Revisiting the concept of Beverton­­–Holt life-history invariants with the aim of informing data-poor fisheries assessment

Abstract

The complexity and cost of assessment techniques prohibits their application to 90% of fisheries. Simple generic approaches are needed for the world's small-scale and data-poor fisheries. This meta-analysis of the relationship between spawning potential and the normalized size and age of 123 marine species suggests that the so-called Beverton–Holt life-history invariants (BH-LHI; Lm/L∞, M/k, M × Agem) actually vary together in relation to life-history strategy, determining the relationship between size, age, and reproductive potential for each species. Although little realized, the common assumption of unique values for the BH-LHI also implies that all species share the same relationship between size, age, and reproductive potential. This implicit assumption is not supported by this meta-analysis, which suggests that there is considerable but predictable natural variation in the BH-LHI ratios and the relationships between size, age, and reproductive potential that they determine. We believe that this reconceptualization of the BH-LHI has potential to provide a theoretical framework for “borrowing” knowledge from well-studied species to apply to related, unstudied species and populations, and when applied together with the assessment technique described by Hordyk et al. (2015b), could make simple forms of size-based assessment possible for many currently unassessable fish stocks.

An evaluation of an iterative harvest strategy for data-poor fisheries using the length-based spawning potential ratio assessment methodology

“…The M/k ratio determines the shape of the unfished size composition in populations 353 under equilibrium (Hordyk et al, 2014a, Prince et al, 2014, and the biological parameters 354 for the MSE were based on three species that covered a range of M/k ratios ( History Invariant (BH-LHI) ratio of 1.5 (Jensen, 1996) to those with a much lower M/k of 368 0.36 (Table 1). To ensure that the catch contained a reasonable number of length classes, the 369 selectivity-at-length curve was set lower than maturity-at-length curve for each species, and 370 assumed constant for each species across scenarios.…”

“…The 565 three species used in this MSE had M/k ratios that ranged from M/k=1.5 (Species I Scomber 566 japonicus), a species where unfished stocks are dominated by small sized individuals and 567 large animals are relatively rare, to M/k= 0.36 (Species III Lutjanus erythropterus), where the 568 unfished length composition is expected to be comprised of almost entirely adult sized 569 animals (Hordyk et al, 2014a). These species represent a range of life histories that are 570 common in marine species, although the M/k ratios for a number of species are considerably 571 greater than 1.5 (e.g., up to 3.5; Prince et al, 2014). The species examined in this study were 572 all relatively long-lived (maximum age of 15 -33 years; Table 1).…”

“…If the M/k ratio of two species with very different life spans and maximum sizes are 575 the same, the relative shape of the unfished length structure (i.e., length standardized to 576 maximum length) is expected to be identical (Hordyk et al, 2014a, Prince et al, 2014. In 577 principle, the LB-SPR methodology should therefore perform similarly across a range of 578 different lifespans, provided that the sampling of the length composition is scaled to the 579 lifespan of the animal.…”

“…Information on the length structure of the catch is often one of the most accessible 594 sources of data for fish stocks (Quinn and Deriso, 1999) However, the ratio of M/k is known to vary less between species than either of the individual 611 parameters in the ratio (Beverton, 1992;Prince et al, 2014). Meta-analysis and comparative 612 studies may be useful for providing estimates of the M/k ratio for data-poor stocks without 613 the need for expensive ageing studies.…”

“…Furthermore, the basic biological parameters required for the LB-SPR method (Hordyk et al, 108 2014a, 2014b) can either be obtained with relatively simple biological studies, or "borrowed" 109 from other similar species by meta-analysis (Prince et al, 2014). Because the LB-SPR model 110 has few data requirements and is relatively simple to understand and apply, the method has 111 potential as a valuable tool for the assessment and management of data-poor fisheries.…”