Genetic variation in populationscan be
described by genotype and allele frequencies.
(not "gene" frequencies)
Consider a diploid autosomal locus
with two alleles and no dominance
(=> semi-dominance: AA , Aa , aa phenotypes are distinguishable)
# AA = x # Aa = y # aa = z x + y + z = N (sample size)
f(AA) = x / N f(Aa) = y / N f(aa) = z / N
f(A) = (2x + y) / 2N f(a) = (2z + y) / 2N
or f(A) = f(AA) + 1/2 f(Aa) f(a) = f(aa) + 1/2 f(Aa)
let p = f(A), q = f(a) p & q are allele frequencies
Properties of p & q
p + q = 1 p = 1 - q q = 1 - p
(p + q)2 = p2 + 2pq + q2 = 1
(1 - q)2 + 2(1 - q)(q) + q2 = 1 [Homework: show this algebraically]
p & q are interchangeable wrt [read, "with respect to"] A & a;
q is usually used for the
rarer, recessive, or deleterious (disadvantageous) allele;
BUT 'common' &
are statistical properties
'dominant' & 'recessive' are genotypic properties
'advantageous' & 'deleterious' are phenotypic properties
*** combination of these properties is possible ***
What happens to p & q in one generation of random mating?
Consider a population of
reproduction by random union of gametes ("tide pool" model)...
of parental alleles coming together in various genotype combinations.
[expectation: the anticipated value of a variable probability]
/ Punnet Square
all show that expectation of f(AA) = p2
expectation of f(Aa) = 2pq
expectation of f(aa) = q2
(2) Re-describe allele frequencies among offspring (A' & a').
= f(AA) + 1/2 f(Aa)
= p2 + (1/2)(2pq) = p2 + pq = (p)(p+q) = p' = p
= f(aa) + 1/2 f(Aa)
= q2 + (1/2)(2pq) = q2 + pq = (q)(p+q) = q' = q
p2 : 2pq : q2 are Hardy-Weinberg proportions (cf. Mendelian ratios 1 : 2 : 1 )
[avoid the phrase "Hardy-Weinberg equilibrium":
H-W proportions occur under non-equilibrium conditions].
The Hardy-Weinberg Theorem holds under "more realistic" conditions:
(1) multiple alleles / locus
p + q + r = 1
(p + q + r)2 = p2 + 2pq + q2 + 2qr + r2 + 2pr = 1
The proportion of heterozygotes
(H = 'heterozygosity')
is a measure of genetic variation at a locus.
Hobs = f(Aa) = observed
Hexp = 2pq = expected heterozygosity (for two alleles)
He = 2pq + 2pr + 2qr = 1 - (p2 + q2 + r2) for three alleles
He = 1 - (qi)2 for n alleles
where qi = freq. of ith allele of n alleles at
Ex.: if q1 = 0.5, q2 = 0.3, & q3 = 0.2
then He = 1 - (0.52 + 0.32 + 0.22) = 0.62
PopGen at ABO locus
(2) sex-linked loci
iff [read: "if and only if"] allele frequencies in males and females are identical
If frequencies are initially unequal, they converge over several generations.
(3) dioecious organisms
sexes are separate
H-W is produced by random mating of individuals (random union of genotypes).
expand (p2 'AA' + 2pq 'AB' + q2 'BB')2 :
nine possible 'matings' among genotypes
[Also holds if no selfing (self-fertilization) is possible]
Genotype proportions in natural
can be tested for H-W conditions
Ho (null hypothesis): no outside factors are acting.
Ex.: MN blood groups in Homo
Among North American whites:
f(M) = [(2)(1787) + 3039] / (2)(6129)= 0.539
f(N) = [(2)(1303) + 3039] / (2)(6129)= 0.461 = 1.0 - 0.539
Chi-square (2) test:
there is only one degree of
because there are only two alleles
Chi-square test on combined data:
populations, each of which shows Hardy-Weinberg proportions,
will not show expected Hardy-Weinberg proportions
if the allele frequencies are different in the separate populations.
Wahlund Effect: an artificial
(or a structured metapopulation)
will have a deficiency of heterozygotes
The Hardy-Weinberg conditions are the
What are the consequences of other genetic / evolutionary phenomena?
How do they interact?
Five major factors:
Change of allele frequencies (q) [read as 'delta q']
occurs due to differential effects of alleles on 'fitness'
Consequences depend on dominance of fitness
Natural Selection is the principle concern of "microevolutionary" theory
A and A' are inter-converted at some rate µ .
If µ(AA') µ'(AA'), net change will occur in one direction.
Net movement of alleles between populations occurs at some rate m .
(Im)migration introduces new alleles, changes frequency of existing alleles.
Inbreeding: preferential mating of relatives at some rate F (see Homework).
Non-random reproduction: variable sex ratio, offspring number, population ize
Chance fluctuations occur in finite populations, especially those with small size N.
Genetic drift: random change of allele frequencies
over time & among populations (see Homework)
The Mathematical Theory of Natural Selection
Selection" is the name given to an evolutionary process
in which "adaptation" occurs in such a way that "fitness" increases.
Under certain conditions, this results in descent with modification.
exists for some trait, and
a fitness difference is correlated with that trait, and
the trait is to some degree heritable (determined by genetics),
Then: the trait distribution will change
over the life history of organisms in a single generation,
and between generations.
of change in the population is called "adaptation"
Natural Selection can be modeled genetically.
variation = variable p & q
fitness = differential phenotypes of corresponding genotypes
heritability = Mendelian principles
Natural Selection results in change
of allele frequency (q)
[read as "delta q"]
in consequence of differences in the relative fitness (W)
of the phenotypes to which the alleles contribute.
Fitness is a
of individual organisms.
Fitness is determined genetically (at least in part).
Fitness is related to success at survival AND reproduction.
Fitness can be measured & quantified (see below).
i.e., the relative fitness of genotypes can be assigned numerical values.
The consequences of natural selection
on the dominance of fitness:
e.g., whether the "fit" phenotype is due to a dominant or recessive allele.
Then, allele frequency change is predicted by the General Selection Equation:
q = [pq] [(q)(W2 - W1) + (p)(W1 - W0)] /
are the fitness phenotypes
of the AA, AB, & BB genotypes, respectively [see derivation]
AA AB BB
phenotype: W0 = W1 W2 (AA and AB have identical phenotypes)
Then the GSE simplifies to q = pq2(W2 - W1) (since W1 - W0 = 0)
If 'B' phenotype is more fit than 'A' phenotype,
W2 > W1 & q > 0 so q increases.
If 'B' phenotype is less fit than 'A' phenotype,
W2 < W1 & q < 0 so q decreases.
(W2 - W1)
: the greater the difference in fitness,
the greater the intensity of selection
and the more rapid the change
Tay-Sachs Disease is caused by an allele
that is rare (q 0.001)
recessive (W0 = W1 = 1)
lethal (W2 = 0)
Then q = pq2(W2 - W1) = -pq2 -q2 (since p 1)
That is, Natural Selection results in a decrease in the
the Tay-Sachs allele of about one part in a million (0.0012) per generation
s = 1 - W
The selection coefficient (s)
is the difference in fitness
of the phenotype relative to some 'standard' phenotype
that has a fitness W = 1
[The math is simpler because only one variable is used for fitness.]
(1) Complete dominance
AA AB BB
phenotype: W0 = W1 W2 (AA and AB have identical phenotypes)
or 1 = 1 1 - s
if 0 < s < 1 : 'B' is deleterious(at
a selective disadvantage)
if s < 0 : 'B' is advantageous
= -spq2 / (1 - sq2)
(2) Incomplete dominance
phenotype: W0 W1 W2 (all phenotypes different)
or 1 - s1 1 1 - s2
& s2 < 1 : overdominance
fitness (heterozygote advantage)
The population has optimal fitness when both alleles are retained:
q will reach an equilibrium where q = 0
0 < < 1 (read as, "q hat")
(s1) / (s1 + s2)
of allele frequency change is due to fitness
(whether the effect of the allele on phenotype is deleterious or advantageous).
Ultimate consequences depend on the dominance of fitness
(whether the allele is dominant, semi-dominant, or recessive).
Rate of change is an interplay of both of these factors (see Lab #1)
AA AB BB Consequence of natural selection [ let q = change in f(B) ]
= W1 = W2 No
selection (neither allele has a
then q = 0, H-W proportions remain constant
= W1 > W2 deleterious
recessive (advantageous dominant):
then q < 0, q 0.00 (loss): how fast? [Does it get there?]
= W1 < W2 advantageous
recessive (deleterious dominant):
then q > 0, q 1.00 (fixation): how fast?
< W1 > W2 overdominance
[special case of semi-dominance]:
q , where q = 0
Short-term measures: "Life Table" parameters
rate of instantaneous increase (r) of a phenotype
dN / dt = rN = rN (K - N)
where K = carrying capacity
net reproductive rate: exp(r)
r is "compound interest" on N
replacement rate (RO):
lifetime reproductive output
~ er(at low density)
components of fitness:
that contribute to survival
Ex.: survivorship (expected survival time)
fecundity (# offspring at age x)
the phenotypic consequence for populations of natural selection on
[cf. adjust / acclimate]
traits that change as a result of selection
are sometimes referred to as "adaptations" or "adaptive characters"
Life table analysis: survivorship and fecundity vary with age
= prob. of survival from birth to
survivorship = probability of survival to age x+1 from age x
mx = fecundity (# offspring) at age x
then (lx)(mx) exp(-rx) = 1 (in a stable population,
x=1 where L = life expectancy)
Ro=(lx)(mx) replacement rate erat low density
is a discrete solution to the continuous logistic
Consider a population with two
These phenotypes correspond to two reproductive 'strategies
iteroparous strategy: offspring produced over several seasons
semelparous strategy: offspring produced all in one season
and fecundity schedule will compare their life histories
life table parameters can be measured experimentally
environmental conditions, survivorship is 50% / year:
both strategies produce 2 young / female / lifetime
=> both phenotypes are equally 'fit' [and N is stable]
times', survivorship increases to 75% / year:
iteroparous strategy produces 4 young / female / lifetime
semelparous strategy produces 3 young / female / lifetime
=> iteroparous phenotype is 'more fit' [and N is increasing]
times', survivorship decreases to 25% / year:
iteroparous Ro = 0.72, semelparous Ro = 1.00
=> semelparous phenotype is 'more fit' [and N is decreasing]
=> Population phenotypes will adapt to changing conditions
environment, K increases:
e.g., productivity of meadow increases
iteroparity more advantageous, population density increases
environment, r increases:
e.g., severity of winter highly variable
semelparity more advantageous, early reproduction favoured
maintain population size N close to K
long-lived, reproduce late, smaller # offspring, lots of parental care
E.g., many bird species, primates (including Homo)
maximize growth potential
short-lived, reproduce early, larger # offspring, little parental care
E.g., most invertebrates, some rodents
We can extend single-locus multilocus quantitative models
Mendel's Laws & H-W Theorem
normal distribution fitness function heritability
Variation can be quantified (see a Primer of Statistics for review)
coefficient of variation (CV) = (/) x 100
size effect when comparing variance:
Ex.: Suppose X = leg length Y = eye width
X = 100 1.0 versus Y = 1.0 0.1
CV of X = 1% CV of Y = 10%
Y is more variable, though X is larger
variation follows "normal distribution"
Multiple loci are involved
Each locus has about the same effect
Each locus acts independently
[interaction variance (see below) is minimal]
Variation has two sources: genetic (G2) & environmental (E2) variance
phenotypic variance P2
additive variance A2 = G2 + E2
heritability h2 = G2/A2 = G2 / (G2 + E2)
"heritability in the narrow sense": ignores GxE2
Identical genotypes produce different phenotypes in different environments.
Ex.: same breed of cows produces different milk yield on different feed
The Norm of Reaction describes the relationship between genetics and environement
organismal variation is highly heritable
ex.: Darwin's pigeon breeding experiments
Artificial selection on agricultural species
Commercially useful traits can be improved by selective breeding
IQ scores in Homo: h2 0.7
[But: IQ scores improve with education: GxE2 is large]
Offsrping / Midparent correlation
For many traits in many organisms:
CV = 5 ~ 10 %
h2 = 0.5 ~ 0.9
genotype & fitness
Function is a continuous variable, rather than discrete values for W0, W1, & W2
=> Most traits vary & are
Many traits do respond to 'artificial' selection.
Many traits should respond to 'natural' selection.
=> To demonstrate & measure
we must show experimentally that heritable variation has consequences for fitness <=
trait distribution can be described as a bell curve
with a particular mean & variance:
What happens to this distribution under Selection?
(1) Directional Selection
function has constant slope:
Trait mean shifted towards favored phenotype
trait variance unaffected
models, the limit of selection is
Elimination of variation by fixation of favored allele
rate is limited by
substitutional genetic load:
"cost" of replacing non-favored allele ( "intensity" of selection)
Mortality is density-dependent
In 'real' stable populations: N(after) N(before)
Survivorship is proportional to fitness up to K: more
Selection will affect recruitment to next generation
Ex.: If the first-born dies of malaria, s/he will be replaced.
More births occur such that N is continually "topped up".
Birth of succeeding offspring will maintain N near K
Selection (AKA truncation selection)
Fitness function has a "peak"
Trait variance reduced around (existing) optimal phenotype,
trait mean unaffected
elimination of variant alleles
or, 'weeding out' of disadvantageous variants
homozygosity at multiple loci:
difficult iff variance due to recessive alleles
inbreeding depression: loss of 'health' in inbred lines
Elimination of non-cryptic pepper moths (Biston)
melanistic variants are eliminated rapidly in light-colored environments
peppered variants are reduced slowly in dark-colored environments
in Homo (Karn & Penrose 1951)
Modal birthweight is optimum for survival
Selection (two kinds)
There is a lot of variation: does selection explain it?
Fitness function has more than one peak (multi-modal)
have superior fitness at a locus
because different alleles are favoured in different environments
sickle-cell hemoglobin in Homo ('Contradictory' selection)
Leucine Aminopeptidase (LAP) & salinity tolerance in Mytilus mussels
multimeric enzymes with polypeptides from different alleles
often show wider substrate specificity, kinetic properties (Vmax & KM)
myoglobin in diving mammals
heterozygosity at multiple loci improves general fitness
Hybrid vigour: crossbreeding of inbred lines improves fitness in F1
epistasis: high 'Hobs' is 'good for you'
Ex.: correlation between phenotype & genotype: antler points in Odocoileus deer
Ex.: fluctuating asymmetry: Acionyx cheetahs are lopsided
Maintaining polymorphic phenotypic variation by selection
Selection (Darwin 1871):
'exaggerated' phenotypes are disadvantageous somatically
but are favoured in competition for mates
secondary sex characteristics:
Sexual dimorphism in mallards, peafowl, & lions
Antlers in Cervidae are used in male-male combat
Tail displays in peacocks attract mates
sexual selection': the Madonna
/ Ozzy Osborne Effect
Females choose males on basis of some distinctive trait
Offspring have exaggerated trait (males) & preference for trait (females)
=> selection reinforces trait & preference for trait simultaneously
New phenotype spreads rapidly in population
Fitness function is a valley
Trait variance increases (like balancing), BUT polymorphism is unstable
[Try NatSel with: q = 0.5, N = 9999, W0 = 1.0, W1 = 0.7, W2 = 1.0]
can usually be maintained only temporarily:
One of the phenotypes will outcompete the other
unless different phenotypes choose different niches (Ludwig Effect)
[and then this becomes Balancing Selection]
bristles in Drosophila (Thoday & Gibson 1962)
Selection for 'high #' versus 'low #' lines
=> 'pseudo-populations' with reduced interfertility
Might disruptive selection contribute to speciation?
Natural selection is ordinarily defined
differential survival & reproduction of individuals:
Can selection operate on other biological units?
Can such selection 'oppose' individual selection?
Differential survival & 'reproduction' of alleles
t-alleles in Mus
tt is sterile (W = 0)
Tt is 'tail-less' (cf. Manx cats) (W < 1)
t alleles are preferentially segregated into gametes (80~90%)
=> f(t) is high in natural populations (40~70%)
even though it is deleterious to individuals
Differential survival & reproduction of related (kin) groups (families)
individuals share alleles: r =
of relationship [see
offspring & parents are related by r = 0.50 [They share half their alleles]
full-sibs " " r = 0.50
half-sibs " " r = 0.25
first-cousins " " r = 0.125
of phenotype for individual i
= direct fitness of i + indirect fitness of relatives j,k,l,...
Wi = ai + (rij)(bij) summed over all relatives j,k,l,...
where: ai = fitness of i due
to own phenotype
bij = fitness of j due to i's phenotype
rij = coefficient of relationship of i & j
If i & j are unrelated
warn: Windividual = 0.0 + (0.0)(1.0) = 0.0
don't warn: Windividual = 1.0 + (0.0)(0.0) = 1.0
=> Such behaviors should not evolve among unrelated individuals
What is the fitness value in a kin group?
Wbrothers = 0.0 + [(0.5)(1.0) + (0.5)(1.0)] = 1.0
Wcousins = 0.0 + [(0.125)(1.0)] = 1.0
"I would lay down my life for two brothers or eight cousins."
alleles are maintained by recurrent mutation.
A stable equilibrium(where q = 0) is reached
when the rate of replacement (by mutation)
balances the rate of removal (by selection).
frequency of new mutant alleles per locus per generation
typical µ = 10-6: 1 in 1,000,000 gametes has new mutant
then =(µ / s) [see derivation]
Ex.: For a recessive lethal allele (s = 1) with a
rate of µ = 10-6
then = û = (10-6 / 1.0) = 0.001
Lowering selection against alleles increases their frequency.
Medical intervention has increased the frequency of heritable conditions
in Homo (e.g., diabetes, myopia)
Eugenics: modification of human condition by selective breeding
'positive eugenics': encouraging people with "good genes" to breed
'negative eugenics': discouraging people with 'bad genes'' from breeding
e.g., immigration control, compulsory sterilization
[See: S. J. Gould, "The Mismeasure of Man"]
eugenics effective at reducing frequency of deleterious alleles?
What proportion of 'deleterious alleles' are found in heterozygous carriers?
(2pq) / 2q2 = p/q 1/q (if q << 1)
if s = 1 as above, ratio is 1000 / 1 : most of
is in heterozygotes,
not subject to selection
selection is balanced by influx of 'immigrant' alleles;
a stable 'equilibrium' can be reached iff migration rate constant.
Consider an island adjacent to a
migration to the island.
The fitness values of the AA, AB, and BB genotypes differ in the two environments,
so that the allele frequencies differ between the mainland (qm) and the island (qi).
B has high fitness on
and low fitness on island.
[For this model only, allele A is semi-dominant to allele B,
so we use t for the selection coefficient to avoid confusion]
freq. of new migrants (with qm)
as fraction of residents (with qi)
if m << t qi = (m / t)(qm) [see derivation]
Gene flow can hinder optimal adaptation of a population to local conditions.
snakes (Natrix sipedon) live on islands
in Lake Erie (Camin & Ehrlich 1958)
Island Natrix mostly unbanded; on adjacent mainland, all banded.
Banded snakes are non-cryptic on limestone islands, eaten by gulls
Suppose A = unbanded B = banded [AB are intermediate]
Let qm = 1.0 ["B" allele is fixed on mainland]
m = 0.05 [5% of island snakes are new migrants]
t = 0.5 so W2 = 0 ["Banded" trait is lethal on island]
then qi = (0.05/0.5)(1) = 0.05
and Hexp = 2pq = (2)(0.95)(0.05) 10%
i.e, about 10% of snakes show intermediate banding, despite strong selection
=> Recurrent migration can maintain a disadvantageous trait at high
is the mating of (close) relatives
or, mating of individuals with at least one common ancestor
Coefficient) = prob. of "identity
Expectation that two alleles in an individual are
exact genetic copies of an allele in the common ancestor
or, proportion of population with two alleles identical by descent
This is determined by the consanguinity (relatedness) of parents.
Hexp by a proportion F
(& increases the proportion of homozygotes). [see derivation]
f(AB) = 2pq (1-F)
f(BB) = q2 + Fpq
f(AA) = p2 + Fpq
affects genotype proportions,
inbreeding does not affect allele frequencies.
increases the frequency of individuals
with deleterious recessive genetic diseases by F/q [see derivation]
Ex.: if q = 10-3 and F
= 0.10 , F/q = 100
=> 100-fold increase in f(BB) births
Inbreeding coefficient of a population can be estimated from experimental data:
F = ( 2pq - Hobs ) / 2pq [see derivation]Ex.: Selander (1970) studied structure of Mus house mice living in chicken sheds in Texas
& q = 0.374 + (1/2)(0.400) = 0.574
Then F = (0.489 - 0.400) /
which is intermediate between Ffull-sib = 0.250
& F1st-cousin = 0.125
=> Mice live
family groups with close inbreeding
[This is typical for small mammals]
However, in combination with natural selection, inbreeding can be
increases rate of evolution in the long-term (q 0 more quickly)
deleterious alleles are eliminated more quickly.
increases phenotypic variance (homozygotes are more common).
advantageous alleles are also reinforced in homozygous form
Drift is stochastic q
(cf. deterministic q [predictable, due to selection, mutation, migration)
Sewall Wright (1889 - 1989): "Evolution and the Genetics of Populations"
is greater than deterministic q
in small populations:
allele frequencies drift more in 'small' than 'large' populations.
Drift is most noticeable if s 0, and/or N small (< 10) [N 1/s]
drifts between generations (variation decreases within
over time) ;
eventually, allele is lost (q = 0) or fixed (q = 1) (50:50 odds)
[Try: q = 0.5, W0 = W1 = W2 = 1.0, and N = 10, 50, 200, 1000;
repeat 10 trials each, note q at endpoint]
drifts among populations (variation
among populations over time);
eventually, half lose the allele, half fix it.
**=> Variation is 'fixed' or 'lost' & populations will diverge by chance <=**
"Gambler's Dilemma" : if you play long enough, you win or lose everything.
All populations are finite: many are very small, somewhere or sometime.
Evolution occurs on vast time scales: "one in a million chance" is a certainty.
Reproductive success of individuals in variable: "The race is not to the swift ..."
What happens in the really long run?
Population Size (Ne)
= size of an 'ideal' population with same genetic variation (measured as H)
as the observed 'real' population.
= The 'real' population behaves evolutionarily like one of size Ne :
e.g., the population will drift like one of size Ne
loosely, the number of breeding individuals in the population
Consider three special cases where Ne < or << Nobs [the 'count' of individuals]:
(1) Unequal sex ratio
Ne = (4)(Nm)(Nf) /
(Nm + Nf)
where Nm & Nf are numbers of breeding males & females, respectively.
"harem" structures in mammals (Nm << Nf)
Ex.: if Nm = 1 "alpha male" and Nf = 200
then Ne = (4)(1)(200)/(1 + 200) 4
A single male elephant seal (Mirounga) does most of the breeding
Elephant seals have very low genetic variation
like ant & bees (Nf << Nm)
Ex.: if Nf = 1 "queen" and Nm= 1,000 drones
then Ne = (4)(1)(1,000)/(1 + 1,000) 4
Hives are like single small families
In stable population, Noffspring/parent = 1
"Random" reproduction follows Poisson distribution (N = 1 1)
(some parents have 0, most have 1, some have 2, a few have 3 or more)
|X||Ne =||Reproductive strategy|
|1||1||Nobs||Breeding success is random|
|1||0||2 x Nobs||A zoo-breeding strategy|
|1||>1||< Nobs||K-strategy, as in Homo|
|1||>>1||<< Nobs||r-strategy, as in Gadus|
(3) Population size variation over time
Ne = harmonic mean
of N = inverse of arithmetic mean of inverses
[a harmonic mean is much closer to lowest value in series]
Ne = n / [ (1/Ni) ] where Ni = pop size in i th generation
exist in changing environments:
Populations are unlikely to be stable over very long periods of time
10-2 forest fire / 10-3 flood / 10-4 ice age
Ex.: if typical N = 1,000,000 & every 100th
= 10 :
then Ne = (100) / [(99)(10-6) + (1)(1/10)] 100 / 0.1 = 1,000
Effect & Bottlenecks:
Populations are started by (very) small number of individuals,
or undergo dramatic reduction in size.
Ex.: Origin of Newfoundland moose (Alces):
2 bulls + 2 cows at Howley in 1904
[1 bull + 1 cow at Gander in 1878 didn't succeed].
Bay Co. trapping
records (Elton 1925)
Population densities of lynx, hare, muskrat cycle over several orders of magnitude
Lynx cycle appears to "chase" hare cycle
The effect of drift on genetic variation in populations
Larger populations are more variable (higher H) than
if s = 0: H reflects balance between loss of alleles by drift
and replacement by mutation
H = (4Neµ) / (4Neµ + 1)
Ex.: if µ= 10-7 & Ne = 106 then Neµ = 1 and Hexp = (0.4)/(0.4 + 1) = 0.29
0.20 which suggests Ne
Most natural populations have a much smaller effective size than their typically observed size.
Stochastic effects may be as or more important than deterministic