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Refining mortality estimates in shark demographic analyses: a Bayesian inverse matrix approach
Author(s) -
Smart Jonathan J.,
Punt André E.,
Espinoza Mario,
White William T.,
Simpfendorfer Colin A.
Publication year - 2018
Publication title -
ecological applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.864
H-Index - 213
eISSN - 1939-5582
pISSN - 1051-0761
DOI - 10.1002/eap.1687
Subject(s) - leslie matrix , population , population model , vital rates , statistics , geography , bayesian probability , ecology , econometrics , mathematics , biology , population growth , demography , sociology
Leslie matrix models are an important analysis tool in conservation biology that are applied to a diversity of taxa. The standard approach estimates the finite rate of population growth (λ) from a set of vital rates. In some instances, an estimate of λ is available, but the vital rates are poorly understood and can be solved for using an inverse matrix approach. However, these approaches are rarely attempted due to prerequisites of information on the structure of age or stage classes. This study addressed this issue by using a combination of Monte Carlo simulations and the sample‐importance‐resampling (SIR) algorithm to solve the inverse matrix problem without data on population structure. This approach was applied to the grey reef shark ( Carcharhinus amblyrhynchos ) from the Great Barrier Reef (GBR) in Australia to determine the demography of this population. Additionally, these outputs were applied to another heavily fished population from Papua New Guinea (PNG) that requires estimates of λ for fisheries management. The SIR analysis determined that natural mortality ( M ) and total mortality ( Z ) based on indirect methods have previously been overestimated for C. amblyrhynchos , leading to an underestimated λ. Updated distributions of Z and λ were produced for the GBR population and corrected obvious error in the demographic parameters for the PNG population. This approach provides opportunity for the inverse matrix approach to be applied more broadly to situations where information on population structure is lacking.