Using catch-per-unit-effort data to solve spatial problems in Orange Roughy abundance estimates

153 Pages·2015·0.71 MB·English

Using catch-per-unit-effort
data to solve spatial problems
in Orange Roughy abundance
estimates
by
Max Schofield
Athesis
submittedtotheVictoriaUniversityofWellington
infulfilmentofthe
requirementsforthedegreeof
MasterofScience
inBiologicalSciences.
VictoriaUniversityofWellington
2015

Abstract
This thesis describes a thorough analysis of the Andes Complex orange
roughy fishery, which started in 1991 and continues to date. The Andes
Complex orange roughy fishery displays a rapid initial decline in catch
rate, followed by a prolonged period of relatively stable catch rate. This
trend is the classic feature of a hyperdepletion catch rate. The trends in
the observed Andes Complex orange roughy catch rates were explored
through the development of eight modified Schaefer Surplus Production
Models(SPM).Eachmodelappliedahypothesisaboutamechanism catal-
ysing the observed trend of the fishery. The SPM was modified by ei-
ther adding new information to the model, or an additional parameter.
The fits of the modified models were optimised to elucidate values of un-
known parameters in the SPM, and these were used to create estimated
abundance indicies for each model. Then I compared each index to the
observed abundance index (catch rate), derived following an Exploratory
Analysis. The best candidate models, which had the smallest likelihoods,
BIC values, and best visual fits, were those assuming population growth
rate changed midway through the fishery, or that the population size de-
creasedfollowinghabitatdamage(fromtrawling).
ii
Acknowledgments
I would like to thank MPI (Ministry for Primary Industries) and NIWA
(National Institute of Water and Atmospheric Research) for their support
ofmypost-graduatestudythroughtheprovisionofapost-graduateschol-
arship in Quantitative Fisheries Science. I am eternally greatful for the
guidance and advice provided by my two supervisors Matt Dunn and
Nokuthaba Sibanda. Thanks to Craig for coming along for the ride and
help when I hit a wall. Thanks to Claudia for your support and encour-
agement. Finally,thankstoMumandDadforyourhelpallalongtheway.
iii
iv ACKNOWLEDGMENTS
Contents
Acknowledgments iii
1 Introduction 3
1.1 CatchPerUnitEffort . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 SpatialStructureofFishPopulations . . . . . . . . . . . . . . 10
1.3 OrangeRoughy . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4 ObjectiveandApproach . . . . . . . . . . . . . . . . . . . . . 17
1.5 HypothesesforStockStructure . . . . . . . . . . . . . . . . . 18
2 ModelStructureandEstimationMethods 21
2.1 SurplusProductionModel . . . . . . . . . . . . . . . . . . . . 21
2.1.1 SchaeferPopulationGrowthModel . . . . . . . . . . 23
2.1.2 ModelEquations . . . . . . . . . . . . . . . . . . . . . 27
2.1.3 ModelErrors . . . . . . . . . . . . . . . . . . . . . . . 31
2.2 MaximumLikelihoodEstimation . . . . . . . . . . . . . . . . 34
2.3 ParameterEstimation . . . . . . . . . . . . . . . . . . . . . . . 36
2.4 GeneralisedLinearModels . . . . . . . . . . . . . . . . . . . . 39
3 ExploratoryAnalysisoftheAndesFishery 43
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vi CONTENTS
3.1 AndesComplex . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 HistoryoftheAndesFishery . . . . . . . . . . . . . . . . . . 46
3.4 TemporalStructureoftheAndesFishery . . . . . . . . . . . 48
3.5 Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6 Subareas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.7 GeneralisedLinearModeling . . . . . . . . . . . . . . . . . . 59
3.8 AndesModel . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.8.1 BinomialModel . . . . . . . . . . . . . . . . . . . . . . 62
3.8.2 NormalModel . . . . . . . . . . . . . . . . . . . . . . 65
3.8.3 CombinedModel . . . . . . . . . . . . . . . . . . . . . 68
3.8.4 FinalModel . . . . . . . . . . . . . . . . . . . . . . . . 72
4 ModelFittingandComparison 77
4.1 ModelAssessment . . . . . . . . . . . . . . . . . . . . . . . . 77
4.1.1 InformationCriteria . . . . . . . . . . . . . . . . . . . 77
4.1.2 ConfidenceIntervalsandLikelihoodProfiles . . . . . 79
4.1.3 VisualAssessment . . . . . . . . . . . . . . . . . . . . 81
4.2 HypothesisedModels . . . . . . . . . . . . . . . . . . . . . . . 82
4.2.1 ClosedPopulationModel . . . . . . . . . . . . . . . . 82
4.2.2 TheChangingGrowthModel . . . . . . . . . . . . . . 87
4.2.3 TheAlteredEnvironmentModel . . . . . . . . . . . . 89
4.2.4 TheDisturbanceModel . . . . . . . . . . . . . . . . . 94
4.2.5 TheHabitatDegradationModel . . . . . . . . . . . . 96
4.3 ModelEvaluation . . . . . . . . . . . . . . . . . . . . . . . . . 101
5 Discussion 105
CONTENTS vii
6 Appendix 115
6.1 AppendixA:Rcode . . . . . . . . . . . . . . . . . . . . . . . 115
6.1.1 Example: UnweightedHabitatDegradationModel . 115
6.2 AppendixB:Likelihoodprofiles . . . . . . . . . . . . . . . . . 121
6.2.1 ChangingGrowthModel . . . . . . . . . . . . . . . . 121
6.2.2 UnweightedHabitatDegradationModel . . . . . . . 122
viii CONTENTS