Gene Flow Up to now, we have dealt with local populations in which all individuals can be viewed as sharing a common system of mating. But in many species, the species is broken up into many local populations with restricted amounts of interbreeding. Therefore, the system of mating within differs from the system of mating between. The system of mating between local populations determines the amount of GENE FLOW. We will start with a simple model in which two, infinitely large local populations experience gene flow by exchanging a portion m of their populations each generation. Consider 1 locus with 2 alleles as follows: Population 1 Population 2 q 1 p 2 q 2 1-m m m 1-m ' q 1 ' p 2 ' q 2 ' With neutrality, one has that ' = (1-m) + mp 2 p 2 '= (1-m)p 2 + m '- = p1 = -m( -p 2 ) p 2 = -m(p 2 - ) These equations show that gene flow acts as an evolutionary force (ie. alters allele frequencies) if 1) m>0 (the local populations are not completely reproductively isolated) and 2) p 2 (the local populations are genetically distinct to some degree - - this will always be true if the local populations are finite in size and had much previous isolation -- this insures divergence by genetic drift). In the special case where =0 and p 2 >0, then gene flow introduces new genetic variability into the population. In this sense, gene flow acts like mutation. However, unlike mutation, gene flow can alter frequencies at many loci simultaneously and can cause radical and extremely rapid shifts in allele frequency.
Conditions causing m>0. Although this appears simple, m in reality represents a complex interaction between the pattern of dispersal and the mating system. For example, inbreeding (in the pedigree sense) can greatly reduce the opportunity for gene flow, even if the individuals are in physical proximity. E.g., the Tauregs (an Arabian tribe) mate almost exclusively with cousins. As a result, this tribe shows almost no gene flow with other tribes with which they are physically intermingled. Assortative mating can also greatly reduce the amount of gene flow. E.g., Western Grebes had apparently split and differentiated into two color morphs (light and dark) in the past. These two morphs now occur together in certain parts of the West. In one population, expected 33% of the mating pairs to be mixed under random mating; but due to strong positive assortative mating, only had 1.2% of pairs mixed. This greatly reduces gene flow and allows the maintenance of all the genetic differences between the color morphs, and not just the loci that determine the color. The reason is simple, although there may be linkage equilibrium within each color phase, with respect to the global population, all loci that are differentiated between the phases will show disequilibrium with the color loci. Another example of this is the European corn borer, which has two pheromone races that are now broadly sympatric. There is strong assortative mating for pheromone phenotype, and hence despite sympatry, the races have maintained much differentiation at isozyme loci that have no impact on the pheromone phenotype directly. In contrast, disassortative mating enhances m for all loci. E.g., D. melanogaster has strong disassortative mating pheromone system, and shows much less differentiation than corn borers and is effectively a single, cosmopolitan species showing little geographical differentiation (except for a handful of selected loci and inversions) on even a continental basis. It is also important to note that the assortative or disassortative mating that determines m for all loci can be based on a non-genetic phenotype. This was already noted for the Amish who have assortative mating based on religion and who, as a consequence, maintain extreme genetic distinctiveness from surrounding populations. Likewise, social castes in Chile are strong determinants of assortative mating, and for historical reasons are correlated with the amount of Indian blood. As a consequence, the Indian and Spanish gene pools are still quite distinct despite 400 years of socially limited gene flow. Another example is provided by whites & blacks in the US vs. N.E. Brazil. In North Amer., European settlers imported black slaves mainly from 1700-1808, with 98% of them coming from West and West- Central Africa. There is a strong tendency for assortative mating on racial category, but when hybrids are formed, they are socially classified as blacks. (Genetically, and phenotypically, the hybrids are intermediate and are no more "black" than they are "white".) This social definition of hybrids as "black" when coupled with assortative mating by racial category and the numerical predominance of "whites" results in a very asymetrical gene flow pattern. Effectively, almost all gene flow is from whites into blacks, with almost none going in the other direction. Let M = the effective amount of gene flow over the entire relevant period of North American history (in
contrast to m, which was a per generation gene flow parameter). Then we can model the North Amer. situation as follows: European West African p a 1 M 1-M p b =M +(1-M)p a Given the allele frequencies, you can estimate M by M = (p b -p a )/( -p a ) e.g., for the Rh + allele, p b =.4381, p a =.5512, and =.0279, so M=.216. In the U.S., estimates of M range from 3% (S.C.) to 27% (Detroit). In the northeast of Brazil, the social definition of hybrids is "white". Hence, NE Brazil had the opposite pattern of gene flow: European West African p a 1-M M 1 =Mp a +(1-M) p a Because the blacks were a minority in Brazil as well, this pattern of gene flow means that most N.E. Brazilians are of mixed European/African ancestry. Eg., in
Northeastern Brazil, the white gene pool is 59% European, 30% African, and 11% Indian. Similarly, can characterize people on basis of skin color from "Most Caucasoid" to "Most Negroid". In US., "most caucasoid" group is about 100% European in origin, and the average "black" about 20% European. In N.E. Brazil, the most Caucasoid group is 71% European, and most Negroid 28%. Thus, the social definitions used in system of mating in the two countries have had a major genetic impact on the composition of their present day populations dispite similar initial conditions. The Genetic Impact of Gene Flow We have already seen that allele frequencies are altered when gene flow occurs between genetically distinct populations. But the alterations are in a specific direction. Let d = p 2. Recall that ' = (1-m) + mp 2 = - m( -p 2 ) = - md p 2 ' = p 2 + md Hence ' - p 2 ' = d' = - md - p 2 -md = d(1-2m) < d for all m>0. After t generations: d t = d(1-2m) t 0 as t. Therefore, GENE FLOW DECREASES GENETIC VARIABILITY BETWEEN POPULATIONS. However, recall that, like mutation, GENE FLOW CAN INTRODUCE NEW ALLELES INTO A POPULATION, AND THEREFORE GENE FLOW INCREASES GENETIC VARIABILITY WITHIN A POPULATION. VERY IMPORTANT -- THE EFFECTS OF GENE FLOW ON WITHIN AND BETWEEN POPULATION GENETIC VARIABILITY ARE THE OPPOSITE OF THOSE OF GENETIC DRIFT. THEREFORE, THE BALANCE BETWEEN DRIFT AND GENE FLOW IS THE PRIMARY DETERMINANT OF THE GENETIC POPULATION STRUCTURE OF A SPECIES. Genetic population structure refers to 1) how genetic variability is distributed within a species (within and between local populations), and 2) how genetic variability in gene pools is related to individual level genotypic variability (this is also highly dependent upon the system of mating). Genetic and genotypic variability provide the raw material for all evolutionary change, including that caused by natural selection. As will be seen later, natural selection operates within the constraints imposed by the genetic structure.
The Balance of Gene Flow and Drift Recall that to measure the impact of genetic drift upon identity by descent, we started with the equation: = 1/(2N ef To examine the balance between drift and mutation, we modified the above equation as follows: = {1/(2N ef }(1-µ) 2 A similar modification can be used to address the following question: suppose two populations of inbreeding effective size N ef are experiencing gene flow at a rate of m per generation. Then, what is the probabilty that two randomly drawn genes from the same subpopulation are identical by descent AND from the same population? That is, if one of the genes came from the other gene pool, we no longer regard it as identical. The equation for this probability is then: = {1/(2N ef }(1-m) 2 which at equilibrium yields F eq 1/(4N ef m + 1) if m is small. These results emphasize the similar impact of gene flow and mutation, as discussed above. This can also be interpreted in the coalescent sense as the probability that two genes randomly drawn from the same subpopulation coalescece back to a common ancestor before either lineage experienced a gene flow even given than either coalescence or gene flow has occurred. This equilibrium equation reflects the balance of gene flow (proportional to m) vs. drift (proportional to 1/N ef ) as measured by their ratio [m/(1/n ef ) = N ef m] upon identity by descent within a subpopulation when alleles drawn from outside are regarded as nonidentical. Wright therefore defined this F as F st where the st designates this as identity by descent in the subpopulation with regard to the t otal population. (Note, just as drift influences both ibd and variances of allele frequencies, resulting in more than one effective size, there is also an alternative definition of F st in terms of variances of allele frequencies, as will be given in the next handout.) As expected, as m goes up, F st goes down, as 1/N ef goes up (drift goes up), F st goes up. What is surprising is how little gene flow is needed to cause two populations to behave effectively as a single evolutionary lineage. E.g., let N ef m =1, that is, one effective migrant per generation. Then, F st = 1/5 =.20. That is, 80% of the gene pairs drawn from the same subpopulation will show gene flow before coalescence (that is, the genes travelled through different geographical areas before they coalesced). The other thing that is surprising is that the proportion of genes shared
by two populations as measured by 1-F st depends only upon the effective number of migrants (N ef m) and not the rate of gene flow (m). For example, two subpopulations of a billion each whould share 80% of their genes by exchanging only 1 individual per generation, as would two subpopulations of size 100. The reason why the same number of migrants is needed for a particular level of F st and not the same rate of gene flow is that F st represents a balance between the rate at which gene flow causes subpopulations to diverge vs. the rate at which gene flow makes them more similar. In large populations, divergence is slow, so small amounts of gene flow are effective in counterbalancing divergence; as populations because smaller, larger and larger rates of gene flow are needed to counterbalance the increasing rate of divergence. Similarly, it is the product N ef m (which reflects the balance of drift vs. gene flow) and not m that determines the relative coalescence times of genes within and among local populations. If there is restricted gene flow among demes, it makes sense that the average time to coalescence (a common DNA molecule) for two genes sampled within a deme will be less than that for two genes sampled at random for the entire species. In particular, Slatkin (Genet. Res. 58: 167-175, 1991) has shown that these relative times are determined by N ef m. The exact relationship depends upon the pattern of gene flow, but consider the simple island model case of a species subdivided into a large number of local demes each of size N ef and each receiving m of its genes per generation from the species at large. Then, N ef m = where t 0 t 0 4 ( t t 0 ) = the average time to coalescence of two genes sampled from the same deme and t = the average time to coalescence of two genes sampled from the entire species Hence, the ratio of within deme coalescence time to entire species coalescence time is: t 0 t = 4 N ef m 1 + 4 N ef m For example, the ratio of coalescence times of Y chromosomes in East Anglia, UK to humans globally has been estimated to be between 0.56 and 0.71 (Cooper et al. Human Molecular Genetics 5, 1759-1766, 1996). This yields an N ef m for Y chromosomes of between 1.22 and 0.64 for humans (note, 2N ef m appears in the ratio equation in this case and not 4N ef m because Y-DNA is haploid). Likewise, F st now has a simple interpretation in terms of coalescence times:
F st = t t o t or t o t = 1 F st In general, there is a lack of appreciation over just how little gene flow is needed to keep populations evolving together as a single unit. For example, F st.15 when the major racial groups of humans are regarded as the subpopulations. This could be explained by only a little more than one effective migrant per generation (1.42) among the races over recent the evolutionary history of humans (a result consistent with coalescent times of Y-DNA -- recall that N ef for Y DNA refers only to males). Likewise, one can convert this F st into the relative coalescence times of genes within races versus humans as an entire species such that the average coalescence time of two genes drawn from within a race is 85% of that for 2 genes randomly drawn from humanity as a whole. Thus, it does not take a lot of exchange between the races to insure that humans evolve as a single evolutionary lineage. This fact is not widely appreciated, as evidenced by the debates over the out-of-africa replacement vs. the multiregional hypotheses concerning the origins of the modern races. The Balance of Gene Flow, Mutation, and Drift If we regard that ibd can be destroyed by both mutation and gene flow, then the appropriate balance equation is: = {1/(2N ef }[(1-µ)(1-m)] 2 If both µ and m are small, then using a Taylor s series, (1-µ)(1-m) 1-µ-m. Hence, F eq 1/[4N ef (µ+m) + 1]. The above equation emphasizes the similar role that the disparate forces of mutation and gene flow have upon genetic variation and identity by descent.