Foraging and movement paths of female reindeer: insights from fractal analysis, correlated random walks, and Lévy flights

2002 ◽  
Vol 80 (5) ◽  
pp. 854-865 ◽  
Author(s):  
Anders Mårell ◽  
John P Ball ◽  
Annika Hofgaard

Food-plant and foraging-site selection by semidomesticated female reindeer (Rangifer tarandus tarandus L.) was studied to shed light on the searching and foraging behaviour of this herbivore. The aims of the study were (i) to determine the role of food biomass and (or) plant nitrogen content in feeding-site selection and (ii) to analyse the extent to which movement patterns of reindeer are related to availability of food resources using several models of searching behaviour (fractal analysis, correlated random walks, and Lévy flights). The study was conducted in summer 1999 in a mountainous area of northern Sweden. Reindeer selected different plant communities during this period and changed search pattern in late summer. We found that reindeer selected feeding sites with higher green biomass of Betula spp. and Salix spp. However, there was no sharp threshold for foraging as suggested by some models. Contrary to qualitative predictions of optimal-foraging theory, we found no selection of feeding sites on the basis of the nitrogen content of food. The changed search pattern in late summer and the discrepancy between reindeer foraging paths and a correlated random walk model suggests that reindeer were responding to their environment by changing their searching behaviour.

1988 ◽  
Vol 53 (1-2) ◽  
pp. 203-219 ◽  
Author(s):  
S. M. T. de la Selva ◽  
Katja Lindenberg ◽  
Bruce J. West

2017 ◽  
Vol 50 (46) ◽  
pp. 465002 ◽  
Author(s):  
Satya N Majumdar ◽  
Philippe Mounaix ◽  
Grégory Schehr

2004 ◽  
Vol 41 (2) ◽  
pp. 483-496 ◽  
Author(s):  
Pieter Allaart

Optimal stopping rules are developed for the correlated random walk when future returns are discounted by a constant factor per unit time. The optimal rule is shown to be of dual threshold form: one threshold for stopping after an up-step, and another for stopping after a down-step. Precise expressions for the thresholds are given for both the positively and the negatively correlated cases. The optimal rule is illustrated by several numerical examples.


The Auk ◽  
1983 ◽  
Vol 100 (3) ◽  
pp. 711-716 ◽  
Author(s):  
Dale L. Rabe ◽  
Harold H. Prince ◽  
Donald L. Beaver

Abstract Live-trapped, adult American Woodcock (Scolopax minor) were tested in a series of laboratory experiments designed to evaluate the role of soil as a proximal cue for selecting feeding sites and to investigate foraging strategies for capturing earthworms (Lumbricidae). Foraging trials were conducted in a circular arena and showed that color, which tends to be correlated with the soil types and moisture regimes preferred by earthworms, was an important proximal cue for selecting feeding sites. Woodcock captured earthworms most efficiently in areas of relatively high prey density, because they used a nonrandom search pattern following an initial capture.


1980 ◽  
Vol 17 (01) ◽  
pp. 253-258 ◽  
Author(s):  
R. B. Nain ◽  
Kanwar Sen

For correlated random walks a method of transition probability matrices as an alternative to the much-used methods of probability generating functions and difference equations has been investigated in this paper. To illustrate the use of transition probability matrices for computing the various probabilities for correlated random walks, the transition probability matrices for restricted/unrestricted one-dimensional correlated random walk have been defined and used to obtain some of the probabilities.


1986 ◽  
Vol 23 (1) ◽  
pp. 201-207
Author(s):  
Gillian Iossif

A correlated random walk on a d-dimensional integer lattice is studied in which, at any stage, the probabilities of the next step being in the various possible directions depend on the direction of the previous step. Using a renewal argument, asymptotic estimates are obtained for the probability of return to the origin after n steps.


2008 ◽  
Vol 45 (01) ◽  
pp. 33-44 ◽  
Author(s):  
Pieter Allaart ◽  
Michael Monticino

Correlated random walks provide an elementary model for processes that exhibit directional reinforcement behavior. This paper develops optimal multiple stopping strategies - buy/sell rules - for correlated random walks. The work extends previous results given in Allaart and Monticino (2001) by considering random step sizes and allowing possibly negative reinforcement of the walk's current direction. The optimal strategies fall into two general classes - cases where conservative buy-and-hold type strategies are optimal and cases for which it is optimal to follow aggressive trading strategies of successively buying and selling the commodity depending on whether the price goes up or down. Simulation examples are given based on a stock index fund to illustrate the variation in return possible using the theoretically optimal stop rules compared to simpler buy-and-hold strategies.


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