Evolution in Subdivided Populations

Discussion Leader: Sun Shan (sunshan@ncifcrf.gov)

Barton NH, Whitlock MC. 1997. The evolution of metapopulation. In Gilpin ME, Hanski I, eds. Metapopulation biology. Ecology, Genetics and Evolution. London: Academic Press, 183-2100. (General Reading)

Coyne, J. A. Barton, N. H. & Turelli M., Perspective: A critique of Sewall Wright’s shifting balance theory of evolution. Evolution, 51(3), 643-671

Abstract:
We evaluate Sewall Wright's three-phase ''shifting balance'' theory of evolution, examining both the theoretical issues and the relevant data from nature and the laboratory. We conclude that while phases I and II of Wright's theory (the movement of populations from one ''adaptive peak'' to another via drift and selection) can occur under some conditions, genetic drift is often unnecessary for movement between peaks. Phase III of the shifting balance, in which adaptations spread from particular populations to the entire species, faces two major theoretical obstacles (1) unlike adaptations favored by simple directional selection, adaptations whose fixation requires some genetic drift are often prevented from spreading by barriers to gene flow; and (2) it is difficult to assemble complex adaptations whose constituent parts arise via peak shifts in different demes. Our review of the data from nature shows that although there is some evidence for individual phases of the shifting balance process, there are few empirical observations explained better by Wright's three-phase mechanism than by simple mass selection. Similarly, artificial selection experiments fail to show that selection in subdivided populations produces greater response than does mass selection in large populations. The complexity of the shifting balance process and the difficulty of establishing that adaptive valleys have been crossed by genetic drift make it impossible to test Wright's claim that adaptations commonly originate by this process. In view of these problems, it seems unreasonable to consider the shifting balance process as an important explanation for the evolution of adaptations.

This is a fairly complete review that critically examines the Shifting Balance Theory. The review goes into significant detail but without using too much mathematics. On one hand they frame the Shifting Balance Theory as a straw man. They spend a significant amount of time concerned about Wright's original intent. On one hand this is valid because it exposes the situation from which the Shifting Balance Theory (SBT) arose. On the other an this may result in a theory which is easier to criticize that had they focused on the current, most developed version of the theory.

They argue that the SBT experienced favoritism because it combined many elements of genetics including epistasis, pleiotropy, and genetic drift.

They begin their critique of the theory by arguing that the adaptive landscape analogy is misleading. Instead of "adaptive peaks" one should use the term stable state. Additionally, the adaptive landscape is often assumed to be static. The metaphor does not adequately capture the fact that the landscape may change depending on density or frequency dependence. In addition with multiple genes the adaptive landscape can be littered with stable states. If landscape is changing due to environmental conditions these stable states may become linked by ridges. There are other methods by which populations might become separated on different peaks without necessarily depending on genetic drift. One of these lies in the difference between individual fitness and mean population fitness. Individual fitness may go through valley will mean fitness the not. Another way involves the evolution order of strategies. For example in competition involving two strategies and intermediate strategy might be in valley, but that may not been the case in the absence of the second strategy. However all of these mechanisms appear to depend on small populations. Therefore the authors see phase I and II of the SBT as plausible.

They raise many questions as the theoretical practicality of phase III. They acknowledge it individual selection can cause the spread of the peak by the movement of a tension zone, i.e. hybrid zone. However, this spread need not be the case. A series of successive peak shifts is theoretically possible but only under a narrow range of parameters. Furthermore, adaptive complexes would be broken up by recombination upon leaving their original peak. Group selection in a metapopulation type structure with colonization and extinction would allow spread in phase III, however the ecological parameters to allow this are rare. While the authors find phase III the theoretically possible, they find it theoretically unlikely.

Finally, they examined a number of empirical examples. All of the examples supported at least one phase of the SBT, but none of the examples simultaneously conformed to all three phases.

Giles, BE, Goudet, J. 1997. A case study of genetic structure in a plant metapopulation. In Gilpin ME, Hanski I, eds. Metapopulation biology. Ecology, Genetics and Evolution. London: Academic Press, 429-454.

Hanski, I 1998 Metapopulation dynamics Nature 396, 41 - 49

Metapopulation biology is concerned with the dynamic consequences of migration among local populations and the conditions of regional persistence of species with unstable local populations. Well established effects of habitat patch area and isolation on migration, colonization and population extinction have now become integrated with classic metapopulation dynamics. This has led to models that can be used to predict the movement patterns of individuals, the dynamics of species, and the distributional patterns in multispecies communities in real fragmented landscapes.

Kimura, M. & Weiss, G. H. 1964 The stepping stone model of population structure and the decrease of genetic correlation with distance. Genetics 49, 561-576.

Mills, L. S. & Allendorf, F. W. 1996 The one-migrant-per-generation rule in conservation and management. Conserv. Biol 10, 1509-1518.

(Becky Raboy)

Goal- minimize the loss of polymorphism and heterozygosity w/in subpops while allowing for divergence in allele frequencies among subpops

It is suggested that one migrant per local population per generation is sufficient to obscure any disruptive effect of drift.

Conservationists have begun using this rule to suggest management policies in fragmented populations.

But- not so simplistic as it seems.
Assumptions
1. island model of migration (migrant equally likely to come from any of the sub-pops. Infinite number of subpops of equal size.
2. Selective neutrality and no mutation
3. Ideal populations. Census number of individuals = Effective pop. Population is half males, half females
4. Demographic equality (same survival and reproductive probabilities)
5. Equilibrium (subpops persist long enough to reach steady-state)
Limitations
When populations become small less migration may be appropriate because of possible social disruption and b/c very small pops not loosing variation as fast as predicted by the Fst approximation.

Need more immigrants if real world immigrants come from nearby populations (rather than any subpop.) Because closer subpops have similar gene frequencies. But continent-island migration is compatible with OMPG (donor pop large- drift minimal within pop)

Need to consider trade-off between within and among population variation. May dictate amount of migration desired to maintain genetic variation.

May not be feasible to move just one individual!

Greater migration may be initially desirable with larger subpops in order to reach equilibrium between gene flow and drift more quickly. (equilibrium reached more quickly in small pops)

Authors' recommendations
One migrant per generation not enough in many circumstances.
But how much is too much to maintain balance?
Authors say "up to 10 migrants per generation is not likely to tip the balance too far by causing uniformity of allele frequencies across subpopulations"

Nagylaki T 1998 The expected number of heterozygous sites in a subdivided population. Genetics 1998 Jul;149(3):1599-604

Abstract: A simple, exact formula is derived for the expected number of heterozygous sites per individual at equilibrium in a subdivided population. The model of infinitely many neutral sites is posited; the linkage map is arbitrary. The monoecious, diploid population is subdivided into a finite number of panmictic colonies that exchange gametes. The backward migration matrix is arbitrary, but time independent and ergodic (i.e., irreducible and aperiodic). With suitable weighting, the expected number of heterozygous sites is 4Neu, where Ne denotes the migration effective population number and u designates the total mutation rate per gene (or DNA sequence). For diploid migration, this formula is a good approximation if Ne >> 1.

Laura Monti Review: In this paper, the author derives a general formula for the mean intrademic coalescence time and the expected number of heterozygous nucleotide sites in a subdivided population. The author first presents Kimura's formula for a panmictic population at equilibrium and with infinitely many sites, 0 = 4NE u, where 0 is the expected number of heterozygous nucleotide sites per individual, NE is the effective number of monoecious, diploid individuals, and u is the total mutation rate per gene. The author cites Slatkin's generalization of that result for subdivided populations, given certain assumptions. Assumptions used in this paper are then specified. Generations are taken to be discrete and non-overlapping, the population is monoecious and diploid, subdivision is into a finite number of panmictic colonies with a fixed pattern of gene exchange, the mutation rate is very low, all adults within a deme produce the same large number of independently dispersing gametes ( self-fertilization is allowed), and mutation and population regulation sequentially follow zygote formation. The author then describes a matrix M of the probabilities mij's that a gamete in deme i was produced in deme j. This matrix is constructed to allow for the possibility that descendants of individuals in one deme can reach any other deme, and to preclude pathological cyclic behavior. The author defines the migration effective population number as a function of the total population number, the proportion of adults in each deme, and the eigenvector of the M matrix for each deme. Using the definition of NE as the probability that two randomly chosen gametes in distinct individuals are descended from the same population, the author then shows mathematically that the mean coalescence time of two distinct, homologous nucleotides chosen at random from adults just before gametogenesis is T0 = 2NE. Using that derivation, then, the author shows that 0 = 2uT0= 4NE u. An alternate proof is then presented. The author goes on to modify his results for the case in which selfing is excluded and zygotes, rather than gametes, disperse. He demonstrates that 2T0- S0= 2NE, where Si is the mean coalescence time within an adult in deme i, while Tij is the coalescence time between two adults, one from deme i and one from deme j. When NE>>1 and migration is conservative, the resultant equations for expected heterozygosity within individuals and between individuals in the same deme are very similar to 0 = 4NE u. In the face of both weak (m<<1) and strong (m not <<1) migration, the same result holds true. Thus, this author introduces the idea of migration effective population number into calculations of expected heterozygosity and coalescence time in a subdivided population and derives general equations for those quantities.

Nagylaki T 1985 Homozygosity, effective number of alleles, and interdeme differentiation in subdivided populations. Proc Natl Acad Sci U S A 1985 Dec;82(24):8611-3

The amount and pattern of genetic variability in a geographically structured population at equilibrium under the joint action of migration, mutation, and random genetic drift is studied. The monoecious, diploid population is subdivided into panmictic colonies that exchange migrants. Self-fertilization does not occur; generations are discrete and nonoverlapping; the analysis is restricted to a single locus in the absence of selection; every allele mutates to new alleles at the same rate. It is shown that if the number of demes is finite and migration does not alter the deme sizes, then population subdivision produces interdeme differentiation and the mean homozygosity and the effective number of alleles exceed their panmictic values. A simple relation between the mean probability of identity and the mean homozygosity is established. The results apply to a dioecious population if the migration pattern and mutation rate are sex independent.

Nagylaki T 1977 Decay of genetic variability in geographically structured populations. Proc Natl Acad Sci U S A 74(6):2523-5

The ultimate rate and pattern of approach to equilibrium of a diploid, monoecious population subdivided into a finite number of equal, large, panmictic colonies are calculated. The analysis is restricted to a single locus in the absence of selection, and every mutant is assumed to be new to the population. It is supposed that either the time-independent backward migration pattern is symmetric in the sense that the probability that an individual at position x migrated from y equals the probability that one at y migrated from x, or it depends only on displacements and not on initial and final positions. Generations are discrete and nonoverlapping. Asymptotically, the rate of convergence is approximately (I-u)2t[I-(2NT)-1]t, where u, NT, and t denote the mutation rate, total population size, and time in generations, respectively; the transient part of the probability that two homologous genes are the same allele is approximately independent of their spatial separation. Thus, in this respect the population behaves as if it were panmictic.

Nei, M. 1972 Genetic distance between populations. Am. Nat. 106, 283-292.

Amy Pedersen review: Nei defined the normalized identity of genes, I, as the proportion ofgenes that are common between two populations being studied. The genetic difference between populations, D, was established from Nei's definition of I. Genetic distance is a measure of the number of allele differences per locus. Both normalized identity of genes and genetic distance between populations depend solely on gene frequencies, as opposed to genotype frequencies, and both I and D are applicable to any kind of organism, regardless of ploidy or or mating scheme. The definition of genetic distance between populations is linearly related to divergence time between populations under sexual isolation if the rate of gene substitutions per year is constant. D is also sometimes linearly related to geographical distance or area.

Nei M, Takahata N 1993 Effective population size, genetic diversity, and coalescence time in subdivided populations. J Mol Evol 37:240-4

A formula for the effective population size for the finite island model of subdivided populations is derived. The formula indicates that the effective size can be substantially greater than the actual number of individuals in the entire population when the migration rate among subpopulations is small. It is shown that the mean nucleotide diversity, coalescence time, and heterozygosity for genes sampled from the entire population can be predicted fairly well from the theory for randomly mating populations if the effective population size for the finite island model is used.

Ohta T 1992 Theoretical study of near neutrality. II. Effect of subdivided population structure with local extinction and recolonization. Genetics Apr;130(4):917-23

Abstract: There are several unsolved problems concerning the model of nearly neutral mutations. One is the interaction of subdivided population structure and weak selection that spatially fluctuates. The model of nearly neutral mutations whose selection coefficient spatially fluctuates has been studied by adopting the island model with periodic extinction-recolonization. Both the number of colonies and the migration rate play significant roles in determining mutants' behavior, and selection is ineffective when the extinction-recolonization is frequent with low migration rate. In summary, the number of mutant substitutions decreases and the polymorphism increases by increasing the total population size, and/or decreasing the extinction-recolonization rate. However, by increasing the total size of the population, the mutant substitution rate does not become as low when compared with that in panmictic populations, because of the extinction-recolonization, especially when the migration rate is limited. It is also found that the model satisfactorily explains the contrasting patterns of molecular polymorphisms observed in sibling species of Drosophila, including heterozygosity, proportion of polymorphism and fixation index.
Tone Rawlings review: The theory of neutrality states that very few alleles contribute to fitness, the rest are selectively neutral. Thus the fate of mutations that are introduced into a population is determined largely by random genetic drift. However, there is some controversy about the behavior of nearly neutral mutations. In this vein, Ohta (1991) explored whether local extinction and recolonization effects weak selection in a subdivided population. He employed the island model with an intermediate migration rate to simulate a subdivided population. Further, he fashioned an extinction-recolonization model that could be extended to a more realistic population structure ñ he called it the one colony-extinction model. This model was created against the sudden expansion model, which corresponds to a speciation event. Ohta argued that extinction-colonization occurs more frequently and takes place more gradually than the sudden expansion model allows. His model was based on the premise that one or a few colonies become extinct and is replaced by a randomly chosen neighbor colony. Thus the model is influenced not only by random genetic drift, and extinction-recolonization but also by migration and spatially varying weak selection.
He examined various quantities of evolution in his simulations: the number of substitutions (the number of colonies that are being replaced by mutant colonies), heterozygosity, number of alleles, probability of polymorphism, and dispersion index .
Ohtaís previous studies on population size and nearly neutral mutations have shown that evolution does not stop, as predicted, but simply slows down for large populations. In this study, he presented data in which the effect of large population size on the substitution rate became even smaller by incorporating extinction-recolonization. Further, periodic extinction was effective for increasing the number of substitutions. Extinction also increased the heterozygosity. However, by increasing the population the substitution rate became lower (but not as low as in a panmitic population) and heterozygosity higher. Thus, at increased sizes for subdivided populations substitution of mutants were dependent on the extinction-colonization rate, especially when the migration rate is limited.
Ohta further explained the contrasting pattern found between the sister species of Drosophila melanogaster and D. simulans. It has been suggested that D. melanogaster has a smaller more subdivided population structure than D. simulans. Ohta choose a low migration rate for D. melanogaster and a high rate for D. simulans. Aquadro et al. (1988, as cited in the paper) results showed that the heterozygosities at the protein level were similar for strictly neutral mutations. However the heterozygosities at the DNA level were disparate. Ohta modelled these two populations under the assumption that the mutation responsible for protein polymorphism was expressed by the sum of nearly neutral and deleterious classes. Further he set the migration rate for D. melanogaster, high and D. simulans, low. He found that in the nearly neutral class, the proportion of polymorphisms was similar for the two sets. Whereas, in the deleterious class, the proportion of polymorphisms was higher in the D. melanogaster set than the D. simulans. His data also showed that deleterious substitutions only slowed down in the subdivided population, where it stops in the panmitic one after one interval of extinction-recolonization.

Slatkin, M. 1993 Isolation by distance in equilibrium and nonequilibrium populations. Evol 47, 264-279.

Swallow review: In reviewing Wright's island models of isolation by distance, Slatkin first discussed coalescence times and genetic distance and distinguished between the probability of identity by descent of two genes sampled within a population and the probability of identity by descent of two genes sampled between two populations. He then shows the relationship between 3 commom measures of genetic distance (Fst, Gst, and theta) using coalescence times.

It is then shown that for allele frequency data a useful measure of the extent of gene flow between pairs of populations is M = (1/Fst-1)/4., which is the estimated level of gene flow in an island model at equilibrium. For DNA sequence data the same formula can be used if Fst is replaced by Nst. He shows that there is a simple relationship between M and geographic distance in both equilibrium and non-equilibrium populations and that this rate is approx independent of mutation rate when that rate is small. Simulation data shows that isolation by distance can be detected. This approach to analyzing isolation by distance is used for 2 allozyme data sets. One from gulls which appears to be in equilibrium and one for pocket gophers which do not.

Tanaka Y 1991 The evolution of social communication systems in a subdivided population. J Theor Biol 1991 Mar 21;149(2):145-63

Evolution of social communication systems is modeled with a quantitative genetic model. The mathematical model describes the coevolutionary process of a social signal (a social character) and responsiveness (a social preference) to the signal. The responsiveness is postulated to influence fitness of senders of the signal. Considerations are extended to subdivided population structure by combining the social selection model with a group selection model. The numerical results derived from the models indicate that the evolutionary rate of social communication systems depends largely on genetic correlation between the signal and the responsiveness. Group selection can reinforce the evolutionary rate and relax its dependence on genetic correlation. The origin of genetic correlation is discussed in relation to group selection.

Varvio SL, Chakraborty R, Nei M 1986 Genetic variation in subdivided populations and conservation genetics. Heredity 1986 Oct;57 ( Pt 2):189-98

The genetic differentiation of populations is usually studied by using the equilibrium theory of Wright's infinite island model. In practice, however, populations are not always in equilibrium, and the number of subpopulations is often very small. To get some insight into the dynamics of genetic differentiation of these populations, numerical computations are conducted about the expected gene diversities within and between subpopulations by using the finite island model. It is shown that the equilibrium values of gene diversities (HS and HT) and the coefficient of genetic differentiation (GST) depend on the pattern of population subdivision as well as on migration and that the GST value is always smaller than that for the infinite island model. When the number of migrants per subpopulation per generation is greater than 1, the equilibrium values of HS and HT are close to those for panmictic populations, as noted by previous authors. However, the values of HS, HT, and GST in transient populations depend on the pattern of population subdivision, and it may take a long time for them to reach the 95 per cent range of the equilibrium values. The implications of the results obtained for the conservation of genetic variability in small populations are discussed. It is argued that any single principle should not be imposed as a general guideline for the management of small populations.

Whitlock MC, Barton NH 1997 The effective size of a subdivided population. Genetics 1997 May;146(1):427-41

(Abstract) This paper derives the long-term effective size, Ne, for a general model of population subdivision, allowing for differential deme fitness, variable emigration and immigration rates, extinction, colonization, and correlations across generations in these processes. We show that various long-term measures of Ne are equivalent. The effective size of a metapopulation can be expressed in a variety of ways. At a demographic equilibrium, Ne can be derived from the demography by combining information about the ultimate contribution of each deme to the future genetic make-up of the population and Wright's FST's. The effective size is given by Ne = 1/(1 + var (upsilon) ((1 - FST)/Nin), where n is the number of demes, theta i is the eventual contribution of individuals in deme i to the whole population (scaled such that sigma theta i = n), and < > denotes an average weighted by theta i. This formula is applied to a catastrophic extinction model (where sites are either empty or at carrying capacity) and to a metapopulation model with explicit dynamics, where extinction is caused by demographic stochasticity and by chaos. Contrary to the expectation from the standard island model, the usual effect of population subdivision is to decrease the effective size relative to a panmictic population living on the same resource.

(Wilkinson review) This paper is motivated by the counter-intuitive claim that population subdivision can increase effective population size. This claim is based on an analysis of Wright's island model (all subpopulations contribute migrants to a pool that can feed back into any subpopulation). One way to understand this result is to consider an extreme case of complete isolation (Fst = 1). In this situation, alleles go to fixation within subpopulations by chance, but never go to fixation in the entire population. Consequently, the effective population size is infinite! This paper uses more realistic models to explore the effects of differential fitness in each subpopulation, variable emigration and immigration rates, extinction and colonization, and correlation across generations within subpopulations in their fitness. They estimate Ne by figuring out how each subpopulation contributes alleles to future populations at demographic equilibria, and estimate Fst.

The basic modeling approach taken is to come up with a recursion for some genetic feature of a population, such as the probability of identity by descent, and use it to estimate the effective population size. They note that effective population size estimates are all relative to an idealized Wright-Fisher (i.e. random mating) population. Often, but not always, different genetic features, such as variance in allele frequency, degree of inbreeding, or loss of heterozygosity, will give the same estimate of Ne. In general, the effective population size is that number of individuals which, under random mating, would give the corresponding statistical estimate for the population.

They find that, in general, population subdivision decreases effective population size relative to a panmictic population living on the same resource.

Throughout the paper they note that recombination has an effect on allele distribution that is analogous to these models for spatial population structure since both will move alleles from one genetic background to another.

Wright, S. 1943 Isolation by distance. Genetics 28, 114-138.