Catching ghosts with a coarse net: use and abuse of spatial sampling data in detecting synchronization

A computational study of density-dependent individual movement and the formation of population clusters in two-dimensional spatial domains

The patterns of collective behaviour in a population emerging from individual animal movement have long been of interest to ecologists, as has the emergence of heterogeneous patterns among a population. In this paper we will consider these phenomena by using an individual-based modelling approach to simulate a population whose individuals undergo density-dependent movement in 2D spatial domains. We first show that the introduction of density-dependent movement in the form of two parameters, a perception radius and a probability of directed movement, leads to the formation of clusters. We then show that the properties of the clusters and their stability over time are different between populations of Brownian and non-Brownian walkers and are also dependent on the choice of parameters. Finally, we consider the effect of the probability of directed movement on the temporal stability of clusters and show that while clusters formed by Brownian and non-Brownian walkers may have similar properties with certain parameter sets, the spatio-temporal dynamics remain different.

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

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 animal 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.

Towards the Development of a More Accurate Monitoring Procedure for Invertebrate Populations, in the Presence of an Unknown Spatial Pattern of Population Distribution in the Field

Studies addressing many ecological problems require accurate evaluation of the total population size. In this paper, we revisit a sampling procedure used for the evaluation of the abundance of an invertebrate population from assessment data collected on a spatial grid of sampling locations. We first discuss how insufficient information about the spatial population density obtained on a coarse sampling grid may affect the accuracy of an evaluation of total population size. Such information deficit in field data can arise because of inadequate spatial resolution of the population distribution (spatially variable population density) when coarse grids are used, which is especially true when a strongly heterogeneous spatial population density is sampled. We then argue that the average trap count (the quantity routinely used to quantify abundance), if obtained from a sampling grid that is too coarse, is a random variable because of the uncertainty in sampling spatial data. Finally, we show that a probabilistic approach similar to bootstrapping techniques can be an efficient tool to quantify the uncertainty in the evaluation procedure in the presence of a spatial pattern reflecting a patchy distribution of invertebrates within the sampling grid.