1.  Multi-state Occupancy

2. Multiple Occupancy States Rather than just presence/absence of the species at a sampling unit, ‘occupancy’ could be categorized into multiple states. breeding/non-breeding/absent disease/no disease/absent index of relative abundance – lots/some/none Key requirements are: highest order state must be observable without error. ambiguity associated with observed lower order states. true state does not change within a season (closure).

3. Multiple Occupancy States Single Season Study 2 occupancy states 0 = not occupied 1 = non-breeders only 2 = at least some breeders Breeding state cannot be identified with certainty Observed state = 2: detection of breeding, evidence is unambiguous (true state = 2) Observed state = 1: no detection of breeding, evidence is ambiguous (true state = 1 or 2) Observed state = 0: no detection (true state = 0, 1, or 2)

4. Multiple Occupancy States: Parameters Pr(unit i is in state m ) Pr(observe state l in survey j of site i | true state = m )

5. Observed State True State012 0100 10 2 Multiple Occupancy States: Parameters

6. Multiple Occupancy States: Reparameterizations Pr(unit is occupied) Pr(unit is in state 2|unit is occupied) Pr(species is detected|true state = 2) Pr(correctly classify as being in state 2)

7. Multiple Occupancy States: Reparameterizations 1-  [1] -  [2] not occ  [1] state=1 Occ w/o breeding state=2 occ w/ breeding 1-  not occ  Occupied breeding  [2] 1-R no breeding R

8. Multiple Occupancy States: Detection History Modeling =  [2] p [1,2] (1-p [1,2] -p [2,2] )p [2,2]

9. Multiple Occupancy States: Detection History Modeling

10. A Probabilistic Model Define state-dependent occupancy and detection vectors.

11. A Probabilistic Model The combination of these statements forms the model likelihood: S L( ,R,p,  | h 1,h 2,…h s )=  Pr(h i ) i =1 Maximum likelihood estimates of parameters can be obtained. However, parameters cannot be site-specific without additional information (covariates).

12. Multiple Occupancy States: Cal. Spotted Owl Reproduction Eldorado National Forest, 2004 Rocky Gutierrez, Mark Seamans 2 states for each occupied territory: Successfully reproduced Did not successfully reproduce Multiple (5 maximum) visits with “mousing” Definitive evidence of reproduction: Detect young (e.g., moused adult feeds young) Much more likely later in season (last 3 visits) Variation in sampling protocol among 5 Sierra study sites precludes meta-analysis for reproductive rate data

13. Multiple Occupancy States: Cal. Spotted Owl Reproduction Naïve estimate: Parameter estimates from model

14. Multiple Occupancy States: Multiple Seasons What about the dynamic processes of change between states over time? Easily accounted for by defining a transition probability matrix.

15. Multiple Occupancy States: Multiple Seasons

16. Calculation of model likelihood for observed histories is same as for the multi-season models described previously. Both parameterizations available in PRESENCE.

17. Example: Cal. Spotted Owl What are the occupancy and reproduction dynamic rates from 1997-2004? Does the state of a territory last year influence the dynamic rates for either process? Similar parameterization to Nichols et al. (2007) 66 potential nesting territories

18. Example: Cal. Spotted Owl 24 models fit to the data Top 2 models accounted for 99% AIC model weights 91% 8%

19. Example: Cal. Spotted Owl 19971998199920002001200220032004 0.75 (0.04) 0.56 (0.06) 0.89 (0.08) 0.55 (0.06) 0.66 (0.04) 0.55 (0.08) 0.48 (0.09) 0.62 (0.04) 0.91 (0.03) 0.79 (0.04) 0.30 (0.07) 0.87 (0.03) 0.97 (0.03) 0.79 (0.03) 0.74 (0.05) 0.80 (0.04) 0.00 (0.00) 0.93 (0.04) 0.79 (0.06) 0.17 (0.15) 0.83 (0.05) 0.85 (0.08) 0.84 (0.05) 0.26 (0.12) 0.85 (0.05)

20. Example: Cal. Spotted Owl State (m) in year t-11998-2004 00.17 (0.11 – 0.26) 10.87 (0.79 – 0.92) 20.91 (0.83 – 0.95)

21. Example: Cal. Spotted Owl

22. Clear indication that probability of a territory being occupied depends on state in previous year. Reproduction also depends on state in previous year, but nature of relationship varies annually.

23. Green Frogs, Maryland USA Up to 280 NAAMP listening stations surveyed 3 times from 2001-2005 Level of activity scored each survey ‘State’ is maximal call index Number of stations in each state each year

24. Green Frogs, Maryland USA Multinomial parameterisation used Analysed in WinBUGS flat priors 2 chains of 50,000 iterations

26. Multiple Occupancy States: Summary Multiple states with uncertain state assignment represent a natural extension of occupancy models. Provides a framework to address interesting ecological questions from landscape-level data. Single- and multiple-season models have been developed to deal with these situations.