What is a Population?

Bob O'HaraDepartment of Mathematics and Statistics

University of HelsinkiFinland

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 fromone 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 groupsMaynard Smith, 1998

The group is primary

Individuals are 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

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

Bromarv Kerimäki Sotkamo Salla

8090

100

110

120

130

Day

s to

bud

set

Variation Between PopulationsBud set 0.364Allozymes 0.02RFLP 0.02Microsats 0.014

Finland

Using neutral markers to separate populations privileges neutral

genetic data

The methods definewhat a population is

Population 2 Population 3Population 1

What Structure does

Note: number of populations pre-defined

What BAPS does

Population 4Population 3Population 1 Population 2

Population 5Population 6Population 7Population 8

The mathematics behind clustering: The Posterior

Pr(M, P | G) ∝ Pr(M) Pr(P) Pr(G | M, P)

M – Population membershipP - allele frequenciesG - Genotypes( data)

Likelihood(effect of the data)

Prior distributions

The Likelihood for Population Membership

Population 2 Population 3Population 1

Assume Hardy-Weinberg equilibriumIf we move an individual from one population to

another, this changes the likelihood

Allele frequencies

p1,l,a

p2,l,a

p3,l,a

P G∣M ,P =∏Pops∏Loci

∏Alleles

p p , l ,an p , l ,a

The Number of Populations: Goodness of fit is penalised by the dimensionAdd 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

5 10 15 20

020

4060

8010

0

Number of Loci

Num

ber o

f Pop

ulat

ions

Defining populations with software

A population is defined using neutral markers

Populations are defined by the amount of data

Prior information very importantarea of developmentallows other factors in

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

Conclusions

“If all you have is a hammer, everything looks like a nail”

Are populations defined by the methods we use?

Human Population Structure

Rosenberg et al. (2002)

93 to 95% of total genetic variation within populations

Identify 6 clusters

Human Population Structure

Manica et al. (2005)

An alternative view: diversity as a cline

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 ResultsEcology & Evolutionary Biology

www.jnr-eeb.org

ReferencesCorander 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