A novel model of predator–prey interactions reveals the sensitivity of forage fish: piscivore fishery trade-offs to ecological conditions

ICES Journal of Marine Science ICES Journal of Marine Science (2015), 72(5), 1349– 1358. doi:10.1093/icesjms/fsu242 Original Article A novel model of predator – prey interactions reveals the sensitivity of forage fish: piscivore fishery trade-offs to ecological conditions Timothy E. Essington 1*, Marissa L. Baskett2, James N. Sanchirico 2, and Carl Walters 3 School of Aquatic and Fishery Sciences, University of Washington, Seattle, USA Department of Environmental Science and Policy, University of California, Davis, CA, USA 3 Fisheries Centre, University of British Columbia, Vancouver, BC, Canada 2 *Corresponding author: tel: +1-206-616-3698; fax: +1-206-685-7471; e-mail: Essington, T. E., Baskett, M. L., Sanchirico, J. N., and Walters, C. A novel model of predator– prey interactions reveals the sensitivity of forage fish: piscivore fishery trade-offs to ecological conditions. – ICES Journal of Marine Science, 72: 1349– 1358. Received 31 July 2014; revised 20 November 2014; accepted 5 December 2014; advance access publication 27 December 2014. Ecosystem-based fisheries management seeks to consider trade-offs among management objectives for interacting species, such as those that arise through predator– prey linkages. In particular, fisheries-targeting forage fish (small and abundant pelagic fish) might have a detrimental effect on fisheries-targeting predators that consume them. However, complexities in ecological interactions might dampen, negate, or even reverse this trade-off, because small pelagic fish can be important predators on egg stages of piscivorous fish. Further, the strength of this trade-off might depend on the extent to which piscivorous fish targeted by fisheries regulate forage species productivity. Here, we developed a novel delaydifferential bioeconomic model of predator– prey and fishing dynamics to quantify how much egg predation or weak top-town control affects the strength of trade-off between forage and piscivore fisheries, and to measure how ecological interactions dictate policies that maximize steady-state profits. We parameterized the model based on ecological and economic data from the North Sea Atlantic cod (Gadus morhua) and Atlantic herring (Clupea harengus). The optimal policy was very sensitive to the ecological interactions (either egg predation or weak topdown control of forage by predators) at relatively low forage prices but was less sensitive at high forage fish prices. However, the optimal equilibrium harvest rates on forage and piscivores were not substantially different from what might be derived through analyses that did not consider species interactions. Applying the optimal multispecies policy would produce substantial losses (.25%) in profits in the piscivore fishery, and the extent of loss was sensitive to ecological scenarios. While our equilibrium analysis is informative, a dynamic analysis under similar ecological scenarios is necessary to reveal the full economic and ecological benefits of applying ecosystem-based fishery management policies to predator– prey fishery systems. Keywords: bioeconomic modelling, ecosystem-based fisheries management, forage fish, predator– prey, trade-offs. Introduction There is growing need to develop tools to identify and measure trade-offs among management objectives for natural resources stemming from species interactions (Link, 2010). In fisheries, there is a potential trade-off between fisheries targeting high trophic level fish species and those targeting forage fish that may be important prey for predators (Hannesson and Herrick, 2010; Hunsicker et al., 2010; Pikitch et al., 2014). Because forage abundance can regulate the productivity of piscivores, it may not be possible to simultaneously maximize yield and revenue in both fisheries (Walters et al., 2005). These types of trade-offs have the potential to be pervasive because fisheries in most ecosystems target multiple trophic levels simultaneously (Essington et al., 2006). Yet, predicting trade-offs is difficult in complex foodwebs (Yodzis, 2000; Essington and Munch, 2014). Direct empirical evidence relating piscivore production to forage fish abundance is often equivocal (Hannesson, 2013) partly because synoptic time series of predator productivity and prey abundance are often lacking or are too short to detect signals, or do not provide sufficient information to distinguish correlation from causation. # International Council for the Exploration of the Sea 2014. All rights reserved. For Permissions, please email: 1 1350 Methods Model development and rationale Our goal was to develop the simplest possible model that enabled us to explore consequences of forage fish egg predation on piscivores, and allow for variable top-down effect of piscivores on forage fish. To this end, we required a model with a minimum of two stages for piscivores, because we needed to distinguish life history stages during which the piscivore consumes forage fish from those that are consumed by forage species. We represent the forage species as a single state variable, because we are not specifically interested in how size-structured predation affects forage species. We then applied equilibrium economic models to identify how the optimal allocation of fishing intensity on each species depends on the underlying ecological system structure. We provide a schematic representation of the model, including state variables with dynamic rate processes and feedbacks in Figure 1. A list of all parameters and parameter values are provided in Table 1. Even this simple model that uses a few state variables requires that we make assumptions about the functional forms of birth, death, and growth processes, we use well-known and widely used functional forms, but these cannot capture all possible relationships in nature (Munch et al., 2005). We use them because their properties are understood, and they allow us to focus on the sensitivity of tradeoffs to a subset of highly uncertain components of ecological interactions. We considered three model scenarios, each generated by adjusting the model parameterization: base model, egg predation, and asymmetric interaction strengths. For our base model, we included no egg predation and set the functional response parameters to generate top-down and bottom-up interactions between forage and piscivores. This produced a typical predator–prey model whereby piscivores exert some top-down control on forage fish and forage fish are always a benefit piscivores. For the egg predation scenario, we added to the base model mortality of piscivore eggs caused by forage fish predation. For the asymmetric scenario, we adjusted Figure 1. Schematic representation of model state variables and key rates that drive dynamics. Boxes with grey shading represent state variables explicitly represented in the model, note that piscivores are represented with two state variables, numerical (n2) and biomass (x2) density, while forage fish are represented with biomass (x (...truncated)