1. Patch Occupancy and Patch Dynamics
Ex. 1: Grey heron
Patch Occupancy and Patch Dynamics
Lecture 09

2. Ex. 1: Grey heron
Resources
D.I. MacKenzie, J.D. Nichols, J.A. Royle, K.H. Pollock, L.L. Bailey, and J.E. Hines Occupancy estimation and modeling. Academic Press. Burlington, MA.

3. Resources Site Occupancy
Ex. 1: Grey heron
Resources
Site Occupancy
D. I. MacKenzie, J. D. Nichols, G. D. Lachman, S. Droege, J. A. Royle, and C. A. Langtimm Estimating site occupancy rates when detection probabilities are less than one. Ecology 83:
Tucker Jr., J.W, W.D. Robinson Influence of season and frequency of fire on Henslow’s sparrows (Ammodramus henslowii) wintering on Gulf Coast pitcher plant bogs. Auk 120:

4. Resources Patch dynamics
Ex. 1: Grey heron
Resources
Patch dynamics
D. I. MacKenzie, J. D. Nichols, J. E. Hines, M.G. Knutson, and A.B. Franklin Estimating site occupancy, colonization, and local extinction when a species is detected imperfectly. Ecology 84:
C. Barbraud, J. D. Nichols, J. E. Hines, and H. Hafner Estimating rates of local extinction and colonization in colonial species and an extension to the metapopulation and community levels. – Oikos 101: 113–126.

5. Ex. 1: Grey heron
Patch Occupancy:
Primarily occupancy of sampling unit by one or more species of interest
pond-dwelling amphibians – pond is unit of interest
terrestrial bird – forest patch, or arbitrary block of land
fish – stream or stream reach

6. Ex. 1: Grey heron
The Problem
Primarily interested in the proportion of sites that are occupied or the probability a particular site is occupied.
Probability is an a priori expectation – e.g. probability of heads on a coin toss
Proportion is the realization of the expectation – proportion of heads in 10 coin tosses
Why?
Occupancy  Abundance  Vital rates

7. Basic sampling protocol
Ex. 1: Grey heron
Basic sampling protocol
Visit sites and spend time looking for individuals of interest or evidence that they are present
Repeated presence-absence surveys
Temporal replication at same site
Spatial replication

8. Still important Study design Scope of inference
Ex. 1: Grey heron
Still important
Study design
Scope of inference
Elements of stratification and randomization
Strength of inference.
Strongest – experimental manipulation
Weaker – constrained designs (e.g., before & after)
Weaker still – a prior modeling
Worst – a posteriori storytelling

9. Ex. 1: Grey heron
Analysis
Historically, estimates of occupancy based on the portion of sites where presence was detected.
Problem – detection is not often perfect e.g., animals present or site was used but no sign was seen.
Biases estimates of use downward
Bias increases with rare and elusive animals – often species of greatest concern
Like capture-mark-recapture methods occupancy analysis explicity deals with the nuisance parameter of detection rate.

10. Important Sources of Variation
Ex. 1: Grey heron
Important Sources of Variation
Spatial variation
Interest in large areas that cannot be completely surveyed
Sample space in a manner permitting inference about entire area of interest
Estimating detection probability essential
Even on surveyed areas
Samples don’t usually detect all animals present

11. Ex. 1: Grey heron
Applications

12. Determining range extent
Ex. 1: Grey heron
Determining range extent
Usually involve the use of presence-absence data,
Frequently by "connecting the dots,"
Extent of occurrence like typical range maps
Can allow for breaks in distribution
Failures to detect under-estimate range

13. Determining range extent
Ex. 1: Grey heron
Determining range extent
Occupancy analysis
Accounts for failures to detect – “false absences”
Allows examining the probabilistic distribution and relationships to biotic and abiotic factors

14. Habitat relationships and resource selection
Ex. 1: Grey heron
Habitat relationships and resource selection
Studies of habitat use seek to identify key habitat attributes to which species respond
Frequently employ presence-absence surveys
Often use logistic regression –
fails to account for "false absences,"
i.e. imperfect detection
Failure to account for detectability biases estimated relationships and variance (too small)

15. Metapopulations (Levins 1969, 1970)
Ex. 1: Grey heron
Metapopulations (Levins 1969, 1970)
Defined: Population composed of localized subpopulations that are connected through animal movements and have some probability of extinction and recolonization
Equivalent to a system of “patches” that are sometimes occupied

16. Metapopulations – single-season approaches
Ex. 1: Grey heron
Metapopulations – single-season approaches
Based on snapshot of occupancy – aka static occupancy
Relation to metapopulation
based on incidence functions
factors that influenced the probability of occurrence (Diamond 1975)
Uses the probability of occupancy to directly estimate metapopulation dynamics (Hanski 1991, 1992)
Probability of occupancy can vary among patch in relation to factors such as size, proximity, configuration, composition, fragmentation, etc.

17. Metapopulations – single-season approaches
Ex. 1: Grey heron
Metapopulations – single-season approaches
Extended to model population viability in relation to the number of viable patches
Rich body of literature based on estimates that do not include detection rates
Failure to incorporate imperfect detection bases incidence function leading to negative bias in estimating extinctions
Underestimating Pr(occupancy)
Overestimating Pr(extinction)

18. Metapopulations – multi-season approaches
Ex. 1: Grey heron
Metapopulations – multi-season approaches
Presence-absence surveys conducted over several seasons or years
Allows direct estimation of local extinction and colonization probabilities

19. Large-scale monitoring programs
Ex. 1: Grey heron
Large-scale monitoring programs
Occupancy (presence-absence) surveys are less costly than estimating abundance or density
Nearly as useful as estimates of abundance or trend
Sometimes incorrectly used as a surrogate for abundance

20. Multi-species occupancy
Ex. 1: Grey heron
Multi-species occupancy
Used to make inference about interactions or relationships among species
Rich literature on species interactions, but not incorporating detectability,
many of the results are questionable

21. Multi-species occupancy from static patterns
Ex. 1: Grey heron
Multi-species occupancy from static patterns
Surveys may be conducted over multiple years or multiple surveys with a year
Basically looking at patterns of where or how many sites are occupied by species A, species B, or both.
Generally comparing null models to deduce patterns, where null assumes no interactions among species.

22. Multi-species occupancy from static patterns
Ex. 1: Grey heron
Multi-species occupancy from static patterns
Potential problem – patterns of co-occurrence may have nothing to do with species interactions
Interactions may be positive or negative
Potentially, can develop a priori models without species interactions that form nulls
Another example, “nested subsets” where sites with smaller biotas (e.g., smaller or more distant islands in an archipelago) are subsets of larger ones – may infer relative colonization and extinction rates

23. Multi-species occupancy from occupancy dynamics
Ex. 1: Grey heron
Multi-species occupancy from occupancy dynamics
Multiple surveys each season or year
Interest is in species interactions as they relate to the dynamics of patch occupancy
Examples:
Examining the effects of invasive species on community organization
Ant communities fit a priori hypotheses in the absence of non- native species.
Structure was random in the presence of the exotic species (Sym and Jones 2000)
Examination of species turnover rates
Treats each species as a site and each site as an occasion
Changes in occupancy equate to species turnover rates across sites.

24. Ex. 1: Grey heron
Methods that do not estimate detection rates lead to biased estimates of occupancy and associated problems with the interpretation of estimated parameters.

25. Ex. 1: Grey heron
Basic Sampling Scheme
N sites are surveyed, each at T distinct sampling occasions
Species is detected/not detected at each occasion at each site

26. Detection History Data
Ex. 1: Grey heron
Detection History Data
1 = detection, 0 = non-detection
Examples:
Detections on occasions 1, 2, 4:
Detections on occasions 2, 3: 0110
No detections at site: 0000
1 detection history for each site sampled

27. Distinct sampling occasions may be:
Ex. 1: Grey heron
Distinct sampling occasions may be:
Repeated visits on different days
Multiple surveys on the same visit
Small time periods within a survey
e.g., detection/non-detection is recorded every minute of a 5-minute auditory survey
Multiple “locations” within a site
Spatial replication
However, want to maintain detection probability at a reasonable level (e.g., >0.10)

28. Model Parameters yi -probability site i is occupied
Ex. 1: Grey heron
Model Parameters
yi -probability site i is occupied
pij -probability of detecting the species in site i at time j, given species is present

29. Model Assumptions The detection process is independent at each site
Ex. 1: Grey heron
Model Assumptions
The detection process is independent at each site
No heterogeneity in occupancy than cannot be explained by covariates
No heterogeneity in detection that cannot be explained by covariates
Sites are closed to changes in occupancy state between sampling occasions

30. A Probabilistic Model Pr(detection history 1001) =
Ex. 1: Grey heron
A Probabilistic Model
Pr(detection history 1001) =
Pr(detection history 0000) =

31. Ex. 1: Grey heron
A Probabilistic Model
The combination of these statements forms the model likelihood
Maximum likelihood estimates of parameters can be obtained
However, parameters cannot be site specific without additional information (covariates)
Suggest parametric bootstrap be used to estimate GOF
As in MARK but see MacKenzie and Bailey (2005)

32. Ex. 1: Grey heron
Summary Statistics
nj - number of sites at which species was detected at time j
n. - total number of sites at which species was detected at least once
N - total number of sites surveyed
Naïve estimate of occupancy:

33. The Likelihood Function
Ex. 1: Grey heron
The Likelihood Function
N – total number of surveyed sites
pj – probability of detection at time j
n. - total number of sites at which species was detected at least once
nj - number of sites at which species was detected at time j

34. Ex. 1: Grey heron
Does It Work?
Simulation study to assess how well y is estimated (MacKenzie et al. 2002)
T = 2, 5, 10
N = 20, 40, 60
 = 0.5, 0.7, 0.9
p = 0.1, 0.3, 0.5
m = 0, 0.1, 0.2

35. Ex. 1: Grey heron
Does It Work?
Generally unbiased estimates when Pr(detecting species at least once) is moderate (p> 0.1) and T> 5
Bootstrap estimates of SE also appear reasonable for a similar range

36. Ex. 1: Grey heron
Including Covariates
y may only be a function of site-specific covariates
covariates of y that do not change during the survey
i.e., habitat type or patch size
p may be a function of site and/or time specific covariates
covariates that may vary with each sampling occasion and possibly site
i.e., cloud cover or air temperature

37. Ex. 1: Grey heron
Including Covariates
e.g., Linear-logistic function: covariates for site (Xi) and sampling occasion (Tij)

38. Ex. 1: Grey heron
Including Covariates
Average Pr(occupancy):

39. Example: Anurans at Maryland Wetlands (Droege and Lachman)
Ex. 1: Grey heron
Example: Anurans at Maryland Wetlands (Droege and Lachman)
Frogwatch USA (NWF/USGS) – now PARC
Volunteers surveyed sites for 3-minute periods after sundown on up to 10 nights
29 wetland sites; piedmont and coastal plain
27 Feb. – 30 May, 2000
Covariates:
Sites: habitat ([pond, lake] or [swamp, marsh, wet meadow])
Sampling occasion: air temperature

40. Example: Anurans at Maryland Wetlands (Droege and Lachman)
Ex. 1: Grey heron
Example: Anurans at Maryland Wetlands (Droege and Lachman)
Spring peeper (Hyla crucifer)
Detections at 24 of 29 sites (0.83)
American toad (Bufo americanus)
Detections at 10 of 29 sites (0.34)

41. Example: Anurans at Maryland Wetlands (H. crucifer)
Ex. 1: Grey heron
Example: Anurans at Maryland Wetlands (H. crucifer)
Model
DAIC wi
y(hab)p(tmp)
0.00
0.85
0.84
0.07
y(.)p(tmp)
1.72
0.15
y(hab)p(.)
40.49
y(.)p(.)
42.18

42. Example: Anurans at Maryland Wetlands (B. americanus)
Ex. 1: Grey heron
Example: Anurans at Maryland Wetlands (B. americanus)
Model
DAIC wi
y(hab)p(tmp)
0.00
0.36
0.50
0.13
y(.)p(tmp)
0.42
0.24
0.49
0.14
y(hab)p(.)
0.22
0.12
y(.)p(.)
0.70
0.18

43. Patch Occupancy as a State Variable: Modeling Dynamics
Ex. 1: Grey heron
Patch Occupancy as a State Variable: Modeling Dynamics
Patch occupancy dynamics
Model changes in occupancy over time
Parameters of interest:
t = t+1/ t = rate of change in occupancy
1-t = Pr(absence at time t+1 | presence at t) = patch extinction probability
t = Pr(presence at t+1 | absence at t) = patch colonization probability

44. Patch Occupancy Dynamics: Pollock’s Robust Design
Ex. 1: Grey heron
Patch Occupancy Dynamics: Pollock’s Robust Design
Sampling scheme:
Primary sampling periods: long intervals between periods such that occupancy status can change
Secondary sampling periods: short intervals between periods such that occupancy status is expected not to change

45. Robust Design Capture History
Ex. 1: Grey heron
Robust Design Capture History
History :
10, 01, 11 = presence
Interior ‘00’ =
Patch occupied but occupancy not detected, or
Patch not occupied (=locally extinct) yet re-colonized later
primary(i)
primary(i)
primary(i)
 secondary(j)
primary(i)
 secondary(j)

46. Robust Design Capture History
Ex. 1: Grey heron
Robust Design Capture History
Parameters:
t: probability of occupancy from t to t+1
p*t: probability of detection in primary period t
p*t = 1-(1-pt1)(1-pt2)
t: probability of colonization in t+1 given absence in t
Pr( ) =

47. Model Fitting, Estimation and Testing
Ex. 1: Grey heron
Model Fitting, Estimation and Testing
Unconditional modeling:
program PRESENCE
Program MARK (Occupancy models)
Conditional modeling: can “trick” either program RDSURVIV or program MARK into estimating parameters of interest using Markovian temporary emigration models:
Fix t = 1 (‘site survival’)
”t : probability of extinction
1-’t : probability of colonization
Probability of history :
”2(1-’3) + (1-”2)(1-p*2)(1-”3)p*3

48. Ex. 1: Grey heron
Main assumptions
All patches are independent (with respect to site dynamics) and identifiable
Independence violated when sub-patches exist within a site
No colonization and extinction between secondary periods
Violated when patches are settled or disappear between secondary periods => breeding phenology, disturbance
No heterogeneity among patches in colonization and extinction probabilities except for that associated with identified patch covariates
Violated with unidentified heterogeneity (reduce via stratification, etc.)

49. Tests and Models of Possible Interest
Ex. 1: Grey heron
Tests and Models of Possible Interest
Testing time dependence of extinction and colonization rates
Testing whether site dynamics reflect a first-order Markov process (i.e., colony state at time t depends on state at time t-1) vs. non-Markovian process (t=t)
Building linear-logistic models and testing the effects of individual covariates : e.g., logit(t or t) = β0 + β1 xt

50. Example: Modeling Waterbird Colony Site Dynamics
Ex. 1: Grey heron
Example: Modeling Waterbird Colony Site Dynamics
Colony-site turnover index (Erwin et al. 1981, Deerenberg & Hafner 1999)
Combines colony-site extinctions and colonization in single metric
Not possible to address mechanistic hypotheses about factors affecting these site-level vital rates
Markov process model of Erwin et al. (1998)
Developed for separate modeling and estimation of extinction and colonization probabilities
Assumes all colonies are detected

51. Example: Purple Heron East: PROTECTED West: DISTURBANCE Central:
Ex. 1: Grey heron
Example: Purple Heron
East:
PROTECTED
West:
DISTURBANCE
Central:
DISTURBANCE

52. Ex. 1: Grey heron
Example: Purple Heron
Time effects on extinction\colonization probabilities over all areas ?
Extinction\colonization probabilities higher in central (highly disturbed) area ?

53. Ex. 1: Grey heron
Other Applications
Northern spotted owls (California study area, )
Potential breeding territory occupancy
Estimated p range (0.37 – 0.59);
Estimated =0.98
Inference: constant Pr(extinction), time-varying Pr(colonization)
Tiger salamanders (Minnesota farm ponds and natural wetlands, )
Estimated p’s were 0.25 and 0.55
Estimated Pr(extinction) = 0.17
Naïve estimate = 0.25

54. Ex. 1: Grey heron
Conclusions
“Presence-absence” surveys can be used for inference when repeat visits permit estimation of detection probability
Models permit estimation of occupancy during a single season or year
Models permit estimation of patch-dynamic rate parameters (extinction, colonization, rate of change) over multiple seasons or years

55. Ex. 1: Grey heron
Advances
D. I. MacKenzie, J. D. Nichols, N. Sutton, K. Kawanishi, and L.L. Bailey Improving inferences in population studies of rare species that are detected imperfectly. Ecology 86:
J. A. Royle, Nichols, J. D. and Kéry, M Modelling occurrence and abundance of species when detection is imperfect. Oikos 110:
J. A. Royle Modeling abundance index data from Anuran calling surveys. Conservation Biology 18:
J. A. Royle N-mixture models for estimating population size from spatially replicated counts. Biometrics 60:
D. I. MacKenzie, and L.L. Bailey Assessing the fit of site-occupancy models. Journal Agricultural, Biological, and Environmental Statistics. 9:

56. Software Windows-based software Program PRESENCE – pwrc.usgs.gov
Ex. 1: Grey heron
Software
Windows-based software
Program PRESENCE – pwrc.usgs.gov
Specialized for occupancy models only
Program MARK
Program R, package Unmarked
Fit both predefined and custom models, with or without covariates
Provide maximum likelihood estimates of parameters and associated standard errors
Assess model fit