Evaluating evidence for alternative natural mortality and process error assumptions using a state-space, age-structured assessment model

Abstract

State-space models explicitly separate uncertainty associated with unobserved, time-varying parameters from that which arises from sampling the population. The statistical aspects of formal state-space models are appealing and these models are becoming more widely used for assessments. However, treating natural mortality as known and constant across ages continues to be common practice. We developed a state-space, age-structured assessment model that allowed different assumptions for natural mortality and the degree of temporal stochasticity in abundance. We fit a suite of models where natural mortality was either age-invariant or an allometric function of mass and interannual transitions of abundance were deterministic or stochastic to observations on Gulf of Maine – Georges Bank Acadian redfish (Sebastes fasciatus). We found that allowing stochasticity in the interannual transition in abundance was important and estimating age-invariant natural mortality was sufficient. A simulation study showed low bias in annual biomass estimation when the estimation and simulation model matched and the Akaike imformation criterion accurately measured relative model performance, but it was important to allow simulated data sets to include the stochasticity in interannual transitions of abundance-at-age.

Disentangling risks to an endangered fish: using a state-space life cycle model to separate natural mortality from anthropogenic losses

“…The model adds to the growing evidence that multiple, simultaneously acting mortality rates may be estimated when observations of the number of mortalities are combined with observations of abundance in a population model. A common approach to fitting population models, especially in fisheries stock assessments, is to assume that natural mortality cannot be estimated and set it to a constant, externally estimated value, but evidence from hierarchical modeling indicates that more information about natural mortality rates can be derived from harvest and abundance data than was previously recognized (Millar and Meyer 2000;Miller and Hyun 2018). Using simulations, we demonstrated that it was possible to extract both entrainment and natural mortality rates, coefficients, and process variance (see Appendix A).…”

Performance of a state‐space multispecies model: What are the consequences of ignoring predation and process errors in stock assessments?

“…These biases could affect stock management as they result in biased reference point estimates on both absolute and relative scales. Assuming a known natural mortality fixed as constant over time and sometimes ages is a common approach used in stock assessment (Johnson et al, ; Lee, Maunder, Piner, & Methot, ; Miller & Hyun, ). It is therefore important to know that, despite a fit to observed data that could be perceived as reasonable (Figure ), misspecifications of natural mortality can affect the perception of fish stock status irrespective of harvest history (EM3 and EM4 had large bias for both constant and varying ), and the consequences of these changes in perception on catch advice can be great.…”

“…The maximum bias was on the variance of the process errors on fish abundance (≃−30%), larger than bias in recruitment process error standard deviation (≃−3%). Underestimating process error variances is common in simulation testing and larger underestimation of variance in process errors on fish abundance compared to recruitment was also observed in state‐space single species models (Miller & Hyun, ). Auger‐Méthé et al () demonstrated that estimation bias can occur when observation errors are larger than process errors.…”

“…However, EM4 showed the largest bias. Similarly, constant natural mortality gave better results than age‐varying mortality in state‐space single species assessment (Miller & Hyun, ). Deroba and Schueller () also concluded that misspecification of temporal variations in M results in more bias than variation with age for single species statistical catch‐at‐age models, when M is assumed known.…”

State-space Modeling Clarifies Productivity Regime Shifts of Japanese Flying Squid

“…Distinguishing recruitment process and observation error is important for 89 accurately detecting regime shifts (King et al 2015;Maunder and Thorson 2019). such as abundance and fishing mortality as random effects have been developed and is 92 effective at separately estimating process and measurement errors (Nielsen and Berg 93 2014;Miller and Hyun 2017;Okamura et al 2018). However, these models are 94 age-structured and not possible to apply to the Japanese flying squid, because its 95 life-span is a single year.…”