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Extinction. Bruce Walsh [email protected] 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. - PowerPoint PPT Presentation
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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
Aaaaaa
Aa
AA
Aa AAAa
Aaaaaa
Aa
AA
Aa
No differences between populations, Fst = 0
AAAa
Aaaaaa
Aa
AA
Aa BaAa
AabbBB
Aa
AA
Aa
Some differences between populations, Fst > 0
AAAa
Aaaaaa
Aa
AA
Aa BBcc
BcbbBB
bb
cc
Bc
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.