1.  1 Modelling Occurrence of Multiple Species

2. 2 Motivation Often there may be a desire to model multiple species simultaneously.  Sparse data.  Compare/contrast among species.  Expect different species to respond to external factors in a similar manner. ‘Species’ could be the different genders or age-classes.

3. 3 Sampling Requirements Detection data for each species is collected under the same protocols for single-species models. Assume that occurrence of each species at a unit is independent.  Recall formal definition of independence. If both species have a higher chance of occurring at a unit because both species have the same habitat preferences, that is not a lack of independence.

4. 4 Interesting Biological Questions Does the occurrence for set of species respond in a similar manner to a particular covariate?  Guild membership

5. 5 Interesting Biological Questions Does the occurrence for set of species respond in a similar manner to a particular covariate?  Guild membership

6. 6 Interesting Biological Questions Occurrence dynamics may be modeled as varying in parallel over time.

7. 7 How to Set Up Data for PRESENCE Input detection data for all species from all units simultaneously.  i.e., if M species and s units, data file will contain M x s rows. Include a series of dummy variables to indicate which set of data is from which species. May need to include interactions between species and other covariates depending on models to be fit.

8.  8 Community-level Studies

9. 9 Many community-level studies collect occupancy-type data. Imperfect detection will also create biases in measures of species richness. Single-species methods covered so far could be applied to investigate patterns and dynamics of species richness.  single or a small number of units.  larger number of units.

10. 10 Single Unit A list of s species of interest is composed. Multiple surveys are conducted for the species.  Either temporal or spatial Species are detected/not detected. Resulting data are similar to the single- species, single-species situation with species on the list being analogous to ‘units’.

11. 11 Single Unit Species richness equates to number of the species on the list present at the unit. State-space formulation is particularly useful because the species list represents the entire population of interest.

12. 12 Single Unit Similar intent to application of mark- recapture methods to estimating species richness. An advantage is attributes of each species could be included as covariates. Multi-season models could be applied to investigate changes in the community or species richness over time.

13. 13 How to Set Up Data for PRESENCE Each row represents the detection/nondetection of a species in the repeated surveys. ‘Site-specific’ covariates represent covariates about the individual species.  e.g., resident, size, colouration

14. 14 Example: Species Richness Number of species present at BBS route in Maryland, USA 50 stops along route, with species detected recorded at each stop. 10-stop summaries used; 5 survey units Data from June 1990

15. 15 Example: Species Richness 85 bird species on master list Established after the fact here Species categorised by migratory status Resident, short distance or neo-tropical 51 species detected at least once in survey

16. 16 Example: Species Richness Analysis conducted in WinBUGS   ’s different for each migratory group   2 chains of 51,000 iterations; 1 st 1,000 discarded as burn-in period

17. 17 Example: Species Richness

18. 18 Example: Species Richness Median = 32, (25, 40)Median = 65, (54, 78) Median = 22, (19, 30) Median = 10, (8, 13)

19. 19 Large Number of 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 (previous slides).  the estimation of species richness across sampled locations and larger areas.

20. 20 Large Number of Units Data collected on M species at s sampling units. Fit single-species models to each species. Species richness at unit i could be defined as: or:

21. 21 Large Number of Units Effect of covariates may be modeled as consistent among sets of species. May also include unit-specific random effects, that may also be correlated (Dorazio et al. 2006).

22. 22 Large Number of Units State-space approach especially useful as many relevant community-level summaries can be calculated directly from the predicted occurrence of the species. Also possible to construct species accumulation curves corrected for detection probability.

23. 23 Large Number of Units Dorazio et al. (2006) also show that the total number of species in an area can be estimated (i.e., including those never detected).  add an arbitrarily-large number of ‘species’ to the data set with the ‘all-zeros’ detection history.  there are now S ‘species’ on the list.  Ω is the fraction of the list that may be real species.

24. 24 Large Number of Units Detectability can not be species-specific without some functional relationship.  Can not estimate detection probability for species never detected. Can also envisage a multi-season extension of Dorazio et al. (2006) allowing colonization and extinction of species at both the entire area and individual unit level.

25. 25 How to Set Up Data for PRESENCE As for previous set of slides, data will consist of M x s rows. More difficult to replicate Dorazio et al. (2006) type analysis in PRESENCE.

26. 26 Summary Plenty of scope for applying single-species models to address community level questions.  Species richness/biodiversity.  Changes in community structure through time.  Response of different species to similar environmental changes.

27.  27 Species Co-occurrence

28. 28 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.

29. 29 Species co-occurrence matrix 12345 1 10010 2 11001 3 01110 4 10001 5 11010 …..... s 10011 Species Units

30. 30 Species co-occurrence matrix 12345 1 1101 1000 2 1011000111 3 001011 01 4 1000 10 5 1110011100 …..... s 1101001011 Species Units

31. 31 Species co-occurrence Direction of interaction may be correctly estimated, but the magnitude of the interaction underestimated, if probability of detecting a species is the same regardless of whether the other species is also present. If detectability of a species differs given the presence/absence of the other species, estimated interaction may be completely misleading.

32. 32 Model parameters = probability unit occupied by species A = probability unit occupied by species B = probability unit occupied by species A and B

33. 33 Unit unoccupied Occupied by species A only Occupied by species B only Occupied by both species A and B

34. 34 Co-occurrence model Consider units to be in one of 4 mutually exclusive ‘states’, or more generally 2 l states. occupied by species A and B occupied by species A only occupied by species B only occupied by neither species

35. 35 Detection probabilities = detection probability for species l, given only species l is present = probability of detecting 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

36. 36 Detection probabilities Define a detection probability vector

37. 37 Building a two-species model Define for each unit i The model likelihood is:

38. 38 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:

39. 39 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:

40. 40 Building a two-species model Consider h A = 00, h B = 00  Description: Both species present with neither ever being detected, OR only species A present and never detected, OR only species B present and never detected, OR both species absent  Math:

41. 41 1. Do the species co-occur more (or less) often than expected? If species occur at units independently then, The level of co-occurrence could be quantified as,

42. 42 1. Do the species co-occur more (or less) often than expected? Suggested reparameterization, Model directly

43. 43 1. Do the species co-occur more (or less) often than expected? Another reparameterization, Estimated parameters are, and.

44. 44 1. Do the species co-occur more (or less) often than expected? A third reparameterization, Equivalent to logistic regression with the presence of sp. A as a predictor variable for the presence of sp. B Estimated parameters are, and.

45. 45 2. Are the species detected independently? Redefine Detections are independent if, Or use similar reparameterizations as for occupancy

46. 46 3. Is the probability of detecting species A affected by the presence of species B ? Consider models with the constraint, Or similarly,

47. 47 Salamander example 88 transects visited 5 times within Great Smoky Mountains National Park between 4/4/99 – 27/6/99 50m natural & artificial cover transects used to detect species at each unit (pooled) Examine patterns for Plethodon jordani (PJ) and P. glutinosus complex (PG)

48. 48 Salamander example Model – log-like K  AIC 736.670.0 747.068.3 761.4520.7 776.0433.4

49. 49 What about covariates? Covariates (e.g., habitat or weather) may be incorporated using either the;  logit link for  log link for

50. 50 Salamander example Elevation was thought to be an important covariate for these species. Does incorporating elevation change the results with respect to co-occurrence?

51. 51 Salamander example Model – log-like K  AIC 617.3120.0 623.6102.3 660.11038.8 675.6850.2 676.1850.8 673.21051.8 671.81152.5 736.67109.3

52. 52 Salamander example

53. 53 Salamander example

54. 54 Salamander example

55. 55 Salamander example Allowing for elevation may (partially) explain the apparent non-random pattern in co-occurrence between PG and PJ

56. 56 Multiple-season species co-occurrence Single-season model only allows inference about the patterns of co-occurrence. To make inferences about the dynamic processes of change in co-occurrence need to survey the species at systematic points in time. Dynamic processes are probabilities of colonization and local extinction, given the presence or absence of other species.

57. 57 Multiple-season species co-occurrence Define a matrix that determines how the occupancy state of units may change between seasons t and t+1.

58. 58 Multiple-season species co-occurrence Define a matrix that determines how the occupancy state of units may change between seasons t and t+1.

59. 59 Multiple-season species co-occurrence Observed data likelihood approach: Complete data likelihood could also be developed and used with EM algorithm or data augmentation

60. 60 Summary Imperfect detection of species may lead to misleading conclusions about species co- occurrence. Similarly, some apparent relationships may be explained by different habitat preferences or different responses to environmental changes. Reliable inferences about change can only be made by observing the system at systematic points in time.