Mattsson et al lbwo pva v2

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  • If there was one word to describe the model we developed, it would be “simple”.
  • We have number of initial adults on X and predicted extinction rate on Y Each line represents one combination of input values that resulted in population persistence When survival and fecundity were at least intermediate, populations were likely to persist despite an initial population size of 5. Otherwise, populations were unlikely to persist.
  • We again have number of initial adults on X and predicted extinction rate on Y {Each line represents a combination of input values that resulted in population persistence} In contrast with life history variation where there was no Allee effect, here when initial population size dropped from 30 to 17, persistence became unlikely. This was only true, however, when survival was at least intermediate. When survival was low, even larger populations were unlikely to persist.
  • Mattsson et al lbwo pva v2

    1. 1. A Stochastic Population Viability Analysis for Rare Large-bodied Woodpeckers… with Implications for the Ivory-billed Woodpecker B. J. Mattsson, R. S. Mordecai, M. J. Conroy, J. T. Peterson, R. J. Cooper, & H. Christensen Warnell School of Forestry & Natural Resources University of Georgia, Athens
    2. 2. Not-So-Large-Bodied Outline <ul><li>Small population paradigm </li></ul><ul><li>Tour of focal species (LBWOs) </li></ul><ul><li>Study goals & objectives </li></ul><ul><li>Population model development </li></ul><ul><li>Findings and implications </li></ul>
    3. 3. Small Population Paradigm <ul><li>Populations with few individuals suffer: </li></ul><ul><ul><li>High inbreeding depression </li></ul></ul><ul><ul><li>Low genetic variation </li></ul></ul><ul><ul><li>Increased value to collectors </li></ul></ul><ul><ul><li>Mate finding difficult </li></ul></ul><ul><ul><li>More susceptible to stochastic events </li></ul></ul><ul><li>Extinction more likely in smaller than in larger populations </li></ul><ul><li>Does this assumption hold for LBWOs? </li></ul>
    4. 4. Helmeted Woodpecker Dryocopus galeatus
    5. 5. Black-bodied Woodpecker Dryocopus shulzi
    6. 6. Guayaquil Woodpecker Campephilus gayaquilensis
    7. 7. Imperial Woodpecker Campephilus imperialis
    8. 8. Andaman Woodpecker Dryocopus hodgei
    9. 9. Ivory-billed Woodpecker Campephilus principalis
    10. 10. Specific Objectives <ul><li>Predict years to extinction under two scenarios for demographic rates and population size </li></ul><ul><li>Assess relative influence of population size, demographic rates, and their interactions for predicting extinction rate </li></ul><ul><li>Evaluate possibility that small populations of Campephilus woodpecker species may have persisted until modern times </li></ul>
    11. 11. Population Model Summary <ul><li>Simple : sparse data available for LBWOs </li></ul><ul><li>Single-population : no “rescue effect” </li></ul><ul><li>Discrete : non-deterministic </li></ul><ul><li>Stage-based : juvenile and adult (females only) </li></ul><ul><li>Stochastic : survival and fecundity vary annually </li></ul>
    12. 12. Population Model Flowchart ♀
    13. 13. Model Inputs and Output <ul><li>Initial number of adults (N 0 ) </li></ul><ul><li>Demographic rates and variances: </li></ul><ul><ul><li>Fecundity (F): juveniles per adult </li></ul></ul><ul><ul><li>Annual adult survival rate (S a ) </li></ul></ul><ul><li>Two parameters for Allee effect: </li></ul><ul><ul><li> 0 : Intercept </li></ul></ul><ul><ul><li> 1 : Slope </li></ul></ul><ul><li>Probability of Extinction (E): </li></ul><ul><ul><li>Proportion of iterations where N t = 0 </li></ul></ul>
    14. 14. Allee Effect (  0,  1 )
    15. 15. Model Assumptions <ul><li>Juveniles reproduce in year following hatch year </li></ul><ul><li>Expected demographic rates & variances constant, but realized values can vary each year ( F t , S at ) </li></ul><ul><li>Demographic rates independent of themselves and of population density </li></ul><ul><li>Annual juvenile survival rate = ½ adult survival rate </li></ul><ul><li>N t ≤ 50 </li></ul>
    16. 16. Model Parameterization <ul><li>N 0 : 5 – 30 </li></ul><ul><li>(Tanner 1942) </li></ul><ul><li>F : 0.67 – 1.65 [ 0.0022 – 0.051 ] </li></ul><ul><li>(Tanner 1942, Bonar 2001, Mattsson & Christensen unpubl.) </li></ul><ul><li>S a : 0.7 – 0.9 [ 0.0076 – 0.096 ] </li></ul><ul><li>(Bonar 2001, Mattsson & Christensen unpubl.) </li></ul>
    17. 17. Analysis: Overview <ul><li>Years of persistence </li></ul><ul><ul><li>No Allee effect </li></ul></ul><ul><ul><li>Worse-case scenario: </li></ul></ul><ul><ul><ul><li>Low N 0 </li></ul></ul></ul><ul><ul><ul><li>Low mean demographic rates </li></ul></ul></ul><ul><ul><ul><li>High variance in demographic rates </li></ul></ul></ul><ul><ul><li>Better-case scenario: intermediate values </li></ul></ul>
    18. 18. Results: Years to Extinction 95 th 75 th 50 th 25 th 5 th 200 iterations
    19. 19. Analysis: Overview <ul><li>Years of persistence </li></ul><ul><ul><li>No Allee effect </li></ul></ul><ul><ul><li>Worse-case scenario: </li></ul></ul><ul><ul><ul><li>Low N 0 </li></ul></ul></ul><ul><ul><ul><li>Low mean demographic rates </li></ul></ul></ul><ul><ul><ul><li>High variance in demographic rates </li></ul></ul></ul><ul><ul><li>Better-case scenario: intermediate values </li></ul></ul><ul><li>Perturbation analysis </li></ul><ul><ul><li>All combinations of input values </li></ul></ul><ul><ul><li>Response of predicted extinction rate </li></ul></ul>
    20. 20. Perturbation Analysis <ul><li>One analysis per set of assumptions </li></ul><ul><li>3 focal input values </li></ul><ul><ul><li>N 0 </li></ul></ul><ul><ul><li>2 demographic parameters </li></ul></ul><ul><ul><ul><li>(means, variances, and/or Allee Effect) </li></ul></ul></ul><ul><li>3 increments per input parameter: </li></ul><ul><ul><li>low, intermediate, high </li></ul></ul><ul><li>3 3 = 27 possible combinations of values </li></ul><ul><li>200 independent iterations per analysis </li></ul>
    21. 21. Perturbation Analysis ctd. <ul><li>Life history variation </li></ul><ul><ul><li>Intermediate variances for demographic rates </li></ul></ul><ul><ul><li>Vary means for demographic rates </li></ul></ul>
    22. 22. Results: Life History Variation <ul><li>Also, but not shown: </li></ul><ul><ul><li>High survival, high fecundity </li></ul></ul><ul><ul><li>Midpt. survival, high fecundity </li></ul></ul><ul><ul><li>High survival, midpt. fecundity </li></ul></ul>
    23. 23. Perturbation Analysis ctd. <ul><li>Life history variation </li></ul><ul><ul><li>Intermediate variances for demographic rates </li></ul></ul><ul><ul><li>Vary means for demographic rates </li></ul></ul><ul><li>Variation in environmental stochasticity </li></ul><ul><ul><li>Intermediate means for demographic rates </li></ul></ul><ul><ul><li>Vary variances for demographic rates </li></ul></ul><ul><li>Variation in Allee effect </li></ul><ul><ul><li>Intermediate variances for demographic rates </li></ul></ul><ul><ul><li>Vary mean survival </li></ul></ul><ul><ul><li>Intermediate mean number of juveniles </li></ul></ul><ul><ul><li>Vary F t (probability of breeding) based on N t </li></ul></ul>
    24. 24. Allee Effect Exposed ♀ Constant Positive feedback: Improved mate finding t = t + 1 t ? 100? END Female i Nads t+1 = Nads t + Njvs t Juvenile produced? P(jvs ) Adult survives? B(ads ) START: Year = t Tally no. adults ( Nads t ) Tally no. juveniles produced ( Njvs t )
    25. 25. Results: Allee Effect <ul><li>Also, but not shown: </li></ul><ul><ul><li>Midpt. survival, high Allee </li></ul></ul><ul><ul><li>High survival, midpt. Allee </li></ul></ul><ul><ul><li>High survival, low Allee </li></ul></ul>
    26. 26. Requirements for Persistence <ul><li>Persistence: E ≤ 0.05 </li></ul><ul><li>S a ≥ 0.8 & F ≥ 1.16 (across other values) </li></ul><ul><li>N 0 ≥ 5 as long as better-case scenarios for other parameters </li></ul><ul><li>N 0 5 to 30 --> E > 0.05 to E ≤ 0.05 (across other values) only when Allee effect was present & S a ≥ 0.8 </li></ul>
    27. 27. Small Population Paradigm <ul><li>Populations with few individuals suffer: </li></ul><ul><ul><li>High inbreeding depression </li></ul></ul><ul><ul><li>Low genetic variation </li></ul></ul><ul><ul><li>Increased value to collectors </li></ul></ul><ul><ul><li>Mate finding difficult </li></ul></ul><ul><ul><li>More susceptible to stochastic events </li></ul></ul><ul><li>Extinction more likely in smaller than in larger populations </li></ul><ul><li>Does this assumption hold for LBWOs? </li></ul>
    28. 28. So, When Does Size Matter? <ul><li>When Allee effect is present: </li></ul><ul><ul><li>When survival is at least intermediate (variances held intermediate) </li></ul></ul><ul><li>When Allee effect is absent: </li></ul><ul><ul><li>When survival is high and fecundity is low (variances held intermediate) </li></ul></ul><ul><li>NOT when demographic variances allowed to vary </li></ul><ul><ul><li>Environmental stochasticity swamps out N 0 </li></ul></ul>
    29. 29. A New, Demographic Robustness Paradigm? Moderate-high demographic rates ensure persistence of small populations despite moderate environmental stochasticity and Allee effect
    30. 30. Could they have survived? <ul><li>N 0 ≥ 5 would have ensured persistence if… </li></ul><ul><ul><li>F ≥ 1.1, S a ≥ 0.8, </li></ul></ul><ul><ul><li>variance in F ≤ 0.04, variance in S a ≤ 0.016 </li></ul></ul><ul><li>N 0 ≥ 30 would have ensured persistence… </li></ul><ul><ul><li>despite a relatively strong Allee effect, </li></ul></ul><ul><ul><li>if variance in S a ≤ 0.016, & either F ≥ 1.65 or S a ≥ 0.9 </li></ul></ul><ul><li>~24 IBWOs remained in 1930s, but demographic rates have remained virtually unknown </li></ul>
    31. 31. Predicted Fate of Rare LBWOs <ul><li>Under worse-case scenario of low demographic rates & high environmental stochasticity, extinction <10 years (2-33) </li></ul><ul><li>Maintaining intermediate (or greater) demographic rates confer persistence, even with small initial population size (5) </li></ul>
    32. 32. Speculations From Findings <ul><li>Could imply that habitat quality, rather than quantity, ensures persistence of LBWOs </li></ul><ul><li>Promote habitat management that improves reproduction and survival rather than expansion of “suitable” habitat </li></ul><ul><li>Build it, and they may not come? </li></ul>
    33. 33. Next Steps <ul><li>Demographic data needed to further calibrate our population model </li></ul><ul><li>Occupancy data currently being collected and analyzed can easily be incorporated and improve our population model </li></ul>
    34. 34. Thank You <ul><li>Funding </li></ul><ul><ul><li>U.S. Fish and Wildlife Service </li></ul></ul><ul><ul><li>U.S. Geological Survey </li></ul></ul><ul><li>Insights and suggestions </li></ul><ul><ul><li>Fellow “Skunk Apes”: C. T. Moore, J. P. Runge, K. W. Stodola </li></ul></ul><ul><ul><li>S. R. Beissinger </li></ul></ul><ul><ul><li>B. R. Noon </li></ul></ul><ul><ul><li>J. Rolstad </li></ul></ul>
    35. 35. Clutch Size & Survival S & C from same study
    36. 36. Clutch Size & Survival
    37. 37. Clutch Size & Survival
    38. 38. Clutch Size & Survival
    39. 39. Perturbation Analysis Overview <ul><li>Life history variation </li></ul><ul><ul><li>Intermediate variances for demographic rates </li></ul></ul><ul><ul><li>Vary means for demographic rates </li></ul></ul><ul><li>Variation in environmental stochasticity </li></ul><ul><ul><li>Intermediate means for demographic rates </li></ul></ul><ul><ul><li>Vary variances for demographic rates </li></ul></ul><ul><li>Variation in Allee effect </li></ul><ul><ul><li>Intermediate variances for demographic rates </li></ul></ul><ul><ul><li>Vary mean survival </li></ul></ul><ul><ul><li>Intermediate mean number of juveniles </li></ul></ul><ul><ul><li>Vary F t (probability of breeding) based on N t </li></ul></ul>
    40. 40. Perturbation Analysis Overview <ul><li>Life history variation </li></ul><ul><ul><li>Intermediate variances for demographic rates </li></ul></ul><ul><ul><li>Vary means for demographic rates </li></ul></ul><ul><li>Variation in environmental stochasticity </li></ul><ul><ul><li>Intermediate means for demographic rates </li></ul></ul><ul><ul><li>Vary variances for demographic rates </li></ul></ul>
    41. 41. Results: Environmental Stochasticity
    42. 42. Perturbation Analysis ctd. <ul><li>Small changes in focal parameters (  i ) </li></ul><ul><li> i = or proportional to 1 initial adult </li></ul><ul><ul><li>N 0 range: 30 – 5 = 25;  No = 25 / 25 = 1 </li></ul></ul><ul><ul><li>S a range: .9 – .7 = .2;  Sa = .2 / 25 = .008 </li></ul></ul><ul><li>Original parameter value (x i ) -> E i </li></ul><ul><li>x i +  i -> E i ’ </li></ul><ul><li>Changes in extinction rates (  E i = E i – E i ’) </li></ul><ul><li>Mean  E i across the 27 combinations </li></ul>
    43. 43. Population Model Volatility <ul><li>Response of E to small changes of inputs </li></ul><ul><li>Most volatile under worse-case scenarios </li></ul><ul><ul><li>Low survival and fecundity </li></ul></ul><ul><ul><li>High variance in survival and fecundity </li></ul></ul><ul><ul><li>Low N 0 , high S a , and strong Allee effect </li></ul></ul><ul><li>Least volatile under better-case scenarios </li></ul><ul><ul><li>High survival or fecundity </li></ul></ul><ul><ul><li>High N 0 and low variance in S a </li></ul></ul><ul><ul><li>High N 0 , ≥ intermediate S a , & weak Allee effect </li></ul></ul><ul><li>N 0 + 1 --> average 0.4-3.2% reduction in E </li></ul>
    44. 44. Results: Life History Variation
    45. 45. Results: Environmental Stochasticity
    46. 46. Results: Allee Effect
    47. 47. To-do’s

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