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Analysis of Two Length‐Based Mortality Models Applied to Bounded Catch Length Frequencies
Author(s) -
Ehrhardt Nelson M.,
Ault Jerald S.
Publication year - 1992
Publication title -
transactions of the american fisheries society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.696
H-Index - 86
eISSN - 1548-8659
pISSN - 0002-8487
DOI - 10.1577/1548-8659(1992)121<0115:aotlmm>2.3.co;2
Subject(s) - estimator , fishing , life span , statistics , mathematics , fish <actinopterygii> , variance (accounting) , fishery , bounded function , econometrics , biology , economics , mathematical analysis , accounting , evolutionary biology
We performed an assessment of the length‐based total mortality model of Beverton and Holt, assuming that catch length‐frequency distributions in tropical artisanal fisheries are constrained by (1) the selective properties of multiple gears used and (2) the spatiotemporal availabilities of certain size classes of fish to operationally restricted fleets. Positive bias always resulted with the Beverton and Holt estimator of Z (total mortality); this estimator assumes an infinite exploitable life span. Estimates of Z were unreasonably biased when exploitable life spans were 50% or less of the biological life span of the species considered in the analyses. Biases were larger at lower levels of fishing mortality rates. We developed a new method from a truncated equation for average fish length. It considers length at first capture and the maximum retainable length actually observed in the fishery catch. The method has no explicit solution for Z , so we used numerical methods to provide its solution. The new estimator has zero bias at equilibrium. We determined variance of the new Z ‐estimator by bootstrap techniques.