Occupancy Sampling and Modeling Species D.pptx

Occupancy Sampling and Modeling Species D

1. Occupancy Sampling & Analysis Lecture sections I: Fundamentals of occupancy II: Types of occupancy models III: Analysis in PRESENCE Sutirtha Dutta

2. Occupancy Number of patches where species occur Number of available patches for the species Proportion of sites occupied or probability of presence at a site as a proxy for population status of a species

3. What is population occupancy?

4. Abundance – Occupancy Relationship Occupancy for coarse estimation of population status … empirical relationship between abundance & area occupied But, factors affecting abundance & occupancy may be different

5. Occupancy Estimation Number of patches where species occur Number of available patches for the species Historically, crude occupancy from single spatial/temporal sampling

6. Why worry about detectability? Study area 1 / Species A Study area 2 / Species B Survey Detect-ability Survey Detect-ability Site 1 2 3 Site 1 2 3 1 1 1 1 1.00 1 1 1 0.67 2 1 1 1 1.00 2 1 0.33 3 0.00 3 0.00 4 1 1 0.67 4 1 0.33 Naïve occ 0.75 Naïve occ 0.75 Actual occ ~ 0.75 Actual occ > 0.75 1 2 3 4 1 2 3 4

7. Ignoring differences in detectability leads to biased inference! Detection history from repeated spatial or temporal surveys at multiple sites provides information on detection probability Occupancy analysis corrects for ‘false absences’ Why worry about detectability? Study area 1 / Species A Study area 2 / Species B Survey Detect-ability Survey Detect-ability Site 1 2 3 Site 1 2 3 1 1 1 1 1.00 1 1 1 0.67 2 1 1 1 1.00 2 1 0.33 3 0.00 3 0.00 4 1 1 0.67 4 1 0.33 Naïve occ 0.75 Naïve occ 0.75 Actual occ ~ 0.75 Actual occ > 0.75

8. Occupancy Estimation ψ = Population parameter – proportion of sites occupied S = count statistic (naïve occupancy) p. = cum. detection probability; Pr(member of ψ appears in S ) Canonical Estimator

9. Maximum Likelihood Estimation Coin tossed 5 times with the result: HHTHT Pr(Head) = p, Pr(Tail) = 1–p So, L( p |HHTHT ) = Pr( HHTHT| p ) = pp(1-p)p(1-p) = p 3 (1-p) 2 Likelihood framework to estimate parameter What parameter value maximizes the probability of observing the data Plug-in different values of p & find which value maximizes likelihood

10. Survey Site 1 2 3 1 1 1 2 1 3 4 1 Occupancy ? Detectability ? Detection histories For e.g., Verbal description: species present at the site AND detected in 1 st & 3 rd surveys, not detected in 2 nd survey Mathematical translation: Occupancy Estimation 2 parameters are estimated: ψ , p

11. Survey Site 1 2 3 1 1 1 2 1 3 4 1 Naïve occ Detectability Detection histories For e.g., Verbal description: species present at the site and was never detected, OR species is absent. Mathematical translation: Pr ( h 3 = 000) = ψ (1- p 1 ) (1- p 2 ) (1- p 3 ) + (1- ψ ) Occupancy Estimation 2 parameters are estimated: ψ , p

12. Observed data likelihood Model likelihood is the product of probability statements Plug-in different values of ψ , p to maximize the likelihood Occupancy Estimation

13. Closure Occupancy status does not change between surveys Solution – for random changes, interpret occupancy as use Detection surveys are independent Observer familiarity, trap response, spatially replicated surveys Solution – spatial sample with replacement or Hines et al 2010 No unmodeled heterogeneity in detection Conditions influencing detectability differs between surveys Solution – model detection probability on site/survey covariates Species identified correctly (no false detections) Occupancy Assumptions

14. Designing Occupancy Surveys Things to consider before you start occupancy surveys What is your objective ? occupancy, trends, habitat-relationships How many sites ? How many surveys ? Trade-off (GENPRES) What should be your site? beat / pond / grid / camera What should be your detector / how should you survey ? Spatial surveys or temporal surveys at a site ? For temporal surveys, what should be your sampling duration ? Remember the assumptions & ensure they are not violated

15. Designing Occupancy Surveys Avoid violating assumptions Sample adequately for robust inference Program GENPRES Be aware of drawbacks

16. Single Species Models Single Season Use of Covariates Single Season Multistate Multi Season Abundance-induced heterogeneity Multi Species Models Single Season Multi Season Models Other extensions community analysis, disease modeling etc. Key Occupancy Models

17. Biological Question: How does a species’ occupancy vary with space depending on habitat characteristics ? Modeling occupancy on site covariates (X i ) and detection probability on site (X i ) & survey covariates (Z ij ) The logistic model Single Season Occupancy with Covariates Any unmodeled heterogeneity in detection probability should be accounted for using covariates as it underestimates occupancy Y X

18. Tiger occupancy Wild prey Detection probability Trail Road Streambed

19. How accurately does the fitted model represent the data? AIC based approach finds the best model not necessarily a good model Over-dispersion parameter > 1 (more variation in data than model) Used in model selection (QAIC) & SE calculation O h = observed probability of history h E h = summed probabilities of observing history h h = 101; Pr( h ) = ψ p 1 (1-p 2 )p 3 Use Chi-square statistic with parametric bootstrapping to test model fit

20. Abundance-induced Heterogeneity Models Heterogeneity in detection due to difference in local abundance between sites Royle & Nichols (2003) : p n = 1 – (1-r) n Local abundance unknown but spatial distribution can be assumed E.g., Poisson distribution Occupancy & index of abundance can be derived Surveys Site 1 2 3 w i 1 1 1 2 2 1 1 1 3 3 4 1 1 Locally abundant Locally rare

21. Multi Season Models Biological Question: Is a population/ metapopulation increasing or decreasing ? How is extinction risk related to factors x, y, z? Parameters for Colonization, Extinction along with Occupancy & Detection Season 1 Season 2 Survey 1 2 3 1 2 3 Sites 1 1 1 1 1 1 2 1 1 1 1 3 4 1 1 Occupancy can change between but not within seasons γ ε ψ t-1 ψ t

22. Multi Species Models Biological Question: Does species’ co-occurrence pattern differ from random chance? Species may not be detected if present Species may differ in their habitat preference Species may influence each other’s detectability ψ AB = Pr (species A & B present at a site) ψ A = Pr (species A present at a site regardless of B) ψ B = Pr (species B present at a site regardless of A) Species Interaction Factor = ψ AB / ψ A * ψ B = 1 (random chance) < 1 (mutual avoidance) > 1 (mutual attraction) Surveys Sites Sp A 1 2 3 1 1 1 1 2 1 1 3 4 1 Surveys Sites Sp B 1 2 3 1 2 3 1 1 4 1 1

23. Species Interaction Factor 0.67 (SE 0.11) - avoidance Example: Two Salamander species in Great Smoky Mountains Do large carnivores (tiger, leopard) avoid each other?