OPEN CAPTURE-RECAPTURE 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) 5

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

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

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

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

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

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 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

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 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

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 NAJFM McKay 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

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

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

BREAK! then ON TO MARK