Pierre Bovet

Spatial analysis of animals' movements using a correlated random walk model*

A probabilistic model was developed that applies to the analysis of erratic movements made by animals foraging in a stochastic environment. This model is a first order correlated random walk model in which the following two biological constraints are integrated into the Brownian motion model: bilateral symmetry and the cephalocaudal polarization that leads to a tendency to go forward. The main properties of the model were studied by numerical simulations using a pseudo-random generator. It was found that the spatial pattern of search paths could be quantified by a single numerical index of sinuosity. Some advice on the concrete use of this model is given. Correlated random walk diffusion was studied in relation to the sinuosity by analysing the probabilistic distribution of the bee-line distance between the first and last points of a path. Some theoretical applications of this model are developed.

Spatial memory in large scale movements: Efficiency and limitation of the egocentric coding process

The orientation abilities exhibited by many species are based on spatial memorization. The location of a place to which an animal intends to return may be memorized either independently of the animals position (location and orientation) by an exocentric coding which consists of processing the location-based (site-dependent) information provided by nearby landmarks perceptible both from the animals location and the place, or in relation to the animals position by an egocentric coding which consists of processing the route-based (site-independent) information provided by the animals movements (rotations and translations). An animal seldom has the opportunity of processing useful location-based information during large scale movements in its home range, except during the terminal adjustment of its path. Consequently, it may memorize the directions and the distances of the preferential places in its home range by processing route-based information. The efficiency of this egocentric coding process was quantified as a function of the path characteristics and the type and magnitude of route-based information estimation errors. This process was found to require a high degree of accuracy in idiothetic (internal) estimations of rotatory movements but not in estimations of translatory movements or in allothetic (compass-based) estimations of rotatory movements. The complementarity of the exocentric and egocentric coding processes during large scale movements is discussed.

How animals use their environment: a new look at kinesis

Abstract The aim of this paper is to show how animals can orient themselves in relation to a stimulation gradient or exploid patchy environments using simple kinetic mechanisms. From a new look at klinokinesis and orthokinesis, the properties of these two mechanisms were determined and their respective contributions to the phenomenon of animal aggregation in the most suitable areas of the environment were specified. When movement regulation is a function of variations in the stimulus intensity, klinokinesis can be seen as an elementary spatial orientation mechanism, whereas orthokinesis seems to have no biological application. In contrast, when movement regulation is a function of the value of stimulus intensity, klinokinesis and orthokinesis can both be seen as elementary space-use mechanisms. Some examples of applications of the models are given. In particular, it is suggested how klinokinetic and orthokinetic models can formalize the ‘area-restricted’ searching behaviour exhibited by many foraging animals. Finally, the place of klinokinetic and orthokinetic mechanisms in the framework of a general theory of spatial orientation and space use in animals is discussed.

Distinguishing between elementary orientation mechanisms by means of path analysis

Abstract It is not always possible to tell by analysing the environmental factors and an organisms receptors whether this organism has reached a given target by chance after making an unoriented movement, or by using one of two types of elementary orientation mechanism, namely taxis and differential klinokinesis. In this paper the main characteristics of these two orientation mechanisms are described. It is then shown how a statistical analysis of the organisms path can be performed to determine which of these two mechanisms is likely to be involved. This type of analysis is illustrated by means of three examples: two simulated paths, one involving taxis and the other differential klinokinesis, and an actual foraging ants path.

Optimal sinuosity in central place foraging movements

Abstract The case of a forager searching for immobile, randomly distributed prey items from a central place and homing straight back was examined to determine the optimal sinuosity of the search path. The optimal policy that was considered consists of minimizing the expected total (searching plus homeward) path length required to survey a given area, depending on the number of prey items the animal is able to load, its search path width and the prey density. The sinuosity of the search path must be low enough to minimize any overlapping between search path loops but high enough to minimize the homeward journey. Because of the complexity of the mathematical approach, the optimal sinuosity formula was derived using computer simulations. For a given prey density, the optimal sinuosity decreased logarithmically with the number of prey items the central place forager was searching for. The optimal sinuosity formula was also extended to deal with patchy environments. The applicability of this formula and its robustness to errors in the animals estimate of the prey density are discussed.

The perception of minimal structures: Performance on open and closed versions of visually presented Euclidean travelling salesperson problems

The planar Euclidean version of the travelling salesperson problem (TSP) requires finding a tour of minimal length through a two-dimensional set of nodes. Despite the computational intractability of the TSP, people can produce rapid, near-optimal solutions to visually presented versions of such problems. To explain this, MacGregor et al (1999, Perception 28 1417–1428) have suggested that people use a global-to-local process, based on a perceptual tendency to organise stimuli into convex figures. We review the evidence for this idea and propose an alternative, local-to-global hypothesis, based on the detection of least distances between the nodes in an array. We present the results of an experiment in which we examined the relationships between three objective measures and performance measures of optimality and response uncertainty in tasks requiring participants to construct a closed tour or an open path. The data are not well accounted for by a process based on the convex hull. In contrast, results are generally consistent with a locally focused process based initially on the detection of nearest-neighbour clusters. Individual differences are interpreted in terms of a hierarchical process of constructing solutions, and the findings are related to a more general analysis of the role of nearest neighbours in the perception of structure and motion.

Role of pinnae and head movements in localizing pure tones.

Twelve blindfolded subjects localized two different pure tones, randomly played by eight sound sources in the horizontal plane. Either subjects could get information supplied by their pinnae (exter...

A comparative study on the paths of five anura species.

The movements of five species of European toads were recorded in the daytime and at night in a 3×3 m area. The paths obtained were analyzed according to the first order correlated random walk model developed by Bovet and Benhamou with which it is possible to characterize each path with two independent indices: its sinuosity and its speed. The analysis showed that the day/night variable affected the sinuosity of the paths but not their mean speed. Significant differences between species were found to exist, however, in the case of both the sinuosity and the speed. It is worth noting that these interspecific behavioural differences did not match the classical phylogenetic classification, as shown by multiple comparison tests.

Biological functions of sinuosity regulation: a reply to Budenberg

Klinokinesis and orthokinesis have been defined as mechanisms regulating the rate of change of direction and the speed of a random search movement as a function of a stimulation (Gunn et al. 1937; Fraenkel & Gunn 1961). We have recently proposed that klinokinesis might be redefined as a mechanism regulating the sinuosity of the path instead of the rate of change of direction (Benhamou & Bovet 1989). The sinuosity is a purely spatial parameter corresponding to the amount of turning associated with a given path length (Bovet & Benhamou 1988). It is necessary to distinguish between the two modes whereby these two mechanisms can operate: in the absolute mode, the regulation is a function of the local value of the stimulus intensity, whereas in the differential mode the regulation is a function of variations in the stimulus intensity. Whatever the definitions used, it must be kept in mind that klinokinesis and orthokinesis are models for the mechanisms actually used. They deal with an animals movement which has been schematized as a discrete step process, i.e. as a sequence of translations (steps) alternating with rotations (changes of direction). Numerous animals, if not all, are probably able to control the distances and turns they perform during the locomotor process as a function of time, but how these parameters are integrated at the neurophysiological level and serve to regulate ongoing movements is unknown. The value of definitions of movement-regulating mechanisms can therefore be discussed only at a model level. In other words, the question is: which models may help us to understand better the space-related behaviour patterns of animals; and not: in which cases it is simpler to use such or such definition to account for the observed behaviour. For the sake of simplicity, we continue this reply as if the rate of change of direction was a reliable parameter of the random search movements of animals, although it actually depends on the arbitrary step duration used in recording the movement (a useful solution consists of replacing it by the square of the amount of turning per unit of time; Dunn 1983). In his conclusion Budenberg (1991) argues that three types of kinesis can be defined, depending on whether the regulation deals with speed, rate of change of direction or sinuosity. This is not appropriate because these three parameters are all mathematically interdependent. It is impossible to state, however, which two parameters an animal actually controls and which one can be said to follow as a consequence, because we lack the requisite neurophysiological knowledge. Similarly, Doucet & Drost (1985) have defined four types ofkinesis. In a subsequent paper, Doucet & Wilschut (1987) reduced this number to three, showing that one type could be taken to be a combination of two others, but they admitted that only two types would suffice. Indeed, as we mentioned previously (Benhamou & Bovet 1989), two of these four types are equivalent forms of klinokinesis whereas one other is a combination of klinokinesis and orthokinesis. In our opinion, our redefinition of klinokinesis should lead to a better understanding of both spatial orientation mechanisms (allowing an animal to move towards a given target) and space-use mechanisms (allowing an animal to regulate the time it spends in the various parts of its environment). Let us first consider the spatial orientation mechanisms. Using the definitions of Fraenkel & Gunn (1961), Rohlf & Davenport (1969) showed that both differential klinokinesis and differential orthokinesis can lead an organism to orient itself in a stimulation gradient field. Although these two types of spatio-temporal kinesis were formalized using two different mathematical methods, they are equivalent at the level of the path structure and orientational performance: the distinction between them arises from the discrete step representation of the organisms movement and has no biological foundations. Our redefinition of klinokinesis makes it possible to account for this type of spatial orientation using a single sinuosity-regulating mechanism.

Monaural azimuth sound localization with linguistic and nonlinguistic stimuli

Many studies have been conducted to measure monaural azimuth sound localization performances with different sounds varying in frequency and complexity, but few are using language. This experimental design included phonologically and semantically different sentences, that is, they either contained fricative consonants or not, and all sentences were presented right way out or reversed. Analysis of response correctness of 30 subjects showed that localization performance is better with the left ear than with the right ear, but that neither the phonological nor the semantic aspect of the stimuli have any influence on localization accuracy. Analysis of response times of the subjects revealed an effect of the stimuli’s nature. Reversed sentences as well as those containing fricative consonants need more time to be localized than other stimuli. These results suggest that monaural sound localization is independent of phonological or semantic attributes of the signal, but that linguistic stimuli are processed more ...