time in generations. The effects of a single population crash on the effective population size can be seen as follows.**Year Nc**1 800 2 1000 3 25 4 500 5 1000 5-year mean of Nc = (800+1000+25+500+1000)/5 = 665 Ne = 1/5(1/800+1/1000+1/25+1/500+1/1000) = 110.5**Two types of Genetically Effective Population Size**Inbreeding Effective Size (Nei)--measures the rate of loss of heterozygous individuals from a local population (a loss of variation within individuals), or simply the increase in inbreeding. Variance Effective Size (Nev)--measures the rate of loss of total genetic variation from a population whether the loss is experienced within individuals or among individuals.**Typically, Nei and Nev differ substantially only**when population size is significantly increasing or decreasing. Unfortunately, no theories or equations exist that simultaneously handle multiple deviations from the ideal situation. Thus, influences of bottlenecks, skewed sex ratios, and family size cannot at present be simultaneously estimated with these equations.**Real Meaning of Effective Population Size**There is no such thing as the “effective population size” in the sense that many people think about this. Effective size is defined with respect to a genetic parameter of interest, and as the parameter of interest changes, the effective size can change. Hence, a population can be characterized by several different “effective sizes” simultaneously.**Thus, the phrase “the effective population size”**is meaningless unless the genetic parameter of interest is also supplied. The important point is that, due to properties associated with sex ratio, family size, and population fluctuations, Ne is nearly always significantly smaller than the census size.**Importance of Small Populations in Conservation**Biology Small or declining populations are more prone to extinction than large stable populations. Population size is the most influential of the five criteria for listing species as endangered under the IUCN. Species whose adult population sizes are less than 50, 250, or 1,000 are listed as critically endangered, endangered, and vulnerable, respectively.**There are special evolutionary problems confronted**by small populations. In small populations, the role of chance predominates and the effects of selection are typically reduced or even eliminated. Chance introduces a random, or stochastic, element into the evolution of populations. Small populations become inbred at a faster rate than do larger populations, as inbreeding is unavoidable.**When a small population reproduces, the subsequent**generation is derived from a sample of parental gametes. Each offspring receives 1 allele, selected at random, from each parent. Just by chance, some alleles, especially rare ones, may not be passed on to the offspring and may be lost.**The frequencies of alleles that are transmitted**to the next generation are likely to differ from those in the parental generation. Over multiple generations, allele frequencies change, or “drift”, from one generation to the next, a process termed “genetic drift”.**Chance Effects -- Genetic Drift**Basic concept of genetic drift -- Evolution can be thought of as a change in allele frequency and finite population size alone ensures that evolution will occur through sampling error. Broadly speaking, there are four consequences of random genetic drift. These are not really consequences, but rather different ways in which the consequences may be seen.**Random Drift -- Random changes of gene frequency**which change in an erratic manner from generation to generation, with no tendency to revert to its original value. Differentiation between subpopulations -- Random genetic drift occurring independently in different subpopulations leads to genetic differentiation between subpopulations.**Uniformity within subpopulations -- Genetic**variation within each subpopulation becomes gradually reduced, and the individuals become more alike genotypically. Increased homozygosity -- Homozygosity increases in frequency at the expense of heterozygosity. This coupled with the general tendency for deleterious alleles to be recessive, is the genetic basis for the loss of fertility and viability that almost always results from inbreeding.**Genetic Drift -- Random sampling of gametes within**small populations has three consequences of major importance in evolution and conservation: Random changes in allele frequencies from one generation to the next. Loss of genetic diversity and fixation of alleles within populations. Diversification among replicate populations from the same original source (e.g. fragmented pops.)**Fixation -- Genetic drift will ultimately cause all**except one allele to be lost and the remaining allele is said to be “fixed”. The probability of losing an allele is dependent on its frequency and the population size. In the case of two alleles, the probability of losing one allele is the probability of fixing the other allele.**The probability that a gamete does not contain**allele A1 is (1 - p). Consequently, the probability that a randomly mating population losses allele A1 (all individuals become A2A2) is: Pr(losing A1) = (1 - p)2N but, = (1 - p)2Ne The rarer the allele, the far greater the probability of being lost.**The gene frequencies in these samples will have**an average value equal to that in the base population and will be distributed about this mean with a variance of: variance = 2 = p0q0/2Ne Although genetic drift is random, we can calculate a 95% confidence interval for the magnitude of change as follows: q ± 2q**Example: You have a population of 200 lions**consisting of 100 males and 100 females, with an allele frequency of the slow allele at the ADH locus of 0.33. The breeding structure of this group is that each male controls a pride of 5 adult, breeding females. Calculate the 95% confidence interval for the change in gene frequency due to genetic drift.**Step I: Calculate effective population size.**Ne = (4NfNm)/(Nf + Nm) = (4 X 100 X 20)/(100 + 20) = 8000/120 = 66.67 Step II: Calculate Variance in q 2 = (p0q0)/2Ne = (0.67 X 0.33)/(2 X 66.67) = 0.221 / 133.34 = 0.0017**Step III: Calculate 95% CI**q ± 2q 2q = 2 X (0.0017)0.5 = 2 X 0.04 = 0.08 Thus, 0.33 ± 0.08 Therefore, in the next generation 0.25 < q < 0.41**Founder Effect -- This occurs when a few**individuals establish a new population, the genetic constitution of which depends upon the genes of the founders. Demographic Bottleneck -- Occurs when a population experiences a severe, temporary reduction in size. The magnitude of loss of genetic variation depends on the size of the bottleneck and the growth rate of the population afterwards.**The proportion of genetic diversity remaining after**one generation, t, the next generation is: 1 - (1/2Ne) This proportion can range from 0.5 (50% variation) with an Ne of 1 (the gametes of 1 individual carry on average 50% of the genetic diversity of the population) to near 1.0 (100%) with a large Ne, (e.g., 1,000)**Generally, a bottleneck rarely has severe genetic**or fitness consequences if population size quickly recovers in a generation or two. Population genetics theory tells us that perhaps more important than depletion of quantitative genetic variation by founder effects, bottlenecks, or genetic drift, is loss of rare alleles from the population.**However, little empirical evidence supports this**idea. We know that rare alleles contribute little to overall genetic diversity but they may be important to a population during infrequent or periodic events such as unusual temperatures or exposure to new pathogens, and may offer unique responses to future evolutionary change.**Impact of a bottleneck on heterozygosity:**H = -(1/2Ne)H0 Impact of a bottleneck on allelic diversity: # alleles A = n - (1 - pi)2Ne i=1 where n is the number of alleles before the bottleneck and pi is the frequency of the ith allele.**Inbreeding -- mating of individuals by common**ancestry. Probability of occurrence increases in smaller populations if mating occurs at random. In a population of bisexual organisms, every individual has 2 parents, 4 grandparents, 8 great grandparents, etc. t generations back, an individual has 2t ancestors.**Not very many generations back, the number of**individuals required to provide separate ancestors for all individuals in the population becomes larger than any real population could attain. For example, 50 generations back, would mean that an individual would have 250 = 1.2 X 1015 ancestors. Therefore, any pair of individuals must be related to each other through one or more common ancestors in the more or less remote past.**The smaller the size of the population in**previous generations, the less remote the common ancestor. Thus, pairs mating at random are more closely related to each other in a small population than a larger population. For this reason, the properties of small populations can be treated as a consequence of inbreeding.**Inbred individuals -- offspring produced by**inbreeding -- may carry two genes at a locus that are replicates of the same gene in a previous generation. There are two types of identity among allelic states -- two types of homozygotes. Identical by Descent or Autozygous -- two genes that originate from the replication of a single gene pair in a previous generation.**Independent by Descent or Allozygous --**homozygous individuals not known to be autozygous. It is the production of autozygosity that gives rise to increase of homozygotes as a consequence of inbreeding. The inbreeding coefficient (F) is the probability that two genes at a locus in an individual are identical by descent and ranges from 0 to 1. F refers to an individual and expresses the degree of relationship between the individuals parents.**If the parents of any generation have mated**randomly, then F of the progeny is the probability that 2 gametes taken at random from the parent generation carry autozygous genes at a locus. This is the average coefficient of inbreeding of all progeny. Individuals of different families will have different inbreeding coefficients because with random mating, some pairs of parents will be more closely related than others.**The degree of relationship expressed in the**inbreeding coefficient is a comparison between the population in question and some specified or implied base populations. Without this reference point, it is meaningless because all genes now present at a given locus would be found to be identical by descent if traced back far enough.**Therefore, F only becomes meaningful if we**specify some time in the past beyond which ancestries will not be considered and at which time all genes in the populations are to be considered allozygous (= independent). This point of reference is the base population and by definition, it has an inbreeding coefficient of zero (F = 0).**Inbreeding in the “Idealized Population”**We will deduce F in successive generations, beginning with the base population. Examine a hermaphroditic marine organism capable of self-fertilization, shedding eggs and sperm into the sea. There are N individuals, each shedding equal numbers of gametes at random.**Because it is the base population, all genes at a**locus have to be considered as non-identical. Therefore, considering only one locus, among the gametes shed there are 2N different sorts, bearing genes A1, A2, A3, . . . . , AN at the “A” locus. The gametes of any one sort carry identical genes, those of different sort carry genes of independent origin.**Question: What is the probability that a pair of**gametes taken at random carry identical genes? This is the inbreeding coefficient of generation 1. Answer: Any gamete has a (1/2N)th chance of uniting with another of the same sort. Therefore, 1/2N is the probability that uniting gametes carry identical genes, and is thus the coefficient of inbreeding of the progeny in generation 1.**Question: What is F in the second generation?**Answer: There are now two ways in which identical homozygotes can be produced. New replication of genes Replication of genes from previous replication. The probability of newly replication genes coming together is again (1/2N) with the remaining portion (1 - 1/2N) of zygotes carrying genes that are independent in their origin from generation 1 but may have been identical in origin in generation 0.**Thus, the total probability of identical homozygotes**in generation 2 is: F2 = [(1/2N) + (1 - 1/2N)F1] An increment attributable to new inbreeding “remainder”, attributable to the previous inbreeding and having the inbreeding coefficient of the previous generation.**We designate the “increment” or new inbreeding**as: F = 1/2N then, Ft = 1 - (1 - F)t where F0 = 0 We can also calculate the probability of pulling out two genes that are NOT identical by descent, or heterozygous as: Ht = 1 -Ft Then by subtracting Ft, we can obtain the rate of change in heterozygosity from random genetic drift as: Ht = (1 - F)t ≈ H0e-(t/2N)