Additional multistate model applications

Unobservable States single observable state, single unobservable state

Example  Colonial seabird (survey colonies)  2 states: Breeder (B) Non-breeder (N)  Only breeders are observable  Non-breeder are temporarily emigrated

B N History B 0 B B N Unobservable What state at occasion 2? State B? (1-p B ) State N? (p N =0) or

History B 0 B: probability statement State B? (1-p B ) State N? (p N =0) or

Unobservable states in MARK Unobservable state If robust design, This case can also be treated as temporary emigration

Unobservable States multiple observable states, one or more unobservable states

A Observable Recapture areas A and B (e.g., 2 br. colonies that are surveyed) B U S i A  i AU S i U  i UA S i B  i BU S i U  i UA S i A  i AB S i B  i BA Unobservable (“rest of the world”) Temporary emigrated animals Multiple observable, 1 unobservable

Important assumption S i U  cannot be estimated separately It must be assumed equal to S i A or S i B This assumption is not required when all states are observables

Unobservable states in MARK >1 observable / Unobservable states

Multiple observable and multiple unobservable states A Pre-Breed A Breed B Pre-breed B Breed A Young B Young Example: Roseate Tern (Lebreton et al. 2003)

History: a 0 0 B We could decompose transitions and survival

A Breeders B Breeders S i Ab  i AbAn S i Bb  i BbAb A Non-breed Unobservable B Non-breed S i Ab  i AnAb S i Ab  i AnBb S i Ab  i AbAn S i Bb  i BnAb S i Bb  i BbBn S i Bb  i BnBb Recapture Areas Paired observable, unobservable

Design Considerations  Exploit opportunity for robust design  Include telemetry (preferably with p =1 and survival monitored)  Create buffer zone around study area ( search for marked animals, non-breeders? )  Collect behavioral cues each time an animal is seen (breeding behavior?)

Conclusions  Multistate models for unobservable states Potential for including unobservable states Not all models identifiable Robust design can be used to improve estimates (more info on p)

Conclusions  Existence of unobservable states should be minimized through design.  Robust design, telemetry, and other sources of information provide means to adjust for unobservable or misclassified states.

Mis-classified or Unknown States

How do we adjust for fact that calves are not seen each time with mother? Photo credit: USGS - Sirenia Project 2 states: C = female with Calf N = female with No calf

Assumption: breeding status is known for each sighted female  Problem: Sometimes a calf is present but not sighted.  Implication: Calf might be missed each time female is sighted and hence misclassified as non-breeder.  Solution: adjust for misclassification (i.e., estimate calf detection probability).

Multi-state Model for Misclassification (Kendall et al. 2003)  CC CN NC

How do we estimate detectability for the calf?  Two sighting occasions per year (robust design). Entire range of population is covered twice in a short period of time so that if female is breeder calf will be there both times. Each time individual is seen the date and presence/absence of first-year calf is noted. Calf detection probability is estimated from sighting history of female and calf combined.

Other examples of mis-classified states  Disease status / dynamics Diseased animals show no symptoms Recovered animals still show symptoms  Sex is mis-assigned Seabirds – behavioral assessment Sharks – claspers not always visible

Multi-event approach (quick overview) Program E-SURGE

E-SURGE  Extension of multistate framework  Hidden Markov Chains

E-SURGE Modeling done in 2 distinct steps: 1- State Transition Matrices (same as multistate modeling) 2- Observation Matrices (allows for misclassification)

Transition Matrices  3 alive states: P, B, N + “dead” PBN† P B N † 0001 True State at time t True State at time t+1

Observation Matrices  4 possible observations (“events”) PBN0 P B N † 0001 True State at time t Observation at time t