Abstract
Capelin (Mallotus villosus) is a short-lived (1–4 years) fish species, that plays a crucial role by dominating the intermediate trophic level in the Barents Sea. Several episodes of extreme biomass decline (collapse) have been observed during the last three decades. We postulate that these collapses might be regulated by food availability (bottom-up effect) and/or by time discrepancy between capelin feeding and abundance of its prey (match-mismatch hypothesis). This paper investigates our postulate using a model consisting of a set of coupled differential equations to describe the predator-prey system, with a single delay term, τ, in description of the predator dynamics. We derive theoretical conditions on τ, as well as determine how changes in these conditions define different stability regimes of the system. Unconstrained optimization is used to calculate optimal model parameters by fitting the predator-prey model to empirical data. The optimization results are combined with those from the theoretical analysis, to make inference about the empirical system stability. Our results show that Hopf bifurcation occurs in the predatory-prey system when τ exceeds a theoretically derived value τ∗>0. This value represents the critical time for prey availability in advance of the optimal predator growth period.Set into an ecological context, our findings provide mathematical evidence for validity of the match-mismatch hypothesis and a bottom-up effect for capelin.
Highlights
Capelin (Mallotus villosus) is a short-lived (1–4 years) fish species with a northern circumpolar distribution (Carscadden and Vilhjálmsson, 2002) that spawn only once in their lifetime and die (Gjøsæter et al, 2002b)
The largest capelin stock belongs to the Barents Sea ecosystem (Gjøsæter Bogstad, 1998) and plays a crucial role there as the dominant feeder on zooplankton, which enters the Barents Sea via the Atlantic water influx (Ingvaldsen and Gjøsæter, 2013)
The goal of this paper is to investigate whether the capelin biomass dynamics may be reconstructed by solely considering a bottom-up regulation process and a single delay term, s, in description of the predator dynamics
Summary
Capelin (Mallotus villosus) is a short-lived (1–4 years) fish species with a northern circumpolar distribution (Carscadden and Vilhjálmsson, 2002) that spawn only once in their lifetime and die (Gjøsæter et al, 2002b). The species is a forage fish (Buren et al, 2014) and play a crucial role by dominating the intermediate trophic level in their respective ecosystems. Such species are sometimes called ”wasp-waist species” and are partly controlled by bottom-up, partly by top-down effects (Cury et al, 2000; Bakun, 2006; Hunt and McKinnell, 2006; Buren et al, 2014). Its selected prey size and type is age-dependent
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