Extinction

Bruce Walshjbwalsh@u.arizona.edu

Dept. Ecology & Evolutionary Biology

University of Arizona

Outline• Death & Destruction: Mass extinctions• Extinction: Basic Ecology Theory• Genetic Extinction Risks• Tools for Assessing extinction risk• Management strategies to mitigate

risk

Greatest Hits: Mass ExtinctionsRoughly 2 BYA: Most of life on earth wiped out due to pollution (O2)Permian Mass extinction 250 MYA 90 - 95% of marinespecies became extinct

K-T (Cretaceous) Event 65 MYA 85% of all species became extinct

End-Ice-Age Mass Extinction (10 TYA)

Current on-going mass extinction.

Causes these mass extinctionsMassive environmental perturbation

Extra-terrestrial impactsVolcanoes

Climate changeBiological agents

Comet Shoemaker- Levy 9 July 1994

Impact size if S-L 9 had hitEarth (12+ such impacts!)

Permian, K-T extinctionsShow strong signals ofimpacts (iridium layer,shock quartz, other signals)

Climate change following impact event

Toba extinction event. 75,000 YA

Toba, Sumatra, Indonesia

Toba Caldera energy release about one gigaton of TNT 3000 times greater than Mount St. Helens

Led to a decrease in average global temperatures by 3 to 3.5 degrees Celsius for several years

Believed to have created population bottlenecksin the various homo species that existed atthe timeEventually leading to the extinction of all the other homo species except for the branch that became modern humans

Most recent mass extinctions likely human -induced (at least in part)

End of ice-age (Quaternary , Holocene) extinctions

Many believe we are in “the sixth great mass extinction”

Extinction of most the the NA/SA mega-fauna

Paul Martin’s notion: hunted to extinction by manOthers argue for climatic causes

Most likely a synergistic interaction between both

Extinction: Ecological Factors

Small population size

Declining habitat

Changes in other species in the ecosystems

DiseaseWhat species will save eastern forest wildflowers?

Ecological Theory of Extinction

MacArthur-Wilson Theory of Island Biogeography

Metapopulation dynamics

Demographic Stochasticity

MacArthur-Wilson Island Biogeography (1967)

Interested in predicting species numberson islands

Numbers represent a balance betweenextinction and immigrationPrediction: lower extinction rateon larger islands

Prediction: higher immigration rateson islands closer to mainland

Size does matter: Species-area curves

Log(S) = a + z*log(A)S = bAz

Key is species-area exponent z

One of MacArthur & Wilson’s key observation was the species-area curve, predicting the number of species S simply from area A.

S (mammals) = 1.188A0.326

S (birds) = 2.526A0.165

Implications of species-area curvesS = bAz

Key is species-area exponent z

Suppose area cut in half, equilibrium prediction S* = b(A/2) z

S*/S = b(A/2)z / b(A)z = (A/2A)z = (1/2)z

In theory, one could predict numberof species lost given a change in area

93% left z = 0.187% left z = 0.281% left z = 0.376% left z = 0.4

This looks somewhat hopefully, as lose some species, but not 50%

Flip side of this:

Suppose you are designing a reserve and want toconvince policy makers to either double or quadruplethe current reserve size. How many more species willbe added?

2A 4A z107% 115% 0.1115% 132% 0.2123% 151% 0.3131% 174% 0.4

Complications

Species-area slope (z): between islands vs. patches within an island

Even if species-area curve exact, only tells us how many species will be lost, NOT which particular ones

Nested-set analysis: Look over our “island” to see ifspecies are randomly lost or if some have a greater thanaverage chance of being lost

Non-equilibrium Island Biogeography

When isolation is increased, the island is no longer in equilibrium and the number of species is expected to decline

Hence, loss of species on ever-isolated islands is expected

Application to conservation biology

Isolated patches of habitats are essentially islands

Need to maximize patch size

Need to maximize exchange between patches

Risk of disease/pathogens spreadingPatches are sufficiently genetically different

When should you NOT maximize exchange?

Meta-population AnalysisEssentially island biogeography with no mainland toserve as a source for immigrants

The metapopulation structure assumes the populationis distributed as a series of discrete, largely isolated,patches

Extinction occurs within a patch, and that patch remainsempty until re-colonized by immigrants from other patches

At any time, not all patches are occupied.

The population persists by being able to colonize patchesbefore all go extinct.

Meta-population Structure

Yellow = species presentblue = species absent

Sources and SinksKey features of the metapopulation modelEmpty patches of habitat are still critical

An occupied patch can either be a source or a sinkIn a source, the long-term growth rate is positive and thispatch contributes immigrants to other (potentially empty) patchesIn a sink, that patch simply absorbs immigrants, and has a net negative growth rate.

Cannot tell a source from a sink without long term studies,esp. involving population movement

Counting species numbersSuppose you are trying to estimate the number of species(say moths) in a patch. You have done a number of surveysand have recorded a total of S species

S is clearly an underestimate for the actual number T ofspecies that use the patch. How can we estimate this?

Simple jackknife estimator: Our estimate of T isjust S + number species seen on just one sampling period

For example, if we have seen 250 species, 40 of which we only seen in one sampling period, our estimate of T is 250 + 40 = 290.

Departures from the metapopulation modelCore-satellite case. A central core source population, with all other patches being sinks.

Patchy population case: Even though the population hasa patchy distribution, dispersal events are too frequent toallow for extinctions. Here individual patches support partsof a single population (as opposed to the metapopulationstructure, where each population is largely separate)

Declining population case: Here each subpopulation isa sink, so that the entire population is on its way toextinction.

Key implications from metapopulation model

A static snapshot of the population distribution isvery misleading

Currently unoccupied habitat may be critical for future success

An occupied habitat may in fact be a sink, so setting only this area aside as the reserve will doom the species

With human intervention, even sink populations are critical,as these can serve as sources to export to currently unoccupied patches

Demographic Stochasticity

Simplest model (but a classic) is due is Ludwig (1971).

Random fluctuations of birth and death rates canlead to extinction, even in a population with a positivegrowth rate

The net growth rate r is the birth rate (b) minus the death rate (d), r = b - d

P =8<:

1 °µd

b∂n0

b> d0 b< d

( )no = starting size, P = probability of persistence

100010010.001

.01

.1

1

Starting Population Size

Prob(extinction)

b/d = 1.01

b/d = 1.1

b/d = 1.2

Ludwig’s model assumes that the population, if it persists, will growth without limit.

More generally, all populations are finite, and hence all (given enough time) will go extinct

As a result, one often tried to estimate the expected time to extinction

Such times generally tend to be exponentially distributed

Pr(extinction time < t) = 1 - Exp[-t/T(n)] where T(n) is the mean extinction time

Ludwig’s model shows that even a population underpositive exponential growth can still go extinct

Prob of extinction given mean time T to extinction

T = 100 yrs

T = 200 yrs

T = 500 yrs

25 years 22.1% 11.8% 4.9%

50 years 39.3% 22.1% 9.5%

100 years 63.2% 39.3% 18.1%

200 years 86.5% 63.2% 33.0%

500 years 99.3% 91.8% 63.2%

Genetic Extinction Risks

Inbreeding depression

Effective Population size

Insufficient Genetic Variation to response

Genetic measures of subpopulation isolation

Inbreeding depressionReduction in population fitness due to inbreeding(mating of relatives)

Measure of the strength of inbreeding is the inbreeding coefficient, F = Prob(both allelesin an individual are identical by descent)

In a finite population, F increases each generation, as F(t+1) = 1/(2N) + [1-1/(2N)]*F(t)

Once your population has a non-zero F value, youare stuck with it, EVEN IF THE POPULATIONGROWS

Changes in the mean under inbreeding

F = 0 - 2Fpqd

Using the genotypic frequencies under inbreeding, the population mean F under a level of inbreeding F isrelated to the mean 0 under random mating by

Genotypes A1A1 A1A2 A2A2 trait value 0 a+d 2aFreq p2 + Fpq (1-F)2pq q2 + Fpq

freq(A1) = p, freq(A2) = q

Increase in homozygotes, decrease in heterozygotes

For k loci, the change in mean isπF=π0°2FkXi=1piqidi=π0°BFHere B is the reduction in mean under complete inbreeding (F=1) , whereB=2Xpiqidi

Inbreeding Depression and Fitness traits

Inbred Outbred

Define ID = 1-F/0 = 1-(0-B)/0 = B/0

Drosophila Trait Lab-measured ID = B/0

Viability 0.442 (0.66, 0.57, 0.48, 0.44, 0.06)Female fertility 0.417 (0.81, 0.35, 0.18)Female reproductive rate 0.603 (0.96, 0.57, 0.56, 0.32)Male mating ability 0.773 (0.92, 0.76, 0.52)Competitive ability 0.905 (0.97, 0.84)Male fertility 0.11 (0.22, 0)Male longevity 0.18Male weight 0.085 (0.1, 0.07)Female weight -0.10Abdominal bristles 0.077 (0.06, 0.05, 0)Sternopleural bristles -.005 (-0.001, 0)Wing length 0.02 (0.03, 0.01)Thorax length 0.02

Estimating BIn many cases, lines cannot be completely inbred due to either time constraints and/or because in many species lines near complete inbreeding are nonviable

In such cases, estimate B from the regression of F on F,

F = 0 - BF

0

0

1

0 - B

F

F

Estimating FSuppose you have a population under study for listing.How can you estimate the amount of inbreeding ithas suffered?

Key: Freq(Heterozygotes) = (1-F)2pq

F = 1 - Observed freq(Heterozygotes)

HW freq(Heterozygotes)

Why do traits associated with fitness show inbreeding depression?

• Two competing hypotheses:– Overdominance Hypothesis: Genetic variance for fitness is

caused by loci at which heterozygotes are more fit than both homozygotes. Inbreeding decreases the frequency of heterozygotes, increases the frequency of homozygotes, so fitness is reduced.

– Dominance Hypothesis: Genetic variance for fitness is caused by rare deleterious alleles that are recessive or partly recessive; such alleles persist in populations because of recurrent mutation. Most copies of deleterious alleles in the base population are in heterozygotes. Inbreeding increases the frequency of homozygotes for deleterious alleles, so fitness is reduced.

Purging Inbreeding Depression

If inbreeding depression is caused by deleteriousrecessives, it may be possible to purge lines ofthese alleles, provided they are not yet fixed.

Strategies have been proposed (expand population andinbred) to attempt to purge captive populations ofinbreeding depression, but these remain controversial

Natural populations that historically have had smallpopulations may have already purged themselves (toat least some degree) of inbreeding depression. Otherwisethey likely would have already gone extinct.

Effective Population size, NeWhen the population is not ideal (changes over time,unequal sex ratio, uneven contribution from individuals),we can still compute an effective population size Newhich gives the size of an ideal population that behavesthe same as our population

We will consider Ne under population bottlenecks unequal sex ratio unequal contribution for all individuals

Ne under varying population sizeIf the actual population size varies over time, theeffective population size is highly skewed towardsthe smallest value

If the populations sizes have been N(1), N(2), …, N(k),the effective population size is given by the harmonic mean

Suppose the population sizesare 10000, 10000, 10000, 100.

Ne becomes 399

Ne = kkX

i=1

1N(i)

Ne under unequal sex ratios

Ne = 4Nm¢N fNm + N f

*

When there are different number of males (Nm) andfemales (Nf), the effective population size is skewedtowards the rarer sex

For example, suppose we used 2 male salmon to fertilizethe eggs of 1000 females. What is Ne in this case?

Ne = (4*2*1000)/(2 + 1000) = 8

Ne under unequal individualcontributions

Not all individuals contribute equally to the nextgeneration. What effect does this have on Ne?

Ne ' 2Næ2

O=2+1

Let 20 be the variance in offspring number for

individuals in the population, then

If contributions follow a Poisson with a mean of2 offspring per parent (male + female replace eachother), then 2

0 =2, and Ne = N

If all individuals contribute EXACTLY the samenumber of offspring, 2

0 =0, and Ne = 2N, so thatthe effective pop size is twice the actual size

In a survey of reproductive success in birds, Grantfound that 2

0/2 ranged from 1.2 to 4.2, giving anNe of only 40 - 90% of the actual number of females

Insufficient Genetic VariationAnother genetic risk factor for the extinction ofsmall populations is their lack of genetic variation.This is related to, but separate from, inbreedingdepression

If all members of the population are geneticallyvery similar, the wrong disease or pathogen can sweepthrough the population

Another issues is that unless the genetic variation issufficiently large, the population will be unable to response to changes in the environment.

Heritability and response to selection

The expected selection response R (change in mean) ina trait under selection is given by the breeders’ equationR = h2 SHere S is the within-generation change in the meanand h2 the heritability of the trait (runs from 0 - 1,typical value around 0.2 - 0.4)

In small populations, inbreeding reduces the heritability,retarding the rate of selection response

h2t = h2

01 ° Ft

1 ° h20 Ft

--

Effect of smaller h2

Suppose a period of excessive heat selects for smallerbody size.

Mean body size before heat stress was 10cm, while the mean of the heat survivors was 6cm, giving S = 6-10 = -4If h2, then the response is 0, with the next generationhaving the same size as the prior generation (beforeselection)

If h2 =0.05, R = h2 S = 0.05*(-4) = -0.2. Hence, the meanBody size in the next generation is 0.2cm smaller.If h2 =0.4 (typical body size value), R = h2 S = 0.4*(-4) = -1.6., so that the mean body size in the next generation is 1.6cm smaller.

Unless response is sufficiently large, the populationcannot track this environmental change and can goextinct.

Genetic measures of subpopulation isolation

Knowledge of the amount of genetic differentiation between (apparently) isolated populations is critical

If sufficiently distinct, need to treat populationsas separate entities

If sufficiently similar, metapopulation approach can be considered

Molecular Genetic markersSTRs (microsatellites). These are highly polymorphic markers whose alleles are simply repeats of a basic unit, e.g. a 3 is AGAGAG, a 4 is AGAGAGAG.

mtDNA markers. The mitochondrial genomeis maternally inherited (only passed ontooffspring from the mother.

Wright’s Fst

Suppose we have two (or more) populations. We can partition the total variation into the fraction withineach population and the fraction due to between-population differences. The later is Wright’s Fst

One standard measure of genetic differentiationbetween populations using the allele frequenciesat molecular markers is Wrights’ Fst statistic

A small Fst value implies very little genetic differentationbetween populations.

AAAa

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Aa

AA

Aa AAAa

Aaaaaa

Aa

AA

Aa

No differences between populations, Fst = 0

AAAa

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Aa

AA

Aa BaAa

AabbBB

Aa

AA

Aa

Some differences between populations, Fst > 0

AAAa

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Aa BBcc

BcbbBB

bb

cc

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Major differences between populations, Fst near(not one, as there is also some variation within eachPopulation, and Fst = between different/total variation

Caveats with using Fst (and other measures)

Fst is a measure of the amount of time that populationshave been separated

This may be very poorly correlated with the amountof adaptive genetic differences between populations

The markers used to compute Fst are specifically chosento be neutral (not under selection), and while theynicely capture time of separation, they DO NOT capturefraction of adaptive change

Inferring Population Structure: A cautionary

taleBowen et al used molecular markers to look atPopulation structure of loggerhead turtles on the East coast of the US.

Autosomal microsatellites showed no population structure

mtDNA showed strong population structure

Females home faithfully to their natal nesting colony, butmales migrate between nesting colonies.

Tools for Assessing extinction risk

Population Viability Analysis, PVA

Sample Model: Leslie Matrices

Comparing PVAs

Minimal viable population, MVP

“Make things as simple as possible, but no simpler” --- Albert Einstein

“No theory should fit all of the facts, because some ofthe facts are wrong” --- Niels Bohr

“To be perfectly intelligible, one must be Inaccurate.

To be perfectly accurate, one must be Unintelligible” --- Bertrand Russell

Words of wisdom regarding theory and modeling

Population Viability Analysis, PVA

Basically, a PVA is a model, often complex, that attemptsto incorporate the ecological and genetic risk factors toobtain a probability (or mean time) of extinction.

Population size (effects on demographic stochasiticity,inbreeding, standing levels of genetic variation)

Demographic parameters (stage-specific birth & deathrates, population carrying capacity)

Population structure, geometry patches and their connectiveness

Sample Model: Leslie Matrices

As an example of some of the complexities introducedinto a PVA, we consider the simplest model withage structure, a Leslie (or projection) matrix.

Populations have an age structure. Different agegroups (on average) likely produce different numbersof offspring. Likewise, different age groups likelyhave different probabilities of surviving into the nextage class.

A Leslie matrix model allows us to model theseage-class differences in viability and fecundity

Denote the numbers in the k age classes at time tby the vector n(t)

n(t) =

0BB@

n1(t)n2(t)

...nk(t)

1CCA

Number in class 1

Survival ni+1(t +1) = vini(t)

Number in class i+1 in next time periodNumber in class i in current time periodSurvival probability for state iBirth: Age class 1 is new-borns. Let bi be the averageNumber of offspring born to individuals in age class i

n1(t +1) =b1n1(t) +b2n2(t) +¢¢¢+bknk(t) =kX

i=1bi ni(t)

Number of offspring from age class 2

We can put these birth and death parameters into matrix form. For the matrix P, let the element in the ith row and jth column be the transition from class j into class i

P =

0BBBBBB@

b1 b2 b3 ¢¢¢ bk °1 bkv1 0 0 ¢¢¢ 0 00 v2 0 ¢¢¢ 0 00 0 v3 ¢¢¢ 0 0... ... ... ... ... ...0 0 0 ¢¢¢ vk °1 0

1CCCCCCA

-

-Row 3, column 2 = moving from class 2 to class 3. This occurs by surviving class 2, v2

Row 1, column 3 = contribution to class 1 from class 3. Occurs by age class 3 individuals having offspring, b3

n(t+1) = P n(t)

n(t) = Pt n(0)

Numbers of individuals in the age classes in time t+1given by matrix multiplication

Numbers in time t, given starting values, n(0), given by

If largest eigenvalue of P > 1, population grows, otherwiseit goes extinct.

Deterministic analysis -- allows for no random effects

Adding random sampling (stochasitty) to demographicparameters

Viability (survival) drawn from a binomial distribution, survive from i to i+1 w.p. vi, w.p. 1-vi don’t survive

Offspring number drawn from a Poisson distribution

For example, if n individuals in stage i, probability ksurvive to stage i + 1 is

Pr(k offspring) = bik Exp(-bi)/k!

n!/[ (n-k)! k! ] vi k (1- vi) n-k

Building up a complex model

A typical model might have a metapopulation structure

Within each population, dynamics given by a stochastic Leslie matrix

Migration then occurs between subpopulations

Model is run with a set of parameters to generate aprobability of extinction or a time to extinction

Comparing (and defending) PVAs

A PVA is an attempt to model a complex process,typically with very incomplete (and potentialrather inaccurate) data.

This is done in an environment wherein the results ofjust above any PVA are likely to be challenged for being both an underestimate AND an overestimate of the risk.

Besides using “the best possible data” (the legal mandate) what else can be done to support thefindings of a PVA?

Any analysis should examine the sensitivity ofthe modeling assumptions --- if we make smallchanges in the parameters, how robust areour findings?

Besides examining sensitivity of the parameters,one also needs to examine the sensitivity of thegeneral structure of the model. For example, in an assumed population structure, what happensif we change a 0 value of immigration betweentwo demes to some very small number?

Any result (time or probability of extinction) should(at a minimum) be reported as a confidence intervalrather than a point estimate.

Bayesian posterior distributions: combining sensitivity analysis and confidence intervals

A scientifically, and statistically, justifiable approachthat jointly deals with BOTH model sensitivityand model outcome uncertainty is offered bygenerating a Bayesian posterior distribution for thePVA parameter of interest.

One can also use this approach to justifiably contrast the PVAs under two different actions (for example, before and after building a campground) to formalize the impact of a proposed project/action

One has prior distributions for model parameters (suchas viability and fecundity). These distribution can reflectstatistical uncertainty in the estimation of the modelparameters and/or any any prior assumptions we haveabout these distribution

One them samples a vector of the model parametersfrom the distribution, using these values in a PVA togenerate a summary statistic. Repeat this samplingfollowed by generating a PVA value several thousand times

The net result is a posterior distribution of the PVAsummary statistic that reflects both model uncertaintyand also incorporates a sensitivity analysis.

Minimal viable population, MVP

A closely-related approach to PVA is a minimalviable population size (and structure when a metapopulation is assumed

One can obtain this by setting some criteria for viability(e.g., > 80% probability of not being extinct in 300 year)and then running different population sizes (and potentially population structures) through a PVA toestimate this value.

Management strategies to mitigate risk

The major take-home points from the Ecologicaland genetic theory are as follows:

Larger N, the better. This usually means a largerarea.

Even populations with a large N can be doomed becauseof lack of genetic variation from previous events

In such cases, crosses to closely related populationsmight be considered. Fst values may help here

Population structure is critical

Currently empty patches of habitat may still becritical

Patches can be sinks or sources, and it is critical tobe able to distinguish between these. Takes long-termdata.

The habitat between patches may also be very criticalto species success

Bottom line: Need dynamic management, constantlyupdating a survival strategy as new information isObtained. This needs to be built into a PVA.