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