Constructing a coherent joint prior while respecting biological realism: application to marine mammal stock assessments

Abstract

Brandon, J. R., Breiwick, J. M., Punt, A. E., and Wade, P. R. 2007. Constructing a coherent joint prior while respecting biological realism: application to marine mammal stock assessments. – ICES Journal of Marine Science, 64: 1085–1100. Bayesian estimation methods, employing the Sampling–Importance–Resampling algorithm, are currently used to perform stock assessments for several stocks of marine mammals, including the Bering–Chukchi–Beaufort Seas stock of bowhead whales (Balaena mysticetus) and walrus (Odobenus rosmarus rosmarus) off Greenland. However, owing to the functional relationships among parameters in deterministic age-structured population dynamics models, placing explicit priors on each life history parameter in addition to the population growth rate parameter results in an incoherent joint prior distribution (i.e. two different priors on the estimated parameters). One solution to constructing a coherent joint prior is to solve for juvenile survival analytically, using values generated from the prior distributions for the remaining parameters. However, certain combinations of model parameter values result in values for juvenile survival that are larger than adult survival, which is biologically implausible. Therefore, to respect biological realism, certain parameter values must be rejected for some or all the remaining parameters. This study investigates several alternative resampling schemes for obtaining a realistic joint prior distribution, given the constraint on survival rates. The sensitivity of assessment results is investigated for data-rich (bowhead) and data-poor (walrus) scenarios. The results based on limited data are especially sensitive to the choice of alternative resampling scheme.

Long‐term abundance trends of the northern form of the short‐finned pilot whale (Globicephala macrorhynchus) along the Pacific coast of Japan

“…The time series of abundance estimates are essential for the stock assessment based on the population dynamics model (Wade 2002, Brandon and Wade 2006, Brandon et al . 2007).…”

Modelling the possible effects of climate change on an Australian multi-fleet prawn fishery

“…The model was then fitted to the observed catch data using a maximum likelihood function and the Bayesian Sampling Importance/Re-sampling (SIR) method (Brandon et al 2007;Ives and Scandol 2007). Owing to computational limitations, Bayesian priors were only applied to a subset of parameters (see also Fay and Punt 2006).…”

Conservation markets for wildlife management with case studies from whaling

“…A very simple decision rule is simply to set the cap at the current level of harvest (if this is deemed safe for the population), but more sophisticated rules are also possible. While a variety of algorithms could be employed to identify a sustainable harvest level (Porch and Fox 1990, Cooke 1999, Givens 1999, McAllister and Kirchner 2001, Reeves 2002, Brandon et al 2007, Smith et al 2008, Haltuch et al 2009, Hillary 2009), we used Notes: Data for bowheads (Balaena mysticetus) are from Brandon et al (2007) and Gerber et al (2007); for gray whale (Eschrictius robustus), data are from Loomis and Larson (1994), Gerber et al (1999), Laake et al (2009), andWade (2010); and for minke whales (Balaenoptera acutorostrata), data are from Amundsen et al (1995), Bulte and vanKooten (1997), Bulte et al (1998), NAMMCO (1998), Horan and Shortle (1999), and Laake et al (2009). the potential biological removal (PBR) approach as an illustrative example, because it is transparent, conservative, and already used to manage marine mammals in the USA (Taylor et al 2000).…”