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Predator and prey interact antagonistically, and theory (e.g. a simple Lotka-Volterra model, but also more sophisticated models) predicts that prey density tends to decay when predators are present. Considering this prediction, efforts made to conserve a prey species can have the opposite effect, as the increase in prey density leads to an increase in predator consumption, resulting in decreased prey density. In this sense, field studies describing species interactions and resulting effects of conservation efforts are essential to validate both theoretical predictions and conservational policies.

California sea otter (Enhydra lutris nereis), in spite of being super cute, are also voracious predators who really like to eat abalones (Haliotis cracherodii). As it turns out, humans also really like to eat abalone, and both human harvesting and sea otter predation are important factors decreasing abalone densities. Both species (sea otter and black abalone) are listed as endangered species and are protected in California coast. A recent study (Raimondi et al. 2015) investigated local abundances of sea otters and black abalones at 12 different sites. The authors found a positive relationship between the predator's and prey's densities. Along with that, the presence of the predator also correlated with the prey's pattern of habitat use. In sites with greater sea otter densities, black abalone were found in places conferring greater refuge, which can difficult illegal human harvest.

The interaction between predator and prey can be far more complex than the one depicted by the Lotka-Volterra model. Propose a mathetical model to describe the essential components needed to understand the dynamics between sea otters and black abalone. Your model should address how conservation efforts targeting one or both species would affect their population densities.

• One interesting (and perhaps counterintuitive) result found by the authors is that the increase in predator population density leads to a positive relation with prey density. The authors propose three hypotheses to explain this pattern. Tailor your mathematical model to describe the processes assumed by at least one of the hypothesis and evaluate it.
• Sea otter density is correlated with black abalone density. How habitat use of prey affects the result found by the authors, specially concerning refuges?

• Raimondi et al. (2015) Evaluating potential conservation conflicts between two listed species: sea otters and black abalone Ecology 96(11): 3102-3108 link