mattsson et al lbwo pva v2
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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
Ye
ars
to
ext
inct
ion
0
10
20
30
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90
100
Scenario
Better-case Worse-case
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Ye
ars
to
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inct
ion
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Scenario
Better-case Worse-case
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95th
75th
50th
25th
5th
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
0.02
0.04
0.06
0.08
0.10
0.12
0 5 10 15 20 25 30
Initial number of adults
Pre
dic
ted
ex
tin
cti
on
ra
te
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
dic
ted
ex
tin
cti
on
ra
te
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
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0 5 10 15 20 25 30
Initial number of adults
Pre
dic
ted
ext
inct
ion
rat
e
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0 5 10 15 20 25 30
Initial number of adults
Pre
dic
ted
ex
tin
cti
on
ra
te
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
ge
in e
xtin
ctio
n r
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
an
ch
an
ge
in e
xti
nc
tio
n r
ate
Results: Allee EffectResults: Allee Effect
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Allee effect Initial no. adults Annual adult survival
0.14 1 0.008
Mea
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