REVIEWS FUNDAMENTAL CONCEPTS IN GENETICS Effective population size and patterns of molecular evolution and variation Brian Charlesworth Abstract | The effective size of a population, Ne, determines the rate of change in the composition of a population caused by genetic drift, which is the random sampling of genetic variants in a finite population. Ne is crucial in determining the level of variability in a population, and the effectiveness of selection relative to drift. This article reviews the properties of Ne in a variety of different situations of biological interest, and the factors that influence it. In particular, the action of selection means that Ne varies across the genome, and advances in genomic techniques are giving new insights into how selection shapes Ne. Genetic drift The effective size of a population (Ne) is one of several core components of the genome (for example, the X chromo- 12 The process of evolutionary concepts introduced into population genetics by Sewall some versus the autosomes ), or because of the effects change involving the random Wright, and was initially sketched in his magnum opus, of selection at one site in the genome on the behaviour of sampling of genes from the Evolution in Mendelian Populations1. Its purpose is to pro- variants at nearby sites13. An important consequence parental generation to produce the offspring generation, vide a way of calculating the rate of evolutionary change of the latter process is that selection causes reduced Ne causing the composition of caused by the random sampling of allele frequencies in a in genomic regions with low levels of genetic recombi- the offspring and parental finite population (that is, genetic drift). The basic theory of nation, with effects that are discernible at the molecular generations to differ. 2–5 14,15 BOX 1 Ne was later extended by Wright , and a further theoreti- sequence level . summarizes the major factors 6 cal advance was made by James Crow , who pointed out influencing Ne, which will be described in detail below. that there is more than one way of defining Ne, depend- In the era of multi-species comparisons of genome ing on the aspect of drift in question. More recently, the sequences and genome-wide surveys of DNA sequence theoretical analysis of the effects of demographic, genetic variability, there is more need than ever before to and spatial structuring of populations has been greatly understand the evolutionary role of genetic drift, and simplified by the use of approximations that resolve its interactions with the deterministic forces of muta- 7 drift into processes operating on different timescales . tion, migration, recombination and selection. Ne there- What biological questions does Ne help to answer? fore plays a central part in modern studies of molecular First, the product of mutation rate and Ne determines evolution and variation, as well as in plant and animal the equilibrium level of neutral or weakly selected breeding and in conservation biology. In this Review, genetic variability in a population8. Second, the effec- I first describe some basic theoretical tools for obtain- tiveness of selection in determining whether a favour- ing expressions for Ne, and then show how the results of able mutation spreads, or a deleterious mutation is applying these tools can be used to describe the proper- eliminated, is controlled by the product of Ne and the ties of a single population, and how to include the effects intensity of selection. The value of Ne therefore greatly of selection. Finally, I describe the effects of structuring of affects DNA sequence variability, and the rates of DNA populations by spatial location or by genotype, and dis- and protein sequence evolution8. cuss the implications of genotypic structuring for patterns The importance of N as an evolutionary factor is of variation and evolution across the genome. Institute of Evolutionary e Biology, School of Biological emphasized by findings that Ne values are often far lower Sciences, University of than the census numbers of breeding individuals in a spe- Describing genetic drift and determining Ne Edinburgh, Edinburgh cies9,10. Species with historically low effective population There are three major ways in which genetic drift can EH9 3JT, UK. sizes, such as humans, show evidence for reduced vari- be modelled in the simplest type of population, which e-mail: ability and reduced effectiveness of selection in compari- are outlined below. These theoretical models lead to a [email protected] 11 doi:10.1038/nrg2526 son with other species . Ne may also vary across different general approach that can be applied to situations of Published online locations in the genome of a species, either as a result greater biological interest, which brings out the utility 10 February 2009 of differences in the modes of transmission of different of the concept of the effective population size. NATURE REVIEWS | GENETICS VOLUME 10 | MARCH 2009 | 195 )''0DXZd`ccXeGlYc`j_\ijC`d`k\[%8cci`^_kji\j\im\[ REVIEWS Poisson distribution The Wright–Fisher population. To see why Ne is so More realistic models of drift. The assumptions of the This is the limiting case of useful, we need to understand how genetic drift can Wright–Fisher population model do not, however, apply the binomial distribution (see be modelled in the simple case of a Wright–Fisher to most populations of biological interest: many species next page), valid when the population1,16,17. This is a randomly mating popula- have two sexes, there may be nonrandom variation in probability of an event is very small. The mean and variance tion, consisting of a number of diploid hermaphro- reproductive success, mating may not be at random, of the number of events are ditic individuals (N). The population reproduces with generations might overlap rather than being discrete, then equal. discrete generations, each generation being counted at the population size might vary in time, or the species the time of breeding. New individuals are formed each may be subdivided into local populations or distinct Coalescent theory generation by random sampling, with replacement, of genotypes. In addition, we need to analyse the effects of A method of reconstructing the history of a sample of alleles gametes produced by the parents, who die immedi- deterministic evolutionary forces, such as selection and from a population by tracing ately after reproduction. Each parent thus has an equal recombination, as well as drift. their genealogy back to their probability of contributing a gamete to an individual The effective population size describes the times- most recent common ancestral that survives to breed in the next generation. If N is cale of genetic drift in these more complex situations: allele. Poisson distribution reasonably large, this implies a of we replace 2N by 2Ne, where Ne is given by a formula Coalescence offspring number among individuals in the population. that takes into account the relevant biological details. The convergence of a pair of A population of hermaphroditic marine organisms, Classically, this has been done by calculations based on alleles in a sample to a which shed large numbers of eggs and sperm that fuse the variance or inbreeding coefficient approaches19–23, common ancestral allele, randomly to make new zygotes, comes closest to such but more recently coalescent theory has been employed7. tracing them back in time. an idealized situation. In general, the use of Ne only gives an approximation to Fast timescale With this model, the rate at which genetic drift the rate of genetic drift for a sufficiently large population approximation causes an increase in divergence in selectively neutral size (such that the square of 1/N can be neglected com- Used to simplify calculations of allele frequencies between isolated populations, or loss pared with 1/N), and is often valid only asymptotically, effective population size, by assuming that the rate of of variability within a population, is given by 1/(2N) that is, after enough time has elapsed since the start of coalescence is slower than (BOX 2). An alternative approach, which has a central the process. Exact calculations of changes in variance the rate at which alleles role in the contemporary modelling and interpretation of allele frequencies or inbreeding coefficient are, there- switch between different of data on DNA sequence variation7,18, is provided by the fore, often needed in applications in which the population compartments of a structured theory of the coalescent process (the coalescent theory) size is very small or the timescale is short, as in animal population as we trace them (BOX 3) back in time. Instead of looking at the properties of the popu- and plant improvement or in conservation breeding lation as a whole, we consider a set of alleles at a genetic programmes19–21,24. Panmictic locus that have been sampled from a population. If we A panmictic population lacks trace their ancestry back in time, they will eventually Determining N : a general method. Coalescent theory subdivision according to spatial e location or genotype, so be derived from the same ancestral allele, that is, they provides a flexible and powerful method for obtaining coalescence (BOX 3) that all parental genotypes have undergone . This is obviously formulae for Ne, replacing the term involving N in the potentially contribute to the BOX 3 closely related to the inbreeding coefficient approach to rate of coalescence in by Ne, which can then be same pool of offspring. drift described in BOX 2, and the rate of the coalescent directly inserted in place of N into the results from coa- (BOX 3) process in a Wright–Fisher population is also inversely lescent theory . A core approach for estimating Ne related to the population size. under different circumstances is outlined briefly below and is discussed in more detail in the following sections of this Review.