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