Immigration Emigration Population Numbers Natural Mortality Fishing Mortality Catch Curves 2 Catch Curve Characteristics F it regression of logCPE on age only for ages on descending limb ID: 1001541
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1. Estimation of MortalityRecruitmentImmigrationEmigrationPopulationNumbersNatural MortalityFishing Mortality
2. Catch Curves2Catch Curve CharacteristicsFit regression of log(CPE) on age only for ages on descending limb.02468100.51.01.52.02.53.03.54.0Age / Timelog(CPE)AscDomeDescending-Z1-Z1
3. Catch Curves3Catch Curve AssumptionsPopulation closed to immigration and emigration.Z is constant.q is constant“Sample” is unbiased regarding any age-group (i.e., be careful of selective gears)Accurate agesFollow a cohort (if longitudinal CC used)Recruitment on descending limb is constant (if cross-sectional CC used)
4. Catch Curves4
5. Components of ZRecruitmentImmigrationEmigrationPopulationNumbersNatural MortalityFishing Mortality
6. DefinitionsInstantaneous ModelsF = instantaneous fishing mortalityM = instantaneous natural mortalityZ = F + MMortality Components6
7. DefinitionsDiscrete (Type I) FisheryF and M operate separately (different times)Realistic for a highly seasonal fisheryMortality Components7
8. DefinitionsContinuous (Type II) FisheryF and M operate at same timeWe will assume constant F & M through yearMortality Components8
9. DefinitionsDiscrete (Annual) Modelsu = annual exploitation rateexpectation of death due to fishingproportion of population that dies due to fishingv = annual natural mortality ratem = annual conditional fishing mortality rateexpectation of death due to fishing IF no other source of mortality existedproportion of population that dies due to fishing IF no other source of mortality existedn = annual conditional natural mortality rateMortality Components9
10. DefinitionsA = m + n – mnmn is that some fish that died from one cause may have ultimately died of the other causeDiscrete (Type I) Fisherymn=0 …. A = m + n = u + vContinuous (Type II) FisheryA ≠ u + vThus, most work on instantaneous scaleMortality Components10
11. Mortality ComponentsAs a manager, which of natural or fishing mortality can you control and, thus, want to know?Controlling F, u, m is a major goal of most fisheries management strategies.Very difficult to estimate precisely
12. Estimating MAssume a constant value for MTypically use M=0.2Is this realistic?Mortality Components12
13. Estimating MAssume a constant value for MRelationship of M to life history traitsSee page 217 in IFARMortality Components13
14. Estimating MCatch Curves14
15. Estimating MCatch Curves15
16. Estimating MAssume a constant value for MRelationship of M to life history traitsFrom f and ZRecall that Z = F+M and F=qfThus, Z = qf+MIf Z is estimated at different f, then …M is the intercept from the Z on f regression.Same as asking what is Z when f = 0.Mortality Components16
17. Estimating F from Expoitation RateIf the ratio of fishing to natural mortality is constant throughout the year then … … describe this … Thus, given an estimate of Z (and A), F can be estimated if u can be estimated. Mortality Components17
18. Estimating uDivide annual harvest by estimate of N.Mortality Components18
19. Estimating uDivide harvested tagged fish by number of tagged fish released.Mortality Components19
20. Estimating uDivide annual harvest by estimate of N.Divide harvested tagged fish by number of tagged fish released.Recall that these estimates are only valid if ratios of fishing and natural mortality are constant throughout the year.Mortality Components20
21. Mortality Components21
22. Mortality Components22Estimating F with Marked FishConsider –The number of fish caught is the proportion of dying fish due to fishing mortalityThis proportion is F/ZTherefore …Consider -- Where the asterisks represent only marked fish
23. Mortality Components23Estimating F with Marked FishSubstitute Nt* equation into catch equationand rearrange for simplicityand take natural logs of both sides
24. Mortality Components24Estimating F with Marked FishExamine this model closely …Slope is an estimate of –ZIntercept is an estimate of …Which can be solved for F
25. Mortality Components25Example400 fish were initially taggedTags were returned from the fishery over the next four yearsConsider the time period to be the midpoints of the years.Use these data to estimate Z & F (see HO).