1. OPEN CAPTURE-RECAPTURE
BRIEF INTRODUCTION TO
OPEN CAPTURE-RECAPTURE
METHODS

2. Open Population Estimation
Populations open between sampling periods
Immigration/emigration
Birth/ death
Population rates often of interest:
Survival
Recruitment
Exploitation
Movement
(abundance)
Lots’o estimators, depends on what you want to know

3. (Band) Recovery models
Survival, recovery, harvest rates and other parameters based on recoveries of tags
Recoveries from animals tagged, released and
Found dead and reported
Harvested, retrieved and reported by anglers
Data structure and models similar to Cormack-Jolly-Seber (CJS) models (next)
Focus on survival and related parameters but not on
Abundance
Recruitment
Parameters: S= survival (time varying, covariates)
f = Recovery/ harvest

4. (Band) Recovery models
Two options in MARK

5. Cormack-Jolly-Seber Models
Sampling conducted over a small area on at least 3 occasions (e.g., years)
Recaps = handling or re-sighting (radio-telemetry)
Parameters
Capture probability, pi: probability that marked fish is captured in period i
Apparent survival, phii: probability that an animal alive in time i survives until i + 1 and does not permanently emigrate
can’t tease apart death from permanent emigration
(generally underestimates true survival) 5

6. Cormack-Jolly-Seber Models
Sampling conducted over a small area on at least 3 occasions (e.g., years)
Release Ri animals each occasion i = 1…, k
Recaps = handling or re-sighting (radio-telemetry)
Parameters conditional on releases of animals
Unmarked animals not part of likelihood
No estimation of abundance or recruitment 6

7. Differences Capture-recapture Recovery
Individuals may be recaptured >1 time
Tagging of unmarked individuals and recaptures at same time, same people
Numbers of marked and unmarked animals random
Number of tagging and recovery periods same
Recovery
Recovered only once
Tagging and recovery at different times, different people
Numbers of marked animals can be predetermined
Can be more recovery than tagging periods

8. CJS Capture history Recaptured Alive Not Recaptured
Fish alive and tagged
1-f f
Recaptured
Not Recaptured p
1-p
Dead
Alive

9. CJS Capture history, k=3 H P(H) 111 f1p2f2p3 110 f1p2(1-f2p3) 101
100
(1-f1) + f1(1-p2)(1-f2p3)

10. CJS Implementation in MARK

11. Assumptions of CJS NO EFFECT OF CAPTURE ON SURVIVAL, RECAPTURE
Marks not lost over overlooked, are read correctly
Sampling periods are instantaneous, animals immediately released
Effectively, short relative to duration of i to i+1 interval
All emigration from study area is permanent
Fates are independent events
These below are relaxed for time specific, multiple stage (age) and other CJS
Every marked animal present in population at sampling period i has same probability of recapture or re of re-sighting
Every marked animal present in population immediately after period i has same probability of survival from i to i+1.

12. Multi-State (Strata) Models
Models of transition
Survival
Over time
To age class
Movement
Other types of transition (e.g., juv-smolt)
Arrival/ “seniority”
Take into account sampling

13. Capture history multi-state model fish movement
Parameters (area, time indexed)
Capture probability, p (area, time)
Apparent survival, S (area)
Movement (transition), ψ
Caught /released
fish in area A
1-SA1
SA1
In Area A
In Area B
ψAB
ψAA
Recaptured
Not Recaptured
pA2
1-pA2
pB2
1-pB2
Dead or perm emigrated
Alive

14. Capture history multi-state fish model
Recaptured
Alive in state 1
Not Recaptured
1- p12
F11
p22
Recaptured
F12
Caught/released
State 1
Alive in state 2
Not Recaptured
1- p22
1- F11-F12
Dead or perm emigrated
Assuming that survival depends only on state at time i:F = Sy

15. Multi-state implementation in MARK

16. Multi-state capture histories
Letters are used in place of “1” to indicate where the fish was captured
e.g., 3 states represented by A, B, C
History: A0ABC
Interpretation: initially captured in state (location) ‘A’ not recaptured second occasion, recaptured 3rd occasion in state ‘A’, recaptured fourth occasion state ‘B’, recaptured fifth occasion state ‘C’

17. Reverse-Time (Pradel) Models
Normally, focus is on estimating the probability of individuals leaving population (e.g., death)
But, we may also be interested in estimating the probability of individuals entering the population (probability of entry, recruitment).
Estimable Parameters
Capture probability, Survival, Recruitment, Population growth rate, abundance
Multiple Formulations!
POPAN
Pradel
Jolly-Seber lambda (Burnham)
Link-Barker Jolly-Seber

18. Comparison of Reverse- Time Formulations
losses on
estimates available for
Formulation
capture
abundance
net
births
recruitment
POPAN
yes no
Link-Barker- JS
Pradel-recruitment
Burnham JS
Pradel - l
Table from the MARK book

19. Pradel and Link-Barker-JS
l:rate of change of the population
li = Ni+1/Ni
f: per capita fecundity
f: survival rate
Ni+1 = Nifi + Ni fi
li = fi + fi

20. JS implementation in MARK
You select the formulation after
setting up JS by selecting
“Change data type”
from the “PIM” pull down menu
You will see this screen:

21. Word of Caution Confounded parameters in Link Barker
(recall Closed Cap-recap example)
Function Interpretation
fK−1pK Final survival and catchability
(f1 + f1)/p1 Initial recruitment and survival
fK−1pK Final recruitment and catchability cannot be cleanly estimated. MARK (and other programs) will report an estimate for this complicated function of parameters but it may not be biologically meaningful.
This information is documented in MARK book and MARK help files

22. Live/Dead Sight-Resight Tag-Recovery Models (Barkers model)
Combines multiple sources of recapture data
live recaptures (e.g., sampling and by anglers)
Resight (angler catch release, telemetry)
Fish may be resighted multiple times within an interval
Dead recoveries (e.g., harvest)

23. Barkers model parameters
Si: probability an animal alive at i is alive at i + 1
Pi: probability an animal at risk of capture at i is captured at i
ri: probability an animal that dies in i, i + 1 is found dead and the tag reported
Ri: probability an animal that survives from i to i + 1 is resighted (alive) some time between i and i + 1.
R'i: the probability an animal that dies in i, i + 1 without being found dead is resighted alive in i, i + 1 before it died (think catch and release mortality using both R).
Fi: probability an animal at risk of capture at i is at risk of capture at i + 1 (i.e., the fish did not leave)
F'i: probability an animal not at risk of capture at i is at risk of capture at i + 1 (i.e., the fish left)

24. Barkers model Movement
Probability of leaving study area before capture at i: 1- Fi
Types of emigration
Random: Fi’ = Fi
Permanent: Fi’ = 0
Capture history
Encounter history in LDLD format
2 columns for each occasion
first column indicates that is was captured and alive on that occasion (0=no, 1=yes)
second column is coded 0,1, or 2:
0 = not resighted or reported dead in the interval
1 = reported dead, 2= resighted alive during interval
*** Important: there can be multiple occasions with a 1 in the L columns, and multiple occasions with a 2 in the D columns, but only one D column can have a 1.

25. Barkers model encounter histories
5-occasion example (notice 10 columns total):
Fish was captured on the first occasion, and recaptured again on the 2nd, 3rd, and 4th occasions.  It was not captured on the 5th occasion, but was detected in a array during the last interval.  
Fish was captured on the 3rd occasion, and caught, released and reported during the 3rd interval.  It was reported harvested during the 4th interval.

26. Barker implementation in MARK

27. Why Covariates?
Site- and individual-level factors can heavily influence the population characteristics we’re interested in.
Most MR approaches – parameters can be modeled as a function of covariates
Site-level
Elevation
Canopy cover
Substrate
Individual-level
Sex
Length
Age
Diseased
Covariates measured because they are thought to influence the population somehow
These thoughts are the underlying basis for hypotheses

28. Illustration: Chattahoochee River, GA Trout Fishery Issues
Urbanization increased > 300% last 30 yrs
Urbanization altered thermal regime
Altered thermal regime negatively effects trout fishery
Runge et al NAJFM
McKay Caston

29. Approach Original (first 2 years) 200 hatchery trout/ mo, floy-tagged
Released 2 sections different thermal regimes
Estimate survival each section, angler tag returns
Very poor returns (< 25 reports) no estimates possible
Modification (last year)
Same number trout and tagging (but some double tagging)
DNR biologists sampled trout 2 days following each release
Multi-state tag recapture -recovery model (live-dead encounters)
Estimated survival, movement, reporting rate, capture probability
Modeled rates using covariates

30. Survival most strongly related to exceedences and angling effort

31. Used survival models and temperature models to
estimate loss of fishing opportunities 10 20 30 40 50 60 70 80
Jun
Jul
Aug
Estimated cumulative
loss of trout (%)
Current
Pre-urbanization

32. Estimated amount of additional release needed
to equal pre-urbanization mortality
Average Flow at Buford Dam (cms) 20 40 60 80
100
120
140
Monthly mortality
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1976
2006

33. BREAK!
then
ON TO MARK