Populations

What is a Population? Bob O'Hara Department of Mathematics and Statistics University of Helsinki Finland

The population is a basic concept in ecology and evolutionary biology

The definition of a population is not precise

Recently, methods have been developed which have been used to infer the existence of populations How useful are they?

An Old Observation Normally the ‘‘population’’ is more or less an abstraction because there is a considerable interchange of individuals between neighboring populations, owing to the absence or incompleteness of physical barriers. Mayr, 1942

Lisa Gannett suggests that populations are not “real” Populations are pragmatically and variably constituted in different sorts of investigations of species genome diversity. Population boundaries are not fixed but vary from one context of inquiry to another. Gannett, 2003

If populations are real, then all methods for defining them should give us similar outcomes If different methods give different answers, this suggests that populations are not “mind independent”

A difference in definitions Local, partially isolated breeding groups Maynard Smith, 1998 The group is primary a group of organisms of the same species living within a sufficiently restricted geographical area that any member can potentially mate with any other member Hartl & Clark , 1997 Individuals are primary

If groups are basic, we should be able to identify them unambiguously i.e. populations are not “mind independent”

Problem: how do we define the edges? ?

If individuals are basic, then we can define a population by interactions between individuals

This definition means that populations can still be defined, even if the edges are vague

This means that we can assign individuals to several populations ... depending on our purpose

We can define populations as groups of interacting individuals, but how are groups separated?

Groups can become separated by barriers reducing gene flow

The Great Wall of China acts as a barrier to gene flow Su, H et al. The Great Wall of China: a physical barrier to gene flow?. Heredity, 90, 212 - 219, (2003).

Experiencing different environments can also lead to separation of groups

Populations can become differentiated phenotypically 130 120 Finland Days to budset 110 100 Variation Between 90 Populations 80 Bud set 0.364 Bromarv Kerimäki Sotkamo Salla Allozymes 0.02 RFLP 0.02 Microsats 0.014

Using neutral markers to separate populations privileges neutral genetic data The methods define what a population is

What Structure does Note: number of populations pre-defined Population 2 Population 3 Population 1

What BAPS does Population 56 Population 7 Population 8 Population Population 2 Population 3 Population 1 Population 4

The mathematics behind clustering: The Posterior Pr(M, P | G) ∝ Pr(M) Pr(P) Pr(G | M, P) Prior Likelihood distributions (effect of the data) M – Population membership P - allele frequencies G - Genotypes( data)

The Likelihood for Population Membership Population 2 Population 3 Population 1 Allele p1,l,a p2,l,a p3,l,a frequencies P G∣M , P =∏ ∏ ∏ n p ,l ,a p p ,l ,a Pops Loci Alleles Assume Hardy-Weinberg equilibrium If we move an individual from one population to another, this changes the likelihood

The Number of Populations: Goodness of fit is penalised by the dimension Add a population: Pr(P) ↓ “Curse of Dimensionality” Pr(G | M, P) ↑

Estimating the number of populations depends on the balance between prior and likelihood Pr(M, P | G) ∝ Pr(M) Pr(P) Pr(G | M, P) Pr(P) ↓ Pr(G | M, P) ↑ Comment: there is no proof the balance is correct - problem in statistics (AIC, BIC, CIC, DIC, FIC, TIC)

Simulations: Clustering Individuals 100 Number of Populations 80 60 40 20 0 5 10 15 20 Number of Loci

Defining populations with software A population is defined using neutral markers Populations are defined by the amount of data Prior information very important area of development allows other factors in

Conclusions There are also biological reasons to be careful interpreting K. The population model that we have adopted here is obviously an idealization. However...clusters may not necessarily correspond to “real” populations. Pritchard, 2000

Are populations defined by the methods we use? “If all you have is a hammer, everything looks like a nail”

Human Population Structure 93 to 95% of total genetic variation within populations Identify 6 clusters Rosenberg et al. (2002)

Human Population Structure An alternative view: diversity as a cline Manica et al. (2005)

The Take Home Message Populations do not exist Populations should be defined according to our purpose Defining populations with dumb software should be done with care

Journal of Negative Results Ecology & Evolutionary Biology www.jnr-eeb.org

References Corander et al. (2003) Bayesian Analysis of Genetic Differentiation Between Populations. Genetics 163: 367–374. Gannett (2003) Making Populations: Bounding Genes in Space and in Time. Philosophy of Science, 70: 989–1001. Hartl & Clark (1997) Principles of Population Genetics Manica et al. (2005) Geography is a better determinant of human genetic differentiation than ethnicity. Human Genetics in press Maynard Smith (1998) Evolutionary Genetics Mayr (1942) Systematics and the Origin of Species Pritchard et al. (2000) Inference of population structure using multilocus genotype data. Genetics, 155: 945–959. Rosenberg et al. (2002) Genetic Structure of Human Populations. Science, 298: 2381-2385 Su et al. (2003) The Great Wall of China: a physical barrier to gene flow? Heredity, 90: 212 – 219.

Gannet suggests that populations are “created”, depending on circumstances If the appropriate ontology ... treats organisms ... as basic and populations as emergent, ... this challenges population- based approaches that assume that populations exist as mind-independent objects ... Gannett, 2003

Populations

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