Steep recruitment relationships result from modest changes in egg to recruit mortality rates
Introduction
Ever since Ricker (Ricker, 1954) introduced the formal analysis of the relationship between spawning stock and subsequent recruitment, there has been interest in how much the recruits per spawner can increase as the abundance of spawners declines. Myers was the first to assemble a large number of spawner-recruit data sets (Myers et al., 1995) and the subsequent analysis (Myers and Barrowman, 1996) showed the pattern across various taxa. Myers’ original data set has now been expanded to include over 1000 fish stocks (Ricard et al., 2012). Most of these data sets show evidence of relatively strong compensatory increase in pre-recruit survival rates at lower stock sizes. When this increase is measured by the ratio of juvenile survival rates at low stock sizes to survival rates at unfished stock sizes, survival rates are often seen to improve by factors of 20 or more. Indeed, that dramatic improvement in survival is the most common ecological basis for sustainable fisheries, though compensatory improvements in body growth and natural morality rates of older fish may also play some role. Rose et al. (Rose et al., 2001) showed that any species that can survive at high rates from egg to recruitment must show dramatic compensation because in the unfished state, total recruitment must be equal to natural mortality of the spawning population.
At first glance, it seems unreasonable or unlikely that juvenile fish could survive at so much higher rates when they are at low densities. In this note, we show that relatively small changes in juvenile survival rates are actually required to explain this and use a range of case examples to demonstrate this effect.
Section snippets
Material and methods
In an unfished population that is stable, the mean annual recruitment rate per spawner must equal the average annual mortality rate of spawners. Given mean fecundity f per spawner and annual spawner mortality rate m, this balance relationship can be expressed in terms of the total pre-recruit mortality rate Mo asfe−Mo = m
This relationship implies that we can calculate Mo given estimates of f and m asMo = -ln(m/f) = ln(f)-ln(m)
For semelparous species like Pacific salmon, m = 1 and Mo is given
Results
For the sample of species in Table 1, fecundities per female vary by three orders of magnitude and mean compensation ratios vary by one order of magnitude; from near four to over 40. As expected from other studies like Goodwin et al., (Goodwin et al., 2006) there is only weak positive covariation between fecundity and CR (Fig. 1), and high fecundity is certainly not a guarantee of strong recruitment compensation. For species with data from multiple stocks, there is considerable intraspecific
Discussion
Much of the post-larval mortality risk (as measured by Mo-Megg) likely occurs soon after hatching when juveniles are small and need to grow and find refuge from predators. The pattern in Fig. 2 can be explained by a behavior hypothesis that when juvenile densities are very low (e.g. when stock size has been severely reduced by fishing), juveniles are spending approximately 20–40 % less time in relatively risky activities. When juveniles are spatially concentrated in the first place (e.g. in
Funding
This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.
Data availability statement
All data used in this analysis are available from published papers that are cited or are shown in Supplemental Table 1.
CRediT authorship contribution statement
Ray Hilborn: Conceptualization, Investigation, Writing - original draft, Writing - review & editing. Carl J. Walters: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Writing - original draft, Writing - review & editing.
Declaration of Competing Interest
The authors report no declarations of interest.
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