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Adaptive Lévy walks in foraging fallow deer.

Focardi S, Montanaro P, Pecchioli E - PLoS ONE (2009)

Bottom Line: Thus two fundamental questions still need to be addressed: the presence of Lévy walks in the wild and whether or not they represent a form of adaptive behaviour.We used maximum likelihood estimation for discriminating between a power-tailed distribution and the exponential alternative and rank/frequency plots to discriminate between Lévy walks and composite Brownian walks.We showed that solitary deer perform Lévy searches, while clustered animals did not adopt that strategy.

View Article: PubMed Central - PubMed

Affiliation: ISPRA, Sede amministrativa INFS, Ozzano Emilia, Italy. stefano.focardi@infs.it

ABSTRACT

Background: Lévy flights are random walks, the step lengths of which come from probability distributions with heavy power-law tails, such that clusters of short steps are connected by rare long steps. Lévy walks maximise search efficiency of mobile foragers. Recently, several studies raised some concerns about the reliability of the statistical analysis used in previous analyses. Further, it is unclear whether Lévy walks represent adaptive strategies or emergent properties determined by the interaction between foragers and resource distribution. Thus two fundamental questions still need to be addressed: the presence of Lévy walks in the wild and whether or not they represent a form of adaptive behaviour.

Methodology/principal findings: We studied 235 paths of solitary and clustered (i.e. foraging in group) fallow deer (Dama dama), exploiting the same pasture. We used maximum likelihood estimation for discriminating between a power-tailed distribution and the exponential alternative and rank/frequency plots to discriminate between Lévy walks and composite Brownian walks. We showed that solitary deer perform Lévy searches, while clustered animals did not adopt that strategy.

Conclusion/significance: Our demonstration of the presence of Lévy walks is, at our knowledge, the first available which adopts up-to-date statistical methodologies in a terrestrial mammal. Comparing solitary and clustered deer, we concluded that the Lévy walks of solitary deer represent an adaptation maximising encounter rates with forage resources and not an epiphenomenon induced by a peculiar food distribution.

Show MeSH
Examples of animal paths.A close-up of the study site (cf. Figure 1) shows the movement of animals in groups of different size. On the left we observed (17 June 1992, from 6:02 to 8:11) a group of seven adult females moving very sinuously and a single deer (light blue) which leaves the group and moves alone southward in a more linear pattern, albeit it stops to forage in several locations. A group composed by an adult female with its fawn (violet and green, respectively) moved on the 26 June 1992 (6:31–7:26) from the road on the south and reached the bushy area at the centre for then returning back using a different path across the pasture. In the upper zone we may observe a single animal (pink, yearling male, observed on the 29 June 1992, 19:01–20:53), moving in the same area of a group of two deer (light green and light blue, an adult female with its fawn, on the 9 September 1992, 17:05–19:33) which exhibit sinuous paths. Two adult females (blue and red) were observed on the 3 May 1992 (5:36–7:55) moving from the central forested zone to the western border. Two other adult females (blue and orange) moved eastward in the bushy area on the 31 July 1992 (18:58–20:04). A solitary female (red) moved on the 18 June 1992 (6:50–7:26) near the eastern border of the study zone.
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pone-0006587-g002: Examples of animal paths.A close-up of the study site (cf. Figure 1) shows the movement of animals in groups of different size. On the left we observed (17 June 1992, from 6:02 to 8:11) a group of seven adult females moving very sinuously and a single deer (light blue) which leaves the group and moves alone southward in a more linear pattern, albeit it stops to forage in several locations. A group composed by an adult female with its fawn (violet and green, respectively) moved on the 26 June 1992 (6:31–7:26) from the road on the south and reached the bushy area at the centre for then returning back using a different path across the pasture. In the upper zone we may observe a single animal (pink, yearling male, observed on the 29 June 1992, 19:01–20:53), moving in the same area of a group of two deer (light green and light blue, an adult female with its fawn, on the 9 September 1992, 17:05–19:33) which exhibit sinuous paths. Two adult females (blue and red) were observed on the 3 May 1992 (5:36–7:55) moving from the central forested zone to the western border. Two other adult females (blue and orange) moved eastward in the bushy area on the 31 July 1992 (18:58–20:04). A solitary female (red) moved on the 18 June 1992 (6:50–7:26) near the eastern border of the study zone.

Mentions: Some examples of trajectories are reported in Figure 2. One can note the level of synchrony in the movement of clustered deer. For instance on the left side there is a solitary deer leaving the zone with ferns and moving in a large open meadow, while a group of seven females use an area rich in bushes (greenish color) with several scattered large oaks. As well, on the upper right side of the image a single animal and a small group, formed by an adult female with its fawn, use a mixed habitat where patches of ferns (dark brown) are intermingled with, more profitable, open meadows (light brown). Some groups could be observed while foraging below the large oaks scattered in the landscape (on the right). To note that groups of every size could be observed in any part of the study area.


Adaptive Lévy walks in foraging fallow deer.

Focardi S, Montanaro P, Pecchioli E - PLoS ONE (2009)

Examples of animal paths.A close-up of the study site (cf. Figure 1) shows the movement of animals in groups of different size. On the left we observed (17 June 1992, from 6:02 to 8:11) a group of seven adult females moving very sinuously and a single deer (light blue) which leaves the group and moves alone southward in a more linear pattern, albeit it stops to forage in several locations. A group composed by an adult female with its fawn (violet and green, respectively) moved on the 26 June 1992 (6:31–7:26) from the road on the south and reached the bushy area at the centre for then returning back using a different path across the pasture. In the upper zone we may observe a single animal (pink, yearling male, observed on the 29 June 1992, 19:01–20:53), moving in the same area of a group of two deer (light green and light blue, an adult female with its fawn, on the 9 September 1992, 17:05–19:33) which exhibit sinuous paths. Two adult females (blue and red) were observed on the 3 May 1992 (5:36–7:55) moving from the central forested zone to the western border. Two other adult females (blue and orange) moved eastward in the bushy area on the 31 July 1992 (18:58–20:04). A solitary female (red) moved on the 18 June 1992 (6:50–7:26) near the eastern border of the study zone.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2719089&req=5

pone-0006587-g002: Examples of animal paths.A close-up of the study site (cf. Figure 1) shows the movement of animals in groups of different size. On the left we observed (17 June 1992, from 6:02 to 8:11) a group of seven adult females moving very sinuously and a single deer (light blue) which leaves the group and moves alone southward in a more linear pattern, albeit it stops to forage in several locations. A group composed by an adult female with its fawn (violet and green, respectively) moved on the 26 June 1992 (6:31–7:26) from the road on the south and reached the bushy area at the centre for then returning back using a different path across the pasture. In the upper zone we may observe a single animal (pink, yearling male, observed on the 29 June 1992, 19:01–20:53), moving in the same area of a group of two deer (light green and light blue, an adult female with its fawn, on the 9 September 1992, 17:05–19:33) which exhibit sinuous paths. Two adult females (blue and red) were observed on the 3 May 1992 (5:36–7:55) moving from the central forested zone to the western border. Two other adult females (blue and orange) moved eastward in the bushy area on the 31 July 1992 (18:58–20:04). A solitary female (red) moved on the 18 June 1992 (6:50–7:26) near the eastern border of the study zone.
Mentions: Some examples of trajectories are reported in Figure 2. One can note the level of synchrony in the movement of clustered deer. For instance on the left side there is a solitary deer leaving the zone with ferns and moving in a large open meadow, while a group of seven females use an area rich in bushes (greenish color) with several scattered large oaks. As well, on the upper right side of the image a single animal and a small group, formed by an adult female with its fawn, use a mixed habitat where patches of ferns (dark brown) are intermingled with, more profitable, open meadows (light brown). Some groups could be observed while foraging below the large oaks scattered in the landscape (on the right). To note that groups of every size could be observed in any part of the study area.

Bottom Line: Thus two fundamental questions still need to be addressed: the presence of Lévy walks in the wild and whether or not they represent a form of adaptive behaviour.We used maximum likelihood estimation for discriminating between a power-tailed distribution and the exponential alternative and rank/frequency plots to discriminate between Lévy walks and composite Brownian walks.We showed that solitary deer perform Lévy searches, while clustered animals did not adopt that strategy.

View Article: PubMed Central - PubMed

Affiliation: ISPRA, Sede amministrativa INFS, Ozzano Emilia, Italy. stefano.focardi@infs.it

ABSTRACT

Background: Lévy flights are random walks, the step lengths of which come from probability distributions with heavy power-law tails, such that clusters of short steps are connected by rare long steps. Lévy walks maximise search efficiency of mobile foragers. Recently, several studies raised some concerns about the reliability of the statistical analysis used in previous analyses. Further, it is unclear whether Lévy walks represent adaptive strategies or emergent properties determined by the interaction between foragers and resource distribution. Thus two fundamental questions still need to be addressed: the presence of Lévy walks in the wild and whether or not they represent a form of adaptive behaviour.

Methodology/principal findings: We studied 235 paths of solitary and clustered (i.e. foraging in group) fallow deer (Dama dama), exploiting the same pasture. We used maximum likelihood estimation for discriminating between a power-tailed distribution and the exponential alternative and rank/frequency plots to discriminate between Lévy walks and composite Brownian walks. We showed that solitary deer perform Lévy searches, while clustered animals did not adopt that strategy.

Conclusion/significance: Our demonstration of the presence of Lévy walks is, at our knowledge, the first available which adopts up-to-date statistical methodologies in a terrestrial mammal. Comparing solitary and clustered deer, we concluded that the Lévy walks of solitary deer represent an adaptation maximising encounter rates with forage resources and not an epiphenomenon induced by a peculiar food distribution.

Show MeSH