 Occupancy Model Extensions

Number of Patches or Sample Units Unknown, Single Season So far have assumed the number of sampling units in the population of interest ( S ) is known. e.g., total number of ponds, total number of quadrats. This is required if the total number of occupied units in the population is required.

Number of Patches or Sample Units Unknown, Single Season In some applications S will be unknown. e.g., insects on host plants, parasites of animal hosts. Given a sample of units (e.g., plants or hosts), probability of occupancy can still be estimated with no modification of previously described methods.

Number of Patches or Sample Units Unknown, Single Season Number of occupied units requires an estimate of number of units. Suggestion: use appropriate method (e.g., capture-recapture, distance sampling) to estimate number of units and then multiply by Pr(occupancy).

Number of Patches or Sample Units Unknown, Multiple Seasons System dynamics are now a function of unit dynamics and occupancy dynamics of units. Combination modeling using both capture- recapture (for units) and occupancy (for species of interest). Should be possible to develop joint likelihoods that incorporate dynamics of both units and occupancy.

Joint Models for Marked Individuals + Occupancy Data: 1 At the species level, units are continually occupied over time. However, there may be turnover/movement of the individuals among units. Joint modeling may allow more mechanistic approach to inferences about: metapopulation “rescue effect” source-sink dynamics

Joint Models for Marked Individuals + Occupancy Data: 1 Current occupancy models 1 - Pr(extinction) = Pr(present at t +1| present at t ) Joint models with marked individuals 1 – Pr(extinction) includes: All new (not present at t ) individuals at t +1 (rescue effect) At least 1 old (present at t ) individual at t +1 Joint models permit separate inference about these 2 components of nonextinction and provide additional information for the modeling of Pr(colonization)

Joint Models for Marked Individuals + Occupancy Data: 2 At a (random) sub-sample of units abundance can be directly estimated from mark-recapture or distance sampling. The Royle and Nichols (2003) approach of abundance-induced heterogeneity could be extended to incorporate the extra information of the estimated abundances. Should lead to improved inferences about abundance at units with occupancy-only data.

Use of Count Data Obtain count of individuals at each survey. Detection histories include counts at occupied units. Maximum count for replicate surveys represents minimum abundance. This minimum abundance “informs” the prior abundance distribution and leads to an estimate of the abundance distribution. Royle (2004) provides methods for estimating mean abundance and the abundance distribution across units using counts. May require careful interpretation of what “abundance” is.

Occupancy-Abundance Relationship Detection probability = f(abundance). Results of most (all?) investigations of occupancy- abundance relationships are influenced by failure to deal with this sampling issue. Remedy: embed occupancy-abundance relationship directly into occupancy modeling, using different hypotheses about prior distributions for abundance (~ Poisson, Negative Binomial, etc.). Occupancy modeling provides natural framework for investigating occupancy-abundance relationship.

Incorporating Telemetry Data Occupancy provides an estimate of the total area being used by a species. For territorial species with little homerange overlap, could estimate abundance if homerange size was known.

Incorporating Telemetry Data For example: 1,000ha region, 70% is estimated to be occupied. Average home range size is 3.5ha. Therefore, 700/3.5 = 200 individuals

Incorporating Telemetry Data Could use telemetry data to estimate the homerange size of collared individuals/groups. Can imagine a joint model such that all sources of uncertainty are accounted for.

Multi-scale Occupancy Dynamics Motivating example: disease dynamics (McClintock et al., 2010, Ecology Letters) Multiple refuges across a landscape and each refuge has multiple water bodies. Sampling at both scales. Imperfect detection of disease within water bodies. Disease dynamics at both refuge and water body scale is of interest.

Conclusions “Presence-absence” surveys can be used for inference when repeat visits permit estimation of detection probability. Models permit estimation of occupancy (state variable) and patch-dynamic rate parameters (extinction, colonization, rate of change) over multiple seasons or years. Many opportunities to revisit interesting ecological questions addressed using poor inference methods. Many interesting extensions and applications.