Behavioral games involving a clever prey avoiding a clever predator: An individual-based model of dusky dolphins and killer whales
Introduction
Predator–prey interactions are a central theme in ecology and predator–prey models have a long history that can be traced back to the early work of Lotka (1925) and Volterra (1926). The vast majority of these models have focused on the population-level consequences of predators killing prey, most frequently in terms of population dynamics mediated by changes in rates of prey mortality and predator natality (Rosenzweig and Macarthur, 1963). More recently, a growing number of studies have focused on non-lethal aspects of predator–prey interactions, viewing predators and prey as clever, dynamically-interacting individuals who influence each other's behavior (Mitchell, 2002, Lima, 2002, Lima, 1998, Lima, 2002, Luttbeg and Sih, 2004, Brown and Kotler, 2004). The short-term consequences of these non-lethal interactions between predator and prey may include shifts in activity budgets, and local dispersion and movement patterns (Lima and Dill, 1990, Sih and Wooster, 1994, Lima, 1998, Wirsing et al., 2008). The long-term consequences may manifest themselves in terms of changes in lifestyle, and ultimately result in hard-wired evolutionary adaptations (reviewed in Dill, 1987, Sih, 1987, Lima, 1998, Verdolin, 2006). While theoretical models have been proposed to represent the costs and benefits associated with shifts in the behavioral tactics of predator and prey (Lima, 1998, Brown et al., 1999, Brown et al., 2001, Brown and Kotler, 2004), sometimes referred to as the “ecology of fear” (Brown et al., 2001), we are unaware of empirically-based models that simulate the reciprocal behavioral interactions of individual predators and prey within a spatially-explicit context.
Specific representation of the interactive nature of predator–prey interactions is particularly important when both predator and prey share similarly complex sensory modalities and behavioral plasticity. In this regard, predator–prey systems involving marine mammals (Jefferson et al., 1990), in which both predator and prey are equally “clever” (Connor, 2000), provide an especially attractive context for exploring these reciprocal behavioral interactions. In marine mammal systems it is often difficult to test predator influence on prey behavioral ecology due to the inaccessibility and unpredictability of the target species, shorter observation periods, and paucity of predation event observations. Despite limitations, long-term data from both opportunistic and dedicated studies reveal clues to understanding habitat use, movement patterns, and behavior of predator and prey. A majority of marine mammal studies thus far have concentrated on effects of predation, and not on the indirect effects of a predator on prey lifestyle (Wirsing et al., 2007), particularly where both predator and prey are marine mammals sharing similar sensory capabilities.
Srinivasan and Markowitz (2009) provided a review of dusky dolphin (Lagenorhynchus obscurus) predator threats and likely survival strategies in terms of changes in habitat use, social organization (group size, group structure, non-maternal adults vs. maternal group behavior), and movement patterns off Kaikoura, NZ. Like most prey, these anti-predator behaviors include short-term tactics such as fleeing and seeking refuge as well as involve long-term strategies such as spatio-temporal changes in movement and habitat use patterns by social type and predator occurrence (Dill, 1987).
It appears that killer whales (Orcinus orca) present a more potent threat to dusky dolphins than sharks in Kaikoura Canyon (Srinivasan and Markowitz, 2009). It is unclear why these dusky dolphin survival strategies evolved and how effective these strategies are in reducing predation risk without compromising food and social needs. But before we attempt to answer the ultimate question of costs vs. benefits for dusky dolphins adopting various predator avoidance strategies, we need to attain a greater understanding of the behavioral relationship between a clever predator (killer whale) and prey (dusky dolphin), as this is an interactive and feedback driven predator–prey association (Lima, 2002, Mitchell, 2002, Lima, 2002). To achieve this, we first developed a spatially-explicit, individual-based model (IBM) simulating a dusky dolphin avoiding killer whales in a heterogeneous marine habitat near Kaikoura, New Zealand based on our current level of understanding of the system. We then use the model to compare evolutionary costs vs. benefits by focusing principally on two parameters, foraging time and number of killer whale encounters for dusky dolphins adopting short and long-term anti-predator behaviors.
Section snippets
Background information
The marine habitat near Kaikoura, New Zealand (42°30′S, 173°35′E) is characterized by the presence of a vast submarine canyon, which begins about 500 m from shore, is roughly 60 km2 long and 1200 m deep, and has a U-shaped profile (Lewis and Barnes, 1999) (Fig. 1). Dusky dolphins near Kaikoura Canyon occasionally are preyed upon by killer whales (Constantine et al., 1998), which are present in the area from November through May (Dahood et al., 2008), and clearly are fearful of killer whale
Model structure
We developed the model as a grid-based, geo-referenced, stochastic IBM (Grimm and Railsback, 2005), programmed in VB.NET© (Microsoft, 2003). Within the IBM, we defined a habitat class, a dusky dolphin class, and a killer whale class. The habitat class contains 1468 instances, each representing a 1 km × 1 km area of the marine habitat in and around Kaikoura Canyon (Fig. 1). We defined spatial extent of the modeled system based on dusky dolphin surveys (Cipriano, 1992, Markowitz, 2004) and dusky
Model evaluation
We evaluated the model by first verifying that simulated dusky dolphins and killer whales moved and responded to each other in qualitatively appropriate manners with regard to the basic movements and behavioral interactions depicted in Fig. 2, and that there was an appropriate level of killer whale presence in the system under the baseline scenario (i.e., killer whales cruising through the system, on average, once every 3 days). We then had a recognized expert perform a Turing test (Turing, 1950
Simulation of predator–prey games
Given the dynamic nature of killer whale-dusky dolphin interactions is poorly understood, we developed the below experimental design to quantitatively explore the costs (=lost foraging time) and benefits (=reduced predator encounters) of several anti-predator strategies.
Discussion
In a behavioral game between a clever prey and clever predator, our prototypical adult dusky dolphin has two general kinds of anti-predator options: fear-driven or fear-impulse strategies that involve a balancing act between short-term loss in hunger vs. long-term cost of death. At the very basic level, foraging time and encounter rate is determined by predator density in the system or the return rate of the killer whales in the system. Thus, increasing presence of killer whales results in
Acknowledgments
We thank Drs. B. Würsig, J. Packard, and X.B. Wu for their expertise, advice, and support throughout the project. The manuscript was greatly improved by comments by B. Würsig and Leigh Torres. The senior author gratefully acknowledges the support of all the Earthwatch volunteers who helped in data collection efforts. Thanks also to Sierra Deutsch and Jennifer Bennett for research assistance and field support. We thank NIWA for providing valuable bathymetry data. Special thanks to I. Bradshaw,
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Current address: US Army Engineer Research and Development Center, Vicksburg, MS 39180-6199, USA.