The Biology of Small Populations:
Genetics
Introduction
In the last lecture we identified four categories of stochastic threats to small populations.1 So
far we have focused on those stochastic threats that directly affect the numbers of individuals
in a population.
1. Demographic stochasticity — not much of a problem in populations with more than
50–100 reproductive individuals
2. Environmental stochasticity — requires large populations, on the order of 1000-10,000
individuals to give a reasonable chance of long-term survival.
3. Demographic heterogeneity — not clear how large populations need to be to buffer its
effects, probably at least as large as for environmental stochasticity.
4. Natural catastrophes — if catastrophes occur at an appreciable frequency and if they
eliminate a large fraction of the population, no single population can survive over the
long term.
Before starting our discussion of how to use what we’ve learned in the management of
threatened species, we have one more stochastic threat to discuss: genetic stochasticity or
genetic drift.
As I mentioned in my introductory lecture, the early literature in conservation biology —
at least the early literature defined as the conservation biology literature of the early 1980’s —
was dominated by studies of the threats to small populations, and genetic threats were among
those most prominently identified. What exactly are those threats? Well, they can be divided
into two basic categories:
1
Don’t forget that stochastic threats are primarily important only after a population is already small and
endangered. Deterministic, systematic forces associated with habitat destruction, environmental degradation, invasive exotics, etc. are the most likely causes of population declines.
c 2001–2015 Kent E. Holsinger
1. Short-term effects on individual viability and fecundity — These are the result of
changes in the genetic structure of populations that potentially have a direct effect
on demographics of the population. They could make it even more susceptible to
extinction than in would be if these factors could be ignored
2. Long-term effects on the ability of populations to respond adaptively to environmental change — Even if genetic stochasticity has no immediate effect on the ability of
populations to persist, it might have some effect on their ability to respond when environmental change occurs, whether we are talking about global climate change or
the introduction of a new pathogen. After all, populations can respond adaptively
to environmental change only if they have the necessary genetic variability, and small
populations tned to harbor less variability than large ones.
Before we talk about the possible effects of genetic changes on short-term and long-term
survival, it is necessary first to talk about the types of genetic changes that happen in small
populations. Only then can we explore their effects.2
Genetic changes in small populations
As suggested by the fact that we refer to these changes as threats due to genetic stochasticity,
the genetic changes specific to small populations are random. To talk about this in more
detail, we need to develop a little background in population genetics, specifically the theory
of genetic drift.
It’s been known for more than 80 years that the randomness associated with reproduction
leads to changes in the genetic composition of a population through time. Consider this:
if gametes are chosen at random to be included in zygotes, the genetic composition of the
zygote pool will, on average, be the same as the gamete pool, but there is a distribution of
possible outcomes. We won’t go into the mathematical details here, but there are four basic
properties of drift important for our purposes:3
1. Allele frequencies tend to change from one generation to the next simply as a result
of sampling error. We can specify a probability distribution for the allele frequency in
the next generation, but can’t say with certainty what the exact value will be.
2
This will be a review for those of you who’ve had my course in population genetics. In fact, I should
probably make you give this part of the lecture, but I won’t.
3
If you want a more complete discussion, refer to chapter 7 of [8] or take my course in population genetics
next fall.
2
Figure 1: Frequency distribution of predicted heterozygosity loss for 80 mammal
species (from [1], Figure 11.4 [7])
2. There is no systematic bias associated with the change in allele frequency, i.e., we can’t
predict which alleles will become more common and which will become rarer.
3. Populations eventually become fixed for one of the alleles originally present in the
population, unless mutation or migration introduces new genetic variation, i.e., they
tend to lose genetic diversity (Figure 1).
4. Time to fixation (and other properties of drift) are inversely proportional to population
size — the larger the population, the smaller the effect of drift (Figure 2). The time to
common ancestry of two randomly chosen alleles in a population is 2Ne . The time to
common ancestry of all alleles in a population is 4Ne [10].
This last point is perhaps the most important, and the most problematic, for it turns out
that simply counting the number of reproductive plants or animals in a population is not
sufficient to determine whether the population is large or small. It is not the census number4
of individuals in the population that matters, but the effective number.5 The formulas that
follow are from [2, p. 362].
4
census number — the number of individuals in a population, simply counting all that are alive
effective population size — the size of a population for purposes of genetic drift, adjusted for unequal
sex-ratio, age structure, variable population size, and the like.
5
3
Figure 2: Fraction of genetic diversity lost in each generation for populations of different
effective size (Figure 11.3 [7]).
Unequal sex ratio
Ne =
4Nf Nm
Nf + Nm
Note: If there is only one reproductive male, the greatest the effective size can ever be is 4.
Management implication — Unequal sex ratios can dramatically increase the susceptibility
of a population to random genetic changes.
Example: one reproductive male mates with 10 reproductive females:
Ne =
4(10)(1)
40
=
≈ 3.6
(10 + 1)
11
Another example: ten reproductive males and 100 reproductive females:
Ne =
4(100)(10)
4000
=
≈ 36.3
(100 + 10)
110
Variation in reproductive success
Ne =
2N
2
1 + σk̄
4
,
where σ 2 is the variance in family size among individuals and k̄ is the average number of
offspring per individual.
Note: If σ 2 = 0, Ne = 2N . If σ 2 = 3k̄, Ne = N/2. Suppose, for example that the
distribution of offspring number is negative binomial with mean 2 and variance 12.6 Then
2N
Ne = 1+(12/2)
≈ 0.28N .
Management implication — Reducing the differences among individuals in the number
of offspring they produce can almost halve the susceptibility of a population to random
genetic changes. There is a complication worth noting here, however. What I just said is
true with respect to loss of genetic diversity as a result of genetic drift, but it’s true only if
the population size is constant with respect to the increase in relatedness among individuals
in the population.7 If the population size is increasing the effective size is close to size of
progeny population (not parental population) and equal reproduction increases the effective
population size by less than a factor of two. In fact, if the population size is increasing
rapidly enough, equalizing the reproductive success of parents would cause relatedness to
accumulate more rapidly if it limits the rate of population growth.
Variation in population size
1
Ne = "
1−
≈ Pt
Qt
k=1
t
1−
1
(k)
2Ne
1/t #
(1)
(2)
1
k=1 N (k)
t
(3)
where Ne(k) is the effective size of the population in generation k.
Note: If N = 1000 for k = 1, 2, · · · 9, but N = 10 for k = 10, Ne = 83 versus a mean of
901. Effective size is much more drastically affected by smallest population size than largest
population size. Management implication — Populations subject to occasional crashes are
more susceptible to random genetic changes than those with relatively stable populations.
6
If you’ve never heard of a negative binomial distribution before, don’t worry about it. All you need to
know is that the variance of a negative binomial distribution is larger than that of a Poisson distribution
with the same mean.
7
The reasons for this are technical and have to do with the difference between the variance and inbreeding
effective size of a population. Ask me if you’re interested in the details.
5
Age-structured populations
The stochastic dynamics of age-structured populations are complicated. To my mind we still
don’t understand them very well. Age structure does tend to reduce effective population size
still further (unless we’re dealing with annual plants that have a seed bank). Management
implication — We have to trust that inferences about management practices without considering age structure aren’t qualitatively changed by age structure. Just be conservative, i.e.,
build in a large margin for error.
Genetic changes during population bottlenecks
There are two components to what is often loosely referred to as “genetic diversity:” additive
genetic variance (the portion of the genetic differences among individuals that can respond
to selection) and allelic diversity (the number of different types of alleles present at any
locus).
Even in the most extreme situation imaginable, a population reduced to one
hermaphroditic individual for one generation, at most 50% of the additive genetic variance
in quantiative traits will be lost if the population rebounds quickly to a large population
size (Figure 3). A less extreme case, 2 males and 2 females would lead to only a 12% reduction in additive genetic variance. Moreover, selection against recessive lethal and deleterious
alleles will retard the loss of variance at other loci, especially those to which they are linked.
In short, several generations of greatly reduced population size are necessary to significantly
deplete the aspect of genetic diversity that is responsible for adaptive responses to natural
selection.
The variety of alleles present, however, is greatly affected by population bottlenecks. Rare
alleles are particularly susceptible to loss. In fact, population geneticists use the difference
between the effect of bottlenecks on diversity and variety to detect the effect of selection or
population size changes on nucleotide diversity.
But for our purposes, the important observation is this: Population bottlenecks have
little effect on the genetic variance responsible for adaptive responses to natural selection,
even though they may have a dramatic effect on the number of alleles present.
Short-term threats to persistence
Drift in small populations has many of the same properties as inbreeding. In fact,
6
Figure 3: Loss and recovery of genetic diversity after a population bottleneck (from [18];
Figure 11.5 [7]).
1
(1 − ft )
= ft + 1 −
2Ne
1
=
2Ne
1 t
= 1− 1−
2Ne
ft+1
1 − ft+1
1 − ft
ft
(4)
(5)
(6)
(7)
where f is the inbreeding coefficient, a measure of the degree of inbreeding. By trial and
error animal breeders have discovered how much inbreeding can be tolerated by domestic
animals before the lines begin to decline in performance and fecundity [5, 19]. Their rule
t+1
of thumb is that the per generation rate of inbreeding 1−f
= 2N1 e should not be greater
1−ft
than 2%–3%. If we want to be a little conservative, we might reduce this to 1%. Thus, we
require8
1
< 0.01
2Ne
8
This calculation is the entire justification for the “50” part of the famous (infamous) 50/500 rule.
7
Ne > 50
An alternative approach is to observe that animal breeders have found a obvious effect
on fecundity in small populations when the inbreeding coefficient approaches 0.5. If we want
our population to be viable for 100 generations
0.5 > 1 − 1 −
1−
1
2Ne
1
2Ne
100
(8)
100
> 0.5
1
> (0.5)0.01 = 0.993
2Ne
1
0.007 >
2Ne
Ne ≥ 73
1−
(9)
(10)
(11)
(12)
(13)
Still another approach is to assume that the deleterious effects noted in these small
populations is primarily the result of the expression of recessive deleterious alleles. Then
using the results of drift theory we can calculate the probability that a population has a
particular allele frequency, given assumptions about the strength of selection and mutation
rates. For a broad range of strentgths of selection and for what are thought to be typical per
locus mutation rates (10−6 per generation) it is possible to calculate the effect on population
mean fitness. This calculation suggests that populations will suffer noticeably (mean fitness
reduction greater than 10%) if Ne < 100–300 [9].
Finally, we can consider a population-level version of Muller’s ratchet. As a result of
genetic drift, there’s always a chance that a deleterious allele can be fixed as a result of
genetic drift. If it does and if it reduces the reproductive capacity of the population, the
population size may get smaller, making it easier for new deleterious mutations to fix, which
will reduce the population size further, and so on, and so on, and so on. Mike Lynch has
called this process the “mutational meltdown” [6, 14]. The expected time to extinction
increases rapidly in mutational meltdown models such that in populations with an effective
size greater than a few hundred, persistence times are well into the hundreds or thousands
of generations (Figure 4).
In addition to the effects of inbreeding depression, which have been found in virtually
every outbreeding organism — plant or animal — that has ever been studied9 , there has been
9
Except those that are known to have survived recent, severe population bottlenecks.
8
Figure 4: Mean time to extinction for monoecious populations with a constant carrying
capacity (open circles and dashed line) and monogamous populations with variable carrying
capacities (lognormal with the indicated coefficients of variation). Mutational parameters
are close to those estimated for Drosophila melanogaster: genomic mutation rate = 1.5,
selection coefficient against recessive homozygotes = 0.015, dominance coefficient = 0.35.
Ten offspring are produced per individual (from [14].)
9
some suggestion that loss of genetic diversity may have an immediate impact on short-term
survival. My (admittedly biased) reading of the evidence is that the evidence on this point
is at best equivocal.
The bottom line? Recall that to buffer the effects of environmental stochasticity we
require populations consisting of thousands or tens of thousands of reproductive individuals.
Ne
is unlikely to be less than 0.1, except in rare circumstances, so populations large enough
N
to buffer environmental stochasticity are almost certainly large enough to buffer genetic
stochasticity. On the other hand, when populations are critically endangered, genetic changes
may pose an additional threat to population persistence.
An example: Populations of the Flordia panther are extremely small. The high proportion of kinked tails and cowlicks among individuals in the population (about 90% in both
cases) coupled with the poorest semen quality ever recorded suggests that the population is
suffering from substantial inbreeding depression. As a result,10 Texas cougars were released
into Florida in 1995 in the hope that individual fitness would rapidly improve. No kinked
tails have been recorded from F1 and F2 offspring, and the proportion of F1 and F2 individuals with the cowlick are far less frequent (about 14%), suggesting that efforts to reduce the
effects of inbreeding depression may have been successful [11].
Another example: Mountain gorillas survive as only two critically endangered populations, and the total population in the wild may consist of no more than 800 individuals. A
recent whole-genome analysis of 13 gorillas, including 7 mountain gorillas, found that chromosomes were typically homozygous over more than 1/3 of their length [21]. Some tracts
of homozygosity were as much as 10Mb long, suggesting recent inbreeding within the small
remaining populations. Nonetheless, the authors conclude that
These subspecies have survived for thousands of generations at low population
levels and may have developed physiological and behavioral strategies to mitigate
inbreeding, such as natal dispersal and gene flow between isolated populations.
The purging of strongly deleterious mutations may also be an important factor.
An exception: loss of self-incompatibility alleles in plants with genetically determined
self-incompatibility. Hymenoxys acaulis: Illinois populations have a single compatibility
type, Ohio populations have only 3-9. Long-term persistence of Illinois populations requires
import of genotypes from Ohio. Reproductive capacity of all populations limited by availability of compatible mates.
But “[T]he observed low genetic diversity in today’s population [of Tasmanian devil]
preceded the Devil Facial Tumor Disease Outbreak by at least 100 y[ears]” [15], although a
more recent analysis [17] argues that the loss of immunodiversity may leave the Tasmanian
10
And after considerable debate, as you can imagine.
10
devil “highly vulnerable to infectious disease.” If that’s the case, then loss of immunodiversity
may be comparable to loss of self-incompatibility alleles.
Long-term threats to persistence
The threats to long-term persistence are those associated with loss of the genetic variability
necessary for adaptation to evnironmental change. One way of assessing this threat is to ask
how large the population must be to balance the loss of additive genetic variance through
drift with the input of additive genetic variance through mutation. Several reviews suggest
that the mutation rate for quantitative characters is on the order of 10−3 [12, 13]. The rate
of loss, recall, is 2N1 e . This would suggest that an Ne of 500 is necessary to ensure longterm evolutionary potential [5].11 Again, it would appear that populations large enough to
buffer environmental stochasticity will also be large enough to maintain the additive genetic
variance necessary to respond adaptively to environmental change.
When we recall that the main effect of population bottlenecks is to reduce the number
of alleles present, there is even more reason to suspect that this is a reasonable conclusion.
• Most of the genetic variance responsible for an evolutionary response to natural selection (the additive genetic variation) is found in high-frequency alleles, precisely those
least likely to be lost in small populations.
• Many low-frequency alleles are probably unconditionally deleterious and are maintained in the population only by recurrent mutation. Their loss may actually benefit
the population.
• Low-frequency alleles have a short lifetime in populations. They are quickly lost
through drift. Current low-frequency alleles are unlikely to provide the source of
evolutionary novelties. They are more likely to arise as a result of mutation in the
future.
• Alleles that are selectively advantageous are unlikely to be lost from populations in a
short time as a result of drift unless the populations are very small.
But it is important to remember that when we manage species, they may respond not
only through changes that are primarily ecological, they may adapt to the new management
regime to which they are subject. This is most obvious when the managed environment is
very different, as when captive populations are bred in zoos, aquaria, or botanical gardens,
11
The “500” part of the 50/500 rule.
11
but it may also happen in the wild if populations are restricted to a part of their former
range.As Stockwell and his colleagues point out, refuge populations may diverge from those
in other parts of their range making it more difficult to use them as source populations for
re-introduction or restoration efforts.
Surviving with low genetic diversity
I argued from first principles that loss of genetic diversity is more likely to be a symptom of
endangerment than a cause of endangerment. Milot et al. [16] present an example that is
consistent with my argument.
The authors compare levels of genetic diversity (as judged with AFLPs12 ) in the wandering albatross and the Amsterdam albatross. Based on molecular clock estimates,
these two taxa diverged from one another about 800,000 years ago. The Amsterdam
albatross is recovering from an extreme bottleneck. When first discovered in the early
1980s, only 5 breeding pairs were known. Approximately 130 adult birds now exist
(http://en.wikipedia.org/wiki/Amsterdam Albatross). Only 5% of AFLP loci are polymorphic in wandering albatross, and only 2% are polymorphic in Amsterdam albatross. In
contrast, other vertebrates show polymorphism at 17-99% of AFLP loci.
Simulations suggest that the low levels of polymorphism are not the result of population
bottlenecks in the species’ evolutionary history.13 Instead, it appears that they both inherited
a low level of polymorphism from their ancestor. If that’s right, then both species have
survived for 800,000 years with very low levels of genetic diversity, suggesting that lack of
diversity is a reflection of their life history and that it did not contribute to very small
population sizes in the Amsterdam albatross.
A caveat
There is one detail about AFLP markers that’s important to know. Differences among
individuals at most AFLP loci probably have little or no impact on survival and reproduction.
Lack of diversity at these loci provides information on levels of adaptively significant variation
only through several steps of logic (low neutral diversity implies small effective population size
means natural selection is less effective means loss of diversity even if it’s favored by selection).
It’s possible that levels of adaptive diversity in wandering and Amsterdam albatrosses are
12
The molecular basis of this variation isn’t important for our purposes. If you’re interested, ask me.
Remember, only the Amsterdam albatross shows evidence of recent recovery from a bottleneck. The
wandering albatross has substantially larger populations.
13
12
markedly higher than at AFLPs. Nonetheless, it seems likely that they are still lower than
levels of adaptive diversity in other vertebrates.
Avoiding inbreeding depression
I mentioned that animals from Texas were introduced into southern Florida in an attempt
to alleviate problems associated with inbreeding depression in the Florida panther, and I
mentioned that evidence suggests that the attempt was successful. I didn’t mention that
beyond the obvious concern that many conservationists have about manipulating populations
in this way, it isn’t always successful.
You may remember from your study of evolutionary biology that barriers to reproduction between species may arise as a result of hybrid breakdown. Hybrid breakdown occurs
when there are epistatic interactions among loci causing only certain combinations of alleles
at different loci to work well together. A phenomenon like hybrid breakdown can occur
when crosses are made between populations of the same species that have become differentially adapted — outbreeding depression. So there’s the risk that in attempting to alleviate
problems associated with inbreeding depression, conservation managers could introduce new
problems associated with outbreeding depression.
The resulting advice is pretty simple in principle, if difficult to put into practice:
“[M]anagers can minimize the risks of both inbreeding and outbreeding by using intentional
hybridization only for populations clearly suffering from inbreeding depression, maximizing
the genetic and adaptive similarity between populations, and testing the effects of hybridization for at least two generations whenever possible” [3, p. 463].14
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14
For a more recent analysis, see [4] for a more recent meta-analysis arguing that we may have been
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13
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