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Lévy Walks Suboptimal under Predation Risk.

Abe MS, Shimada M - PLoS Comput. Biol. (2015)

Bottom Line: However, some empirical studies did not support this hypothesis, and the relationship between search strategy and ecological factors is still unclear.This occurred because higher target encounter rates simultaneously led searchers to higher predation risks.Our findings indicate that animals may not perform Lévy walks often, and we suggest that it is crucial to consider the ecological context for evaluating the search strategy performed by animals in the field.

View Article: PubMed Central - PubMed

Affiliation: Department of General Systems Studies, Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan.

ABSTRACT
A key challenge in movement ecology is to understand how animals move in nature. Previous studies have predicted that animals should perform a special class of random walks, called Lévy walk, to obtain more targets. However, some empirical studies did not support this hypothesis, and the relationship between search strategy and ecological factors is still unclear. We focused on ecological factors, such as predation risk, and analyzed whether Lévy walk may not be favored. It was remarkable that the ecological factors often altered an optimal search strategy from Lévy walk to Brownian walk, depending on the speed of the predator's movement, density of predators, etc. This occurred because higher target encounter rates simultaneously led searchers to higher predation risks. Our findings indicate that animals may not perform Lévy walks often, and we suggest that it is crucial to consider the ecological context for evaluating the search strategy performed by animals in the field.

No MeSH data available.


The relationship between relative encounter rates of targets and predators.Data in (A–C) and (D–F) correspond to life-cycle types I and II, respectively. (A and D) The lower encounter rate condition, kBW = 0.1 (e.g., lower predator density or slower predators). (B and E) The middle encounter rate condition, kBW = 1. (C and F) The higher encounter rate condition, kBW = 10 (e.g., higher predator density or faster predators). The colors represent the fitness of LW (or any search strategies) compared to BW. The result shows that the life-cycle type and the three parameters, encounter rate to targets, that to predators and strength of predation pressure critically determine the fitness. When the strength of predation pressure is high (C and F), the LW obtains lower fitness even if the encounter rate with targets is high.
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pcbi.1004601.g004: The relationship between relative encounter rates of targets and predators.Data in (A–C) and (D–F) correspond to life-cycle types I and II, respectively. (A and D) The lower encounter rate condition, kBW = 0.1 (e.g., lower predator density or slower predators). (B and E) The middle encounter rate condition, kBW = 1. (C and F) The higher encounter rate condition, kBW = 10 (e.g., higher predator density or faster predators). The colors represent the fitness of LW (or any search strategies) compared to BW. The result shows that the life-cycle type and the three parameters, encounter rate to targets, that to predators and strength of predation pressure critically determine the fitness. When the strength of predation pressure is high (C and F), the LW obtains lower fitness even if the encounter rate with targets is high.

Mentions: To investigate these results, the relationship between the relative fitness and the encounter rate with targets and predators was examined (Fig 4). This result is not limited to our simulation results or to the relative fitness of LW or BW, but it describes a general trend. The relative encounter rates with targets and predators and the expected encounter number of BW for our simulation are presented in Fig 5. When the encounter rate with predators was low (i.e., low kBW), the fitness of random search strategies clearly depended on the encounter rate with targets (Fig 4A and 4D). Hence, LW had higher fitness in our simulation (Fig 5A). On the other hand, for intermediate or high kBW, fitness also changed depending on the encounter rate with predators (Fig 4B, 4C, 4E and 4F). Furthermore, fast predators displayed the same high predator encounter rates of high kBW and (Fig 5B and 5C). Thus, LW had higher fitness under the fast-predator conditions for life-cycle type I and almost equal fitness for life-cycle type II. Similarly, the fitness of other random search strategies was determined by the encounter rate with targets and predators. The degree of encounter rate improvement not only depends on the search strategy, but also on the distribution or density of the targets [5,7], suggesting that the conditions for the optimal search strategy are complex.


Lévy Walks Suboptimal under Predation Risk.

Abe MS, Shimada M - PLoS Comput. Biol. (2015)

The relationship between relative encounter rates of targets and predators.Data in (A–C) and (D–F) correspond to life-cycle types I and II, respectively. (A and D) The lower encounter rate condition, kBW = 0.1 (e.g., lower predator density or slower predators). (B and E) The middle encounter rate condition, kBW = 1. (C and F) The higher encounter rate condition, kBW = 10 (e.g., higher predator density or faster predators). The colors represent the fitness of LW (or any search strategies) compared to BW. The result shows that the life-cycle type and the three parameters, encounter rate to targets, that to predators and strength of predation pressure critically determine the fitness. When the strength of predation pressure is high (C and F), the LW obtains lower fitness even if the encounter rate with targets is high.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4636162&req=5

pcbi.1004601.g004: The relationship between relative encounter rates of targets and predators.Data in (A–C) and (D–F) correspond to life-cycle types I and II, respectively. (A and D) The lower encounter rate condition, kBW = 0.1 (e.g., lower predator density or slower predators). (B and E) The middle encounter rate condition, kBW = 1. (C and F) The higher encounter rate condition, kBW = 10 (e.g., higher predator density or faster predators). The colors represent the fitness of LW (or any search strategies) compared to BW. The result shows that the life-cycle type and the three parameters, encounter rate to targets, that to predators and strength of predation pressure critically determine the fitness. When the strength of predation pressure is high (C and F), the LW obtains lower fitness even if the encounter rate with targets is high.
Mentions: To investigate these results, the relationship between the relative fitness and the encounter rate with targets and predators was examined (Fig 4). This result is not limited to our simulation results or to the relative fitness of LW or BW, but it describes a general trend. The relative encounter rates with targets and predators and the expected encounter number of BW for our simulation are presented in Fig 5. When the encounter rate with predators was low (i.e., low kBW), the fitness of random search strategies clearly depended on the encounter rate with targets (Fig 4A and 4D). Hence, LW had higher fitness in our simulation (Fig 5A). On the other hand, for intermediate or high kBW, fitness also changed depending on the encounter rate with predators (Fig 4B, 4C, 4E and 4F). Furthermore, fast predators displayed the same high predator encounter rates of high kBW and (Fig 5B and 5C). Thus, LW had higher fitness under the fast-predator conditions for life-cycle type I and almost equal fitness for life-cycle type II. Similarly, the fitness of other random search strategies was determined by the encounter rate with targets and predators. The degree of encounter rate improvement not only depends on the search strategy, but also on the distribution or density of the targets [5,7], suggesting that the conditions for the optimal search strategy are complex.

Bottom Line: However, some empirical studies did not support this hypothesis, and the relationship between search strategy and ecological factors is still unclear.This occurred because higher target encounter rates simultaneously led searchers to higher predation risks.Our findings indicate that animals may not perform Lévy walks often, and we suggest that it is crucial to consider the ecological context for evaluating the search strategy performed by animals in the field.

View Article: PubMed Central - PubMed

Affiliation: Department of General Systems Studies, Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan.

ABSTRACT
A key challenge in movement ecology is to understand how animals move in nature. Previous studies have predicted that animals should perform a special class of random walks, called Lévy walk, to obtain more targets. However, some empirical studies did not support this hypothesis, and the relationship between search strategy and ecological factors is still unclear. We focused on ecological factors, such as predation risk, and analyzed whether Lévy walk may not be favored. It was remarkable that the ecological factors often altered an optimal search strategy from Lévy walk to Brownian walk, depending on the speed of the predator's movement, density of predators, etc. This occurred because higher target encounter rates simultaneously led searchers to higher predation risks. Our findings indicate that animals may not perform Lévy walks often, and we suggest that it is crucial to consider the ecological context for evaluating the search strategy performed by animals in the field.

No MeSH data available.