A Stochastic Population A Stochastic Population Viability Analysis for Rare Viability Analysis for Rare

Large-bodied Woodpeckers…Large-bodied Woodpeckers…

with Implications for the Ivory-billed with Implications for the Ivory-billed WoodpeckerWoodpecker

B. J. Mattsson, R. S. Mordecai, M. J. Conroy, J. T. B. J. Mattsson, R. S. Mordecai, M. J. Conroy, J. T. Peterson, R. J. Cooper, & H. ChristensenPeterson, R. J. Cooper, & H. Christensen

Warnell School of Forestry & Natural ResourcesWarnell School of Forestry & Natural ResourcesUniversity of Georgia, AthensUniversity of Georgia, Athens

Not-So-Large-Bodied Not-So-Large-Bodied OutlineOutline

Small population paradigmSmall population paradigm

Tour of focal species (LBWOs)Tour of focal species (LBWOs)

Study goals & objectivesStudy goals & objectives

Population model developmentPopulation model development

Findings and implicationsFindings and implications

Small Population ParadigmSmall Population Paradigm Populations with few individuals Populations with few individuals

suffer:suffer: High inbreeding depressionHigh inbreeding depression Low genetic variationLow genetic variation Increased value to collectorsIncreased value to collectors Mate finding difficultMate finding difficult More susceptible to stochastic eventsMore susceptible to stochastic events

Extinction more likely in smaller than Extinction more likely in smaller than in larger populationsin larger populations

Does this assumption hold for LBWOs?Does this assumption hold for LBWOs?

Helmeted Woodpecker Helmeted Woodpecker Dryocopus galeatusDryocopus galeatus

Black-bodied Woodpecker Black-bodied Woodpecker Dryocopus shulziDryocopus shulzi

Guayaquil Woodpecker Guayaquil Woodpecker Campephilus gayaquilensis

Imperial Woodpecker Imperial Woodpecker Campephilus imperialisCampephilus imperialis

Andaman Woodpecker Andaman Woodpecker Dryocopus hodgeiDryocopus hodgei

Ivory-billed Woodpecker Ivory-billed Woodpecker Campephilus principalisCampephilus principalis

Specific ObjectivesSpecific Objectives

1.1. Predict years to extinction under two Predict years to extinction under two scenarios for demographic rates and scenarios for demographic rates and population sizepopulation size

2.2. Assess relative influence of population Assess relative influence of population size, demographic rates, and their size, demographic rates, and their interactions for predicting extinction rateinteractions for predicting extinction rate

3.3. Evaluate possibility that small Evaluate possibility that small populations of populations of CampephilusCampephilus woodpecker woodpecker species may have persisted until modern species may have persisted until modern timestimes

Population Model SummaryPopulation Model Summary SimpleSimple: sparse data available for LBWOs: sparse data available for LBWOs

Single-populationSingle-population: no “rescue effect”: no “rescue effect”

DiscreteDiscrete: non-deterministic: non-deterministic

Stage-basedStage-based: juvenile and adult (females : juvenile and adult (females only)only)

StochasticStochastic: survival and fecundity vary : survival and fecundity vary annuallyannually

Population Model FlowchartPopulation Model Flowchart

♀

t = t + 1 t ≤ 100? END

Femalei

Nadst+1 = Nadst + Njvst

Juvenile produced?

P(jvs)

Adult survives?

B(ads)

START: Year = t

Tally no. adults (Nadst)

Tally no. juveniles produced

(Njvst)

Model Inputs and OutputModel Inputs and Output

Initial number of adultsInitial number of adults (N (N00)) Demographic rates and variances:Demographic rates and variances:

Fecundity (F): juveniles per adultFecundity (F): juveniles per adult Annual adult survival rate (SAnnual adult survival rate (Saa))

Two parameters for Allee effect:Two parameters for Allee effect: 00: Intercept: Intercept 11: Slope: Slope

Probability of Extinction (E):Probability of Extinction (E):Proportion of iterations where NProportion of iterations where Nt t = 0= 0

Allee Effect (Allee Effect (0, 0, 11))

-10,1.5

-7,3.25

-4,5

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12

No. adults in a given year

Pro

bab

ility

of

bre

edin

g .

Model AssumptionsModel Assumptions

1.1. Juveniles reproduce in year following Juveniles reproduce in year following hatch yearhatch year

2.2. Expected demographic rates & Expected demographic rates & variances constant, but realized variances constant, but realized values can vary each year ( Fvalues can vary each year ( Ft t , S, Sat at ))

3.3. Demographic rates independent of Demographic rates independent of themselves and of population densitythemselves and of population density

4.4. Annual juvenile survival rate = ½ Annual juvenile survival rate = ½ adult survival rateadult survival rate

5.5. NNtt ≤ ≤ 5050

Model ParameterizationModel Parameterization

NN00 :: 55 – – 30 30 (Tanner 1942)(Tanner 1942)

FF : : 0.670.67 – – 1.651.65 [[0.00220.0022 – – 0.0510.051]]

(Tanner 1942, Bonar 2001, Mattsson & Christensen (Tanner 1942, Bonar 2001, Mattsson & Christensen unpubl.)unpubl.)

SSa a : : 0.70.7 – – 0.9 0.9 [[0.00760.0076 – – 0.0960.096]]

(Bonar 2001, Mattsson & Christensen unpubl.)(Bonar 2001, Mattsson & Christensen unpubl.)

Analysis: OverviewAnalysis: Overview

Years of persistenceYears of persistence No Allee effectNo Allee effect Worse-case scenario:Worse-case scenario:

Low NLow N00

Low mean demographic ratesLow mean demographic rates High variance in demographic ratesHigh variance in demographic rates

Better-case scenario: intermediate Better-case scenario: intermediate valuesvalues

Results: Years to ExtinctionResults: Years to Extinction

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95th

75th

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200 iterations

Analysis: OverviewAnalysis: Overview Years of persistenceYears of persistence

No Allee effectNo Allee effect Worse-case scenario: Worse-case scenario:

Low NLow N00

Low mean demographic ratesLow mean demographic rates High variance in demographic ratesHigh variance in demographic rates

Better-case scenario: intermediate Better-case scenario: intermediate valuesvalues

Perturbation analysisPerturbation analysis All combinations of input valuesAll combinations of input values Response of predicted extinction rateResponse of predicted extinction rate

Perturbation AnalysisPerturbation Analysis One analysis per set of assumptionsOne analysis per set of assumptions 3 focal input values3 focal input values

NN0 0

2 demographic parameters 2 demographic parameters (means, variances, and/or Allee Effect)(means, variances, and/or Allee Effect)

3 increments per input parameter:3 increments per input parameter:low, intermediate, highlow, intermediate, high

3333 = 27 possible combinations of values = 27 possible combinations of values 200 independent iterations per analysis200 independent iterations per analysis

Perturbation Analysis ctd.Perturbation Analysis ctd.

1.1. Life history variationLife history variation Intermediate variances for demographic ratesIntermediate variances for demographic rates Vary means for demographic ratesVary means for demographic rates

Results: Life History Results: Life History VariationVariation

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 5 10 15 20 25 30

High survival, low fecund.All midpt.Low survival, high fecund.

0.00

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Initial number of adults

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Also, but not shown:

• High survival, high fecundity

• Midpt. survival, high fecundity

• High survival, midpt. fecundity

Perturbation Analysis ctd.Perturbation Analysis ctd.

1.1. Life history variation Life history variation Intermediate variances for demographic ratesIntermediate variances for demographic rates Vary means for demographic ratesVary means for demographic rates

2.2. Variation in environmental stochasticity Variation in environmental stochasticity Intermediate means for demographic ratesIntermediate means for demographic rates Vary variances for demographic ratesVary variances for demographic rates

3.3. Variation in Allee effectVariation in Allee effect Intermediate variances for demographic rates Intermediate variances for demographic rates Vary mean survivalVary mean survival Intermediate mean number of juvenilesIntermediate mean number of juveniles Vary FVary Ftt (probability of breeding) based on N (probability of breeding) based on Ntt

Allee Effect ExposedAllee Effect Exposed

♀

t = t + 1 t ? 100? END

Femalei

Nadst+1 = Nadst + Njvst

Juvenile produced?

P(jvs)

Adult survives?

B(ads)

START: Year = t

Tally no. adults (Nadst)

Tally no. juveniles produced

(Njvst)Constant

Positive feedback: Improved mate

finding

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0 5 10 15 20 25 30

Initial number of adults

Pre

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Results: Allee EffectResults: Allee Effect

Also, but not shown:

• Midpt. survival, high Allee

• High survival, midpt. Allee

• High survival, low Allee

Requirements for Requirements for PersistencePersistence

Persistence: E ≤ 0.05Persistence: E ≤ 0.05

SSaa ≥ 0.8 & F ≥ 1.16 (across other values) ≥ 0.8 & F ≥ 1.16 (across other values)

NN0 0 ≥ 5 as long as better-case scenarios for ≥ 5 as long as better-case scenarios for other parameters other parameters

NN0 0 5 to 30 --> E > 0.05 to E ≤ 0.05 (across 5 to 30 --> E > 0.05 to E ≤ 0.05 (across other values) only when Allee effect was other values) only when Allee effect was present & Spresent & Saa ≥ 0.8 ≥ 0.8

Small Population ParadigmSmall Population Paradigm Populations with few individuals Populations with few individuals

suffer:suffer: High inbreeding depressionHigh inbreeding depression Low genetic variationLow genetic variation Increased value to collectorsIncreased value to collectors Mate finding difficultMate finding difficult More susceptible to stochastic eventsMore susceptible to stochastic events

Extinction more likely in smaller than Extinction more likely in smaller than in larger populationsin larger populations

Does this assumption hold for LBWOs? Does this assumption hold for LBWOs?

So, When Does Size Matter?So, When Does Size Matter?

When Allee effect is present:When Allee effect is present:When survival is at least intermediate When survival is at least intermediate

(variances held intermediate)(variances held intermediate) When Allee effect is absent:When Allee effect is absent:

When survival is high and fecundity is low When survival is high and fecundity is low (variances held intermediate)(variances held intermediate)

NOT when demographic variances NOT when demographic variances allowed to varyallowed to varyEnvironmental stochasticity swamps out Environmental stochasticity swamps out

NN00

A New, Demographic A New, Demographic Robustness Paradigm?Robustness Paradigm?

Moderate-high demographic rates ensure Moderate-high demographic rates ensure persistence of small populations despite persistence of small populations despite

moderate environmental stochasticity and moderate environmental stochasticity and Allee effectAllee effect

Could they have survived?Could they have survived? NN00 ≥ 5 would have ensured persistence if… ≥ 5 would have ensured persistence if…

F ≥ 1.1, SF ≥ 1.1, Saa ≥ 0.8, ≥ 0.8, variance in F ≤ 0.04, variance in Svariance in F ≤ 0.04, variance in Saa ≤ 0.016 ≤ 0.016

NN0 0 ≥ 30 would have ensured persistence…≥ 30 would have ensured persistence… despite a relatively strong Allee effect, despite a relatively strong Allee effect, if variance in Sif variance in Saa ≤ 0.016, & either F ≥ 1.65 or S ≤ 0.016, & either F ≥ 1.65 or Saa

≥ 0.9≥ 0.9 ~24 IBWOs remained in 1930s, but ~24 IBWOs remained in 1930s, but

demographic rates have remained demographic rates have remained virtually unknownvirtually unknown

Predicted Fate of Rare Predicted Fate of Rare LBWOsLBWOs

Under worse-case scenario of low Under worse-case scenario of low demographic rates & high demographic rates & high environmental stochasticity, environmental stochasticity, extinction <10 years (2-33)extinction <10 years (2-33)

Maintaining intermediate (or Maintaining intermediate (or greater) demographic rates confer greater) demographic rates confer persistence, even with small initial persistence, even with small initial population size (5)population size (5)

Speculations From FindingsSpeculations From Findings Could imply that habitat quality, rather Could imply that habitat quality, rather

than quantity, ensures persistence of than quantity, ensures persistence of LBWOsLBWOs

Promote habitat management that Promote habitat management that improves reproduction and survival improves reproduction and survival rather than expansion of “suitable” rather than expansion of “suitable” habitathabitat

Build it, and they may not come?Build it, and they may not come?

Next StepsNext Steps

Demographic data needed to further Demographic data needed to further calibrate our population modelcalibrate our population model

Occupancy data currently being Occupancy data currently being collected and analyzed can easily be collected and analyzed can easily be incorporated and improve our incorporated and improve our population modelpopulation model

Thank YouThank You

FundingFunding U.S. Fish and Wildlife ServiceU.S. Fish and Wildlife Service U.S. Geological SurveyU.S. Geological Survey

Insights and suggestionsInsights and suggestions Fellow “Skunk Apes”: C. T. Moore, J. P. Fellow “Skunk Apes”: C. T. Moore, J. P.

Runge, K. W. StodolaRunge, K. W. Stodola S. R. BeissingerS. R. Beissinger B. R. NoonB. R. Noon J. RolstadJ. Rolstad

Clutch Size & SurvivalClutch Size & Survival

S & C from same study

Clutch Size & SurvivalClutch Size & Survival

Clutch Size & SurvivalClutch Size & Survival

Clutch Size & SurvivalClutch Size & Survival

Perturbation Analysis Perturbation Analysis OverviewOverview

1.1. Life history variationLife history variation Intermediate variances for demographic ratesIntermediate variances for demographic rates Vary means for demographic ratesVary means for demographic rates

2.2. Variation in environmental stochasticityVariation in environmental stochasticity Intermediate means for demographic ratesIntermediate means for demographic rates Vary variances for demographic ratesVary variances for demographic rates

3.3. Variation in Allee effectVariation in Allee effect Intermediate variances for demographic rates Intermediate variances for demographic rates Vary mean survivalVary mean survival Intermediate mean number of juvenilesIntermediate mean number of juveniles Vary FVary Ftt (probability of breeding) based on N (probability of breeding) based on Ntt

Perturbation Analysis Perturbation Analysis OverviewOverview

1.1. Life history variationLife history variation Intermediate variances for demographic ratesIntermediate variances for demographic rates Vary means for demographic ratesVary means for demographic rates

2.2. Variation in environmental stochasticityVariation in environmental stochasticity Intermediate means for demographic ratesIntermediate means for demographic rates Vary variances for demographic ratesVary variances for demographic rates

Results: Environmental Results: Environmental StochasticityStochasticity

0.00

0.01

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0 5 10 15 20 25 30

Initial number of adults

Pre

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Initial number of adults

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Var(fecundity) highAll at midpt.Var(fecundity) low

Perturbation Analysis ctd.Perturbation Analysis ctd.

Small changes in focal parametersSmall changes in focal parameters ( (ii)) i = or proportional to 1 initial adult = or proportional to 1 initial adult

NN0 0 range: 30 – 5 = 25; range: 30 – 5 = 25; NoNo = 25 / 25 = 1 = 25 / 25 = 1 SSaa range: .9 – .7 = .2; range: .9 – .7 = .2; SaSa = .2 / 25 = .008 = .2 / 25 = .008

Original parameter value (xOriginal parameter value (xi) -> E) -> Eii

xxii + + ii -> E -> Eii’’ Changes in extinction rates Changes in extinction rates ((EEii = E = Eii – E – Eii’)’) Mean Mean EEii across the 27 combinations across the 27 combinations

Population Model VolatilityPopulation Model Volatility Response of E to small changes of inputsResponse of E to small changes of inputs Most volatile under worse-case scenariosMost volatile under worse-case scenarios

Low survival and fecundityLow survival and fecundity High variance in survival and fecundity High variance in survival and fecundity Low NLow N00, high S, high Saa, and strong Allee effect , and strong Allee effect

Least volatile under better-case scenariosLeast volatile under better-case scenarios High survival or fecundity High survival or fecundity High NHigh N0 0 and low variance in Sand low variance in Saa

High NHigh N00, , ≥ ≥ intermediate Sintermediate Saa, & weak Allee effect , & weak Allee effect

NN00 + 1 --> average 0.4-3.2% reduction in E + 1 --> average 0.4-3.2% reduction in E

Results: Life History Results: Life History VariationVariation

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Initial no. adults Annual adult survival Fecundity

1 0.008 0.039

Mea

n c

han

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in e

xtin

ctio

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ate

Results: Environmental Results: Environmental StochasticityStochasticity

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Var(Fecundity) Initial no. adults Scale(Annual adultsurvival)

0.0089 1 0.0422

Me

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Results: Allee EffectResults: Allee Effect

0.00

0.01

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Allee effect Initial no. adults Annual adult survival

0.14 1 0.008

Mea

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