1. 1 Occupancy models extension: Species Co-occurrence

2. 2 Species co-occurrence Do some species tend to occur more (or less) often together than expected? A great deal of literature has been published during past 30 years on methods for assessing patterns of co- occurrence, but not accounting for detectability.

3. 3 Species co-occurrence If detectability of a species is influenced by the presence of the other species, estimated interaction may be completely misleading. => Need to control for imperfect detectability

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6. Multi-Species Models Model occurrence and detection of species A and B jointly Model the influence of presence of species A (B) on Pr(occupancy) of species B (A) = interaction term Model the influence of presence of species A (B) on Pr(detection) of species B (A) 6

7. 7 Model parameters (state process) = probability site occupied by species A = probability site occupied by species B = probability site occupied by species A and B

8. 8 Site unoccupied Occupied by species A only Occupied by species B only Occupied by both species For each site: 4 possible occupancy states

9. 9 Detection probabilities (obs. process) = detection probability for species l, given only species l is present = probability of detecting both species A and B = probability of detecting species A, but not B = probability of detecting species B, but not A = probability of detecting neither species pApA pBpB

10. 10 Building a two-species model Define for each site i: Probability of observing any given pair of h The model likelihood is:

11. 11 Building a two-species model Consider h A = 11, h B = 01  Description: Both species present, only species A detected in survey 1, both detected in survey 2  Math:

12. 12 Building a two-species model Consider h A = 11, h B = 00  Description: Both species present, only species A detected in either survey, OR only species A present and was detected in surveys 1 & 2  Math:

13. 13 Do the species co-occur more (or less) often than expected? If species occur at sites independently then, The level of co-occurrence could be quantified as, >1: “attraction”: sp. co-occur more frequently than expected <1: “exclusion”

14. 14 Suggested re-parameterization, Model directly Do the species co-occur more (or less) often than expected?

15. 15 Are the species detected independently? Redefine Detections are independent if, Bailey et al. (2009) in Biological Conservation

16. 16 What about covariates? Covariates (e.g., habitat) may be incorporated using either the:  logit link for  log link for

17. 17 What you should know… Imperfect detection of species may lead to misleading conclusions about species co- occurrence. Similarly, some apparent relationships may be explained by different habitat preferences (correlative vs. causation)

18. 18 Community-level Studies

19. 19 Community-level Studies Focus on species richness Imperfect detection will also create biases in measures of species richness Single-species methods covered so far could be applied to investigate patterns of species richness.  Single unit (= single site)  Multiple spatial units

20. 20 Single Unit A list of s species of interest Multiple surveys are conducted on a single spatial unit Species are detected/not detected. Data similar to the single-season, single-species situation with species on the list being analogous to sites

21. 21 Single Unit Species richness (SR) = number of the species present at the unit. Number of species detected Number of species present, but never detected Estimated Pr.(occupancy) of a species (i), conditional upon its non- detection

22. 22 How to Set Up Data for PRESENCE Each row represents the detection/nondetection of a species in the repeated surveys. (s rows total) ‘Site-specific’ covariates represent covariates about the individual species.  e.g., resident, size, coloration -> heterogeneity among species

23. Multiple Units 23

24. 24 Multiple Units Same data type as for single-species models, but collected for many species. Focus may be:  Investigating similarities in occupancy dynamics or detectability among species  Estimating species richness across sampled locations and larger areas.

25. 25 Multiple Units (= multiple sites) Data collected on M species at s sampling units. Fit single-species models to each species. Species richness at site i could be defined as: or: Sum of Pr(Occ) of all species

26. 26 Multiple Units Effect of site covariates may be modeled as consistent among sets of species. Data: M x s rows Each row is detection history of a given species at a given site

27. 27 Multiple Units State-space approach especially useful as many relevant community-level summaries can be calculated directly from the predicted occurrence of the species.

28. 28 What you should know… Use of occupancy models to estimate Species Richness Single units (s species) Multiple units (M species, S sites)