BRIEF INTRODUCTION TOBRIEF INTRODUCTION TOOPEN CAPTURE-RECAPTURE OPEN CAPTURE-RECAPTURE
METHODS METHODS
Open Population Open Population EstimationEstimation
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(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(Band) Recovery models
Two options in MARK
Cormack-Jolly-Seber ModelsCormack-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 ModelsCormack-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
Capture-recapture
•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
Differences
CJS Capture history
Fish alive and tagged
1-
Recaptured
Not Recaptured
p
1-p
Dead
Alive
111 1p22p3
110 1p2(1-2p3)
101 1(1-p2)2p3
100 (1-1) + 1(1-p2)(1-2p3)
CJS Capture history, k=3
H P(H)
CJS Implementation in MARK
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.
Assumptions of CJSCJS
Multi-State (Strata) ModelsMulti-State (Strata) Models
Models of transitionSurvival
Over timeTo age class
MovementOther types of transition (e.g., juv-
smolt) Arrival/ “seniority”
Take into account sampling
Capture history multi-state Capture history multi-state model fish movementmodel fish movement
Caught /released fish in area A
1-SA1
SA1
In Area A
In Area BψAB
ψAA
Recaptured
Not Recaptured
Recaptured
Not Recaptured
pA2
1-pA2
pB2
1-pB2
Dead or perm emigrated
Alive
Parameters (area, time indexed)
Capture probability, p (area, time)Apparent survival, S (area)Movement (transition), ψ
Capture history multi-state fish Capture history multi-state fish modelmodel
Caught/releasedState 1
11
Recaptured
Not Recaptured
p12
Dead or perm emigrated
Alive in state 1
1- p12
Recaptured
Not Recaptured
p22
Alive in state 2
1- p22
12
1- 11-12
Assuming that survival depends only on state at time i:S
Multi-state implementation in MARK
Multi-state capture histories 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’
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
Reverse-Time (Pradel) Reverse-Time (Pradel) ModelsModels
Comparison of Reverse-Comparison of Reverse-Time FormulationsTime Formulations
losses on estimates available forFormulation capture abundance 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 - yes no no no yes
Table from the MARK book
:rate of change of the population
i = Ni+1/Ni
f: per capita fecundity survival rate
Ni+1 = Nifi + Ni i
i = fi + i
Pradel and Link-Barker-JS
JS implementation in MARK
You select the formulation after setting up JS by selecting “Change data type” from the “PIM” pull down menuYou will see this screen:
Confounded parameters in Link Barker (recall Closed Cap-recap example)
Function InterpretationK−1pK Final survival and catchability
(1 + 1)/p1 Initial recruitment and survival
K−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
Word of CautionWord of Caution
Live/Dead Sight-ResightTag-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-levelElevationCanopy coverSubstrate
Individual-levelSexLengthAgeDiseased
Covariates measured because they are thought to influence the population somehow
These thoughts are the underlying basis for hypotheses
McKay Caston McKay Caston
Illustration: Illustration: Chattahoochee River, GA Chattahoochee River, GA
Trout Fishery IssuesTrout Fishery Issues• Urbanization increased > 300% last 30 yrsUrbanization increased > 300% last 30 yrs
• Urbanization altered thermal regime Urbanization altered thermal regime
• Altered thermal regime negatively effects trout fisheryAltered thermal regime negatively effects trout fishery
Runge et al. 2008 NAJFM
ApproachApproach
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
0.0
0.2
0.4
0.6
0.8
1.0
500
1000
1500
2000
2500
30000
1020
3040
5060
Survival most strongly related to exceedences and angling effort
CurrentPre-urbanization
0
10
20
30
40
50
60
70
80
Jun Jul Aug
Est
ima
ted
cu
mu
lativ
e lo
ss o
f tr
ou
t (%
)
Used survival models and temperature models to estimate loss of fishing opportunities
1976
2006
Average Flow at Buford Dam (cms)
0 20 40 60 80 100 120 140
Mon
thly
mort
alit
y
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Estimated amount of additional release neededto equal pre-urbanization mortality
BREAK!then
ON TO MARK