Frank and Brickman 2000 - Gulf of Maine Research Institute

More documents

Recommendations

Info

514 Can. J. Fish. Aquat. Sci. Vol. 57, 2000 Table 1. Visual display of the conceptual model showing the time course of sampling stock and recruitment data from each of the eight substocks within a hypothetical management unit. Year Substock 1 Substock 2 Substock 3 Substock 4 Substock 5 Substock 6 Substock 7 Substock 8 Total 1 S 1 , R 1 S 2 , R 2 S 3 , R 3 S 4 , R 4 S 5 , R 5 S 6 , R 6 S 7 , R 7 S 8 ,R 8 S tot , R tot 2 "," "," "," "," "," "," "," "," "," 3 "," "," "," "," "," "," "," "," "," 4 "," "," "," "," "," "," "," "," "," 5 S crit "," "," "," "," "," "," "," "," 6 " "," "," "," "," "," "," "," "," 7 " S crit "," "," "," "," "," "," "," 8 " " "," "," "," "," "," "," "," 9 S ext " "," "," "," "," "," "," "," 10 " "," "," "," "," "," "," "," 11 S ext "," "," "," "," "," "," "," . S crit "," "," "," "," "," "," . " "," "," "," "," "," "," . S ext "," "," "," "," "," "," 43 "," "," "," "," "," "," 44 S crit "," "," "," "," "," 45 " "," "," "," "," "," 46 " S crit "," "," "," "," 47 " " "," "," "," "," 48 S ext " S crit "," "," "," 49 " " "," "," "," 50 S ext " S crit "," "," 51 " " "," "," Note: The thresholds (S crit , the critical spawning stock biomass level below which no recruitment occurs, and S ext , the extinction of the spawning stock) are reached at different times because of the different starting values of S. At the end of the simulation (run length equal 51 years), five of the eight substocks are extinct. The final column in the table shows the sum of the stock and recruitment data from all of the substocks, the level of data aggregation normally available for analysis of stock and recruitment relationships. Please note that the simulation did not run precisely in the manner depicted but is presented for illustrative purposes only. though the time scales for recovery of collapsed stocks may be difficult to predict, it is clear that stocks that decline the most are the slowest to recover. Why is it that so many collapsed stocks have failed to recover? A recent study suggests that the most frequent form of fish population regulation is compensatory population dynamics (Myers et al. 1995). The Ricker and Beverton and Holt stock (SSB) and recruitment (R) models rely on a compensatory response — increasing per capita reproductive success (R/SSB) with decreasing stock size. In other words, increasing prerecruit survival compensates for reductions in egg production associated with decreasing SSB. This leads to the assumption that when fishing mortality is eliminated from an overfished stock it should recover to a stable equilibrium at relatively high levels of SSB. However, the failure of collapsed stocks to recover suggests that other mechanisms are influencing the production dynamics at low population levels. An infrequently encountered population dynamic model, but one consistent with the lack of recovery of collapsed stocks, is depensatory population dynamics. In this model, juvenile survival decreases at low stock levels and a second, lower equilibrium point exists that is unstable. If the stock is reduced to levels below this secondary equilibrium, it will collapse. A number of mechanisms may explain how depensation might occur and nearly all concentrate on predation. Recent studies (e.g., Shelton and Healey 1999) have suggested that this alternative form of population regulation may not be as infrequent as previously suggested by Myers et al. (1995). The former authors argue that depensation is difficult to detect because of limited and variable data associated with low spawning stock sizes and it would be prudent to allow for the possibility of depensation in fish population dynamics. Oddly, a major assumption associated with both the compensatory and depensatory stock and recruitment relationships is that the curve should pass through the origin, despite the lack of data at low population levels. A more widespread, ecological phenomena associated with collapsed populations are the so-called Allee effects (see Myers et al. 1995 for reference to Allee). In contrast to depensation, the mechanisms underlying Allee effects are physiological and behavioral. These result in decreased reproduction at low population sizes. Examples of Allee effects include difficulty in finding a mate, a breakdown in social structure and migration patterns, difficulty in fending off predators or competitors, and a requirement for exceeding a critical population size before food resources can be properly exploited. Species for which Allee effects have been demonstrated or hypothesized include Pacific sardine, Downs herring, scallops, abalone, sea urchins, giant clams, muskrats, flour beetles, sheep ticks, and passenger pigeons. No S–R relationship incorporating Allee effects has ever been devised. Such a model would have one outstanding feature — a non-zero intercept defining a species-specific SSB threshold associated with absolute recruitment failure. In practice, such a relationship would probably be statistically indistinguishable from a depensatory S–R relationship. We remain faced with two difficulties: (i) how to explain © 2000 NRC Canada
Rapid communication / Communication rapide 515 Fig. 1. (a) The assumed stock and recruitment relationships for each of the eight substocks contained within a hypothetical management unit. The closed circle on each curve represents the randomly selected starting point for the sampling (or incremental depletion) of each substock. Although each of the stock and recruitment relationships have varying amplitudes, model runs using equal amplitudes yield nearly identical results. (b) Recruitment and spawning stock data from the hypothetical management unit (equivalent to R tot and S tot from Table 1, respectively) generated during the 51 years. The best fitting curve to the data is a Ricker model passing through the origin. (c) The temporal trend in stock richness (number of substocks). using meristic and morphometric techniques, tagging, otolith chemistry, and genetic methods have supported this fact. This wealth of evidence has led to the conclusion that there are few fisheries in the world that are truly single-stock fisheries; the potential for complex stock structure is nearly always present. Unfortunately, fisheries management has generally failed to protect or maintain this complexity (Sinclair et al. 1996). Before the collapse of Northern cod, several substocks were present in the management unit. After the collapse of this stock, only one or two substocks remained (deYoung and Rose 1993). Both North Sea herring and eastern Scotian Shelf cod showed similar erosion of stock structure prior to collapse (see Cury et al. (2000) and Sinclair et al. (1996), respectively). The other feature common to these three examples is that the S–R data exhibit strong compensatory dynamics at the scale of the management unit (Myers et al. 1995). However, compensatory population dynamics are incapable of addressing the erosion of substock structure. What if Allee effects are indeed operative? Can they be shown to account for the dynamics of individual substocks in a manner consistent with the compensatory dynamics at the management unit scale? Simulation model Consider a stock complex consisting of numerous substocks existing within a single management unit, with each substock exhibiting a unique S–R relationship characterized by an Allee effect (i.e., their S–R relationships do not intersect the origin, but rather exhibit zero recruitment at some minimum stock size). The simulation was, in essence, a sampling experiment in which each of the underlying substocks was “fished down” to generate annual estimates of SSB and R. The depletion of the individual substocks began at different starting values of SSB, resulting in the gradual elimination of the substocks through time. The question is whether the aggregate (all substocks combined) S–R relationship would exhibit one of the properties of compensatory population dynamics, namely that the curve passes through the origin. the fact that most S–R data from collapsed stocks conform to compensatory S–R dynamics but many do not recover and (ii) given the lack of S–R data at low population sizes, how to determine whether or not Allee effects are operative as they would be consistent with failed recovery. We will attempt to answer the first of these questions in two ways: first, by reminding ourselves that stocks within management units are generally a heterogeneous mix of smaller substocks and, second, through simulation modeling. Stock complexes It is widely recognized that many stocks have a complex structure, consisting of a heterogeneous mix of small substocks within a given management unit. Numerous studies Methods The simulated stock complex consisted of a management unit made up of M = 8 substocks, each having a S–R relationship that incorporates the Allee effect: R i (S) =A i (S–S1)exp(–B(S –S1)) where i is the substock, R is recruitment, S is some measure of the spawning stock, S1 = 750 is the offset from the origin representing the zero recruitment value (Allee effect), and A and B are constants. To simulate distinct substocks with differing initial size, we set (see table 11.5 of Ricker 1975) B = 0.001 and A i = 2.718 1 (where 1 is a random number between 0 and 1) and chose S 0 , the initial S, at random. Subsequent values for S decreased by S and increased by some fraction of recruitment R i , where R i equals 1 R i , and S was chosen as a fraction of the maximum S 0 (i.e., maximum initial substock size) such that it was likely that after the N = 51-year run length, there would be some stocks remaining. If R i (S) 0, then R i was set to zero. If S i 0, then the substock was considered extinct. For each year, the total S and R was calculated (S tot , R tot ) summed over the M substocks, and the number of nonextinct stocks was noted. The unidirectional decrement of the individual spawning © 2000 NRC Canada
Page 1: 513 RAPID COMMUNICATION / COMMUNICA
Page 5: Rapid communication / Communication

Frank and Brickman 2000 - Gulf of Maine Research Institute

Create successful ePaper yourself

Delete template?

Save as template?