BRIEF INTRODUCTION TO
OPEN CAPTURE-RECAPTURE
METHODS
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
(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
(Band) Recovery models
Two options in MARK
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)
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
Differences
Capture-recapture
Recovery
• Individuals may be recaptured >1 time
• Recovered only once
• Tagging of unmarked individuals and
• Tagging and recovery at different
recaptures at same time, same people
• Numbers of marked and unmarked
animals random
• Number of tagging and recovery
periods same
times, different people
• Numbers of marked animals can be
predetermined
• Can be more recovery than tagging
periods
CJS Capture history
p
Recaptured
Alive
f
1-p
Fish alive and tagged
1-f
Dead
Not Recaptured
CJS Capture history, k=3
H
P(H)
111
f1p2f2p3
110
f1p2(1-f2p3)
101
f1(1-p2)f2p3
100
(1-f1) + f1(1-p2)(1-f2p3)
CJS Implementation in MARK
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.
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
Capture history multi-state model
fish movement
Parameters
(area, time indexed)
Capture probability, p (area, time)
Apparent survival, S (area)
ψAA
Movement (transition), ψ
pA 2
In Area A
1-pA2
Alive
SA
1
ψAB
Caught /released
fish in area A
1-SA1
Dead or perm emigrated
Recaptured
pB2
Not Recaptured
Recaptured
In Area B
1-pB2
Not Recaptured
Capture history multi-state fish model
p1 2
Recaptured
Alive in state 1
1- p12
F11
F12
Caught/released
State 1
p2 2
Not Recaptured
Recaptured
Alive in state 2
1- p22
Not Recaptured
1- F11-F12
Dead or perm emigrated
Assuming that survival depends only on state at time i:F = Sy
Multi-state implementation in MARK
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’
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
Comparison of ReverseTime Formulations
Formulation
losses on
capture abundance
estimates available for
net
births recruitment
POPAN
yes
yes
yes
no
no
Link-Barker- JS
yes
no
no
yes
yes
Pradel-recruitment
no
no
no
yes
no
Burnham JS
yes
yes
yes
no
yes
Pradel - l
yes
no
no
no
yes
Table from the MARK book
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
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:
Word of Caution
Confounded parameters in Link Barker
(recall Closed Cap-recap example)
Function
fK−1pK
Interpretation
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
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)
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)
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.
Barkers model encounter histories
5-occasion example (notice 10 columns total):
1010101002
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.
0000120100
Fish was captured on the 3rd occasion, and caught, released and reported
during the 3rd interval. It was reported harvested during the 4th interval.
Barker implementation in MARK
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
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. 2008
McKay NAJFM
Caston
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
Survival most strongly related to exceedences and angling effort
1.0
0.8
0.6
Survival
0.4
0.2
1500
e
nc
de
e
ce
Ex
0.0
500
1000
2000
40
30
2500
3000
20
10
0
ure
ress
P
r
le
Ang
50
60
Used survival models and temperature models to
estimate loss of fishing opportunities
80
Estimated cumulative
loss of trout (%)
70
Current
Pre-urbanization
60
50
40
30
20
10
0
Jun
Jul
Aug
Estimated amount of additional release needed
to equal pre-urbanization mortality
1.0
Monthly mortality
0.9
0.8
0.7
1976
0.6
2006
0.5
0.4
0.3
0.2
0
20
40
60
80
100
120
Average Flow at Buford Dam (cms)
140
BREAK!
then
ON TO MARK