Effect of density-dependent individual movement on emerging spatial population distribution: Brownian motion vs Levy flights

Abstract

Individual animal movement has been a focus of intense research and considerable controversy over the last two decades, however the understanding of wider ecological implications of various movement behaviours is lacking. In this paper, we consider this issue in the context of pattern formation. Using an individual-based modelling approach and computer simulations, we first show that density dependence ("auto-taxis") of the individual movement in a population of random walkers typically results in the formation of a strongly heterogeneous population distribution consisting of clearly defined animals clusters or patches. We then show that, when the movement takes place in a large spatial domain, the properties of the clusters are significantly different in the populations of Brownian and non-Brownian walkers. Whilst clusters tend to be stable in the case of Brownian motion, in the population of Levy walkers clusters are dynamical so that the number of clusters fluctuates in the course of time. We also show that the population dynamics of non-Brownian walkers exhibits two different time scales: a short time scale of the relaxation of the initial condition and a long time scale when one type of dynamics is replaced by another. Finally, we show that the distribution of sample values in the populations of Brownian and non-Brownian walkers is significantly different.

Movement patterns of the grey field slug (Deroceras reticulatum) in an arable field

“…Understanding movement behaviour of invertebrates is important for many practical reasons, in particular because species such as slugs can cause significant damage to crops 17,18 . There is theoretical and empirical evidence that the pattern of individual movement is a factor influencing population abundance over space and time [19][20][21][22][23] . This has a variety of implications in ecology and agroecology; in the context of pest control the knowledge of the pest population's spatial distribution is important when developing more sustainable control measures 24,25 .…”

“…In identifying patterns of individual animal movement, it is particularly important to take account of density dependent responses (if any) which can significantly affect the population spatial distribution. Population density can be a factor resulting in the formation of high density patches by modifying animal movement both on a shorter within-generation time 19 and on a longer multi-generation time scale 21,26,27 . In this study, we focus on movement of slugs in agricultural environments.…”

“…There is considerable field evidence that patches of high slug density are stable in time, at least within a given season 28,48 . In addition, there are many theoretical results showing that density dependent individual movement is a factor that can increase patch stability and even lead to patch (cluster) formation 19,21,49,50 . Correspondingly, in this section we analyse the field data on slug movement in the context of patch dynamics.…”

Quantitatively Inferring Three Mechanisms from the Spatiotemporal Patterns

“…It describes the change and the stability of spatial structure with time. There are still many other potential mechanisms to generate spatially self-organized patterns in the ecosystems [47,48] such as animal aggregation due to taxis and density-dependence [49], but they are beyond the scope of the discussion here. It is interesting for further comparison in the future research.…”

Analysing the impact of trap shape and movement behaviour of ground‐dwelling arthropods on trap efficiency

“…The mechanisms behind individual insect movement can be more complicated than what BM and the CRW propose. In the literature, other more complicated processes have been documented, such as; intermittent stop‐start movement (Mashanova, Olive, & Jansen, ), behavioural intensive‐extensive changes (Knell & Codling, ), individual interactions (De Jager, Weissing, Herman, Nolet, & de Koppel, ), density or time dependent diffusion (Ahmed & Petrovskii, ; Ellis, Petrovskaya, & Petrovskii, ), Lévy walks (LW; Sims et al., ) or even a mixture or composition of the above (Auger‐Méthé, Derocher, Plank, & Codling, ). The issue is more perplexing, since movement patterns can be misidentified (Petrovskii, Mashanova, & Jansen, ) or even, in the context of trapping, almost identical trap counts can be reproduced for inherently different movement models (Ahmed, Petrovskii, & Tilles, ).…”