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UI WLF 448 - Mortality

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MortalityMortality = (1-Survival)IntroductionConstant survival models for fish and birds (Catch curves)Age-/Stage-specific modelsBand recovery analysisMARKIntroductionCrude mortality rate = deaths/starting N = (Nx-Nx+1)NxAge-specific mortality rateSurvival rate = 1-mortality rate = Nx+1/NxSimplest approach (model) assumes constant rates for different ages/yearsCatch Curves= “Kill Curves” in birds and mammalsBased on these simplest assumptions about rates (i.e. constant for ages and years)Catch Curves <5 6-7 9 12 14 16 18 19020406080100CatchSize of FishCatch CurvesIf 100 are born and 50% survive, then there will be 50 one-year oldsIf 50% survive, 25 two-year oldsIf 50% survive, 12 three-year oldsIf 50 % survive, 6 four-year oldsCatch CurvesNumber alive = Number X SurvivalN1 = No SN2 = No S SN2 = No S2Nt = No Stlog Nt = log No + t log SCatch CurvesSince S (survival rate) is less than 0log S is always negativeLet Z = -log SZ = Instantaneous total mortalityThen log Nt = log No - Z tCatch Curves 4 6 9 12 14 16 18 1900.511.52log Nt tCatch Curves 4 6 9 12 14 16 18 1900.511.52log Nt = log Nr - Z t t=age=lengthlog NtFishing and Natural MortalityFishing: c=catch/N=1-e-FNatural: n=natural deaths/N = 1-e-MCombining them as finite rates is complicated: Total= m+n+m*nBut easy as instantaneous rates: Total mortality = 1-e-(F+M)= 1-e-Z (Z=F+M)Catch Curves1. Mortality is constant with age2. No change in mortality over time3. Fishing and natural mortality are uniform4. Recruitment is constant5. Fish fully recruited to gear by age rLife TablesMore realistic approach relaxes assumption of equal age-specific survival ratesIdeal approach marks a “cohort” at birth/young age and counts how many still alive each year[=cohort life table]Summarize easily by plotting survivorship (lx = no. alive at age x)Survivorship CurvesExamples:MammalsHumansBirdsFishTypes of Survivorship (Pearl 1930,Deevey 1947)Stage-specific rates?Band Recovery AnalysisSuppose we had banded 1603 adult male mallards in August of 1980How could we predict how many we would receive bands from in 1980, 1981, 1982, etc ?It will depend on the fraction of the birds shot in a year and turned in to us (Band recovery rate) and the survival of birds (Survival rate)Band Recovery AnalysisN1 = Number banded in year 1f1 = band recovery rate in year 1S1 = survival rate in year1R12 = recoveries in year 2 from birds banded in year 1R11 = N1 f1R12 = (N1 S1) f2Program MARKWe can use the program MARK written by Gary White at CSU to estimate these survival and recovery rates from banding data as well as estimates for a variety of other survival, recovery and mark-resight models.To do this we use the PIM or Parameter Information MatrixProgram MARKFor band recovery data we Select Data Type =Brownie et al. Recoveries orRecoveries onlyPIM - Parameter Information Matrix Survival Parameter (S)123456234563456456566Occasions135time = 1 2 3 4 5 6 PIM - Parameter Information Matrix Recovery Parameter (f)7 8 91011128 9 10 11 12910111211 1212time = 1 2 3 4 5 6 Comparing ModelsWith MARK we can estimate a large variety of models.We can compare models using AIC or Akaike’s Information Criterion.AIC measures the deviation of observed data from the model adjusted for the numberof parameters in the model.AIC = -2 ln(L) + 2 n pThe lower the AIC the better the model.For nested models we could also use Likelihood Ratio Tests.Mark-recapture or -resight DataSelect Data Type = Recaptures onlyPIM - Parameter Information Matrix Apparent Survival Parameter (Phi)123456234563456456566time = 1 2 3 4 5 6 PIM - Parameter Information Matrix Recapture Parameter (p)7 8 91011128 9 10 11 12910111211 1212time = 1 2 3 4 5 6CJSThese PIMs describe the Jolly-Seber model,more formally this is calledfully time-dependent Cormack-Jolly-Seber model.Cohort Lifetable - Age-specific Survival (Sx)123456time = 1 2 3 4 5 6 Time-specific Lifetable - Age-specific Survival (Sx)123456time = 1 2 3 4 5 6 Catch Curve - Survival (S)1111111time = 1 2 3 4 5


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UI WLF 448 - Mortality

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