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

The most reliable estimates of the population abundance of ground-dwelling arthropods are obtained almost entirely through trap counts. Trap shape can be easily controlled by the researcher, commonly the same trap design is employed in all sites within a given study. Few researchers really try to compare abundances (numbers of collected individuals) between studies because these are heavily influenced by environmental conditions, e.g. temperature, habitat structure and food sources available, directly affecting insect movement activity. We propose that useful insights can be obtained from a theoretical-based approach. We focus on the interplay between trap shape (circle, square, slot), the underlying movement behaviour and the subsequent effect on captures. We simulate trap counts within these different geometries whilst considering movement processes with clear distinct properties, such as Brownian motion (BM), the correlated random walk (CRW) and the Lévy walk (LW). (a) We find that slot shaped traps are far less efficient than circular or square traps assuming same perimeter length, with differences which can exceed more than two-fold. Such impacts of trap geometry are only realized if insect mobility is sufficiently large, which is known to significantly vary depending on type of habitat. (b) If the movement pattern incorporates localized forward persistence then trap counts accumulate at a much slower rate, and this rate decreases further with higher persistency. (c) If the movement behaviour is of Lévy type, then fastest catch rates are recorded in the case of circular trap, and the slowest for the slot trap, indicating that trap counts can strongly depend on trap shape. Lévy walks exacerbate the impact of geometry while CRW make these differences more inconsequential. In this study we reveal trap efficiencies and how movement type can alter capture rates. Such information contributes towards improved trap count interpretations, as required in ecological studies which make use of trapping systems

On the Consistency of the Reaction-Telegraph Process Within Finite Domains

Reaction-telegraph equation (RTE) is a mathematical model that has often been used to describe natural phenomena, with specific applications ranging from physics to social sciences. In particular, in the context of ecology, it is believed to be a more realistic model to describe animal movement than the more traditional approach based on the reaction-diffusion equations. Indeed, the reaction-telegraph equation arises from more realistic microscopic assumptions about individual animal movement (the correlated random walk) and hence could be expected to be more relevant than the diffusion-type models that assume the simple, unbiased Brownian motion. However, the RTE has one significant drawback as its solutions are not positively defined. It is not clear at which stage of the RTE derivation the realism of the microscopic description is lost and/or whether the RTE can somehow be ‘improved’ to guarantee the solutions positivity. Here we show that the origin of the problem is twofold. Firstly, the RTE is not fully equivalent to the Cattaneo system from which it is obtained; the equivalence can only be achieved in a certain parameter range and only for the initial conditions containing a finite number of Fourier modes. Secondly, the Dirichlet type boundary conditions routinely used for reaction-diffusion equations appear to be meaningless if used for the RTE resulting in solutions with unrealistic properties. We conclude that, for the positivity to be regained, one has to use the Cattaneo system with boundary conditions of Robin type or Neumann type, and we show how relevant classes of solutions can be obtained

Statistical mechanics of animal movement: Animals's decision-making can result in superdiffusive spread

Peculiarities of individual animal movement and dispersal have been a major focus of recent research as they are thought to hold the key to the understanding of many phenomena in spatial ecology. Superdiffusive spread and long-distance dispersal have been observed in different species but the underlying biological mechanisms often remain obscure. In particular, the effect of relevant animal behavior has been largely unaddressed. In this paper, we show that a superdiffusive spread can arise naturally as a result of animal behavioral response to small-scale environmental stochasticity. Surprisingly, the emerging fast spread does not require the standard assumption about the fat tail of the dispersal kernel

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect

Traditionally, mathematical modeling in population ecology is mainly focused on asymptotic behavior of the model, i.e. as given by the system attractors. Recently, however, transient regimes and especially long-term transients have been recognized as playing a crucial role in the dynamics of ecosystems. In particular, long-term transients are a potential explanation of ecological regime shifts, when an apparently healthy population suddenly collapses and goes extinct. In this paper, we show that the interplay between delay in maturation and a strong Allee effect can result in long-term transients in a single species system. We first derive a simple ‘conceptual’ model of the population dynamics that incorporates both a strong Allee effect and maturation delay. Unlike much of the previous work, our approach is not empirical since our model is derived from basic principles. We show that the model exhibits a high complexity in its asymptotic dynamics including multi-periodic and chaotic attractors. We then show the existence of long-term transient dynamics in the system, when the population size oscillates for a long time between locally stable stationary states before it eventually settles either at the persistence equilibrium or goes extinct. The parametric space of the model is found to have a complex structure with the basins of attraction corresponding to the persistence and extinction states being of a complicated shape. This impedes the prediction of the eventual fate of the population, as a small variation in the maturation delay or the initial population size can either bring the population to extinction or ensure its persistence

A random acceleration model of individual animal movement allowing for diffusive, superdiffusive and superballistic regimes

Patterns of individual animal movement attracted considerable attention over the last two decades. In particular, question as to whether animal movement is predominantly diffusive or superdiffusive has been a focus of discussion and controversy. We consider this problem using a theory of stochastic motion based on the Langevin equation with non-Wiener stochastic forcing that originates in animal's response to environmental noise. We show that diffusive and superdiffusive types of motion are inherent parts of the same general movement process that arises as interplay between the force exerted by animals (essentially, by animal's muscles) and the environmental drag. The movement is superballistic with the mean square displacement growing with time as 〈x 2 (t)〉 ∼ t 4 at the beginning and eventually slowing down to the diffusive spread 〈x 2 (t)〉 ∼ t. We show that the duration of the superballistic and superdiffusive stages can be long depending on the properties of the environmental noise and the intensity of drag. Our findings demonstrate theoretically how the movement pattern that includes diffusive and superdiffusive/superballistic motion arises naturally as a result of the interplay between the dissipative properties of the environment and the animal's biological traits such as the body mass, typical movement velocity and the typical duration of uninterrupted movement

The "Lévy or diffusion" Controversy: How important is the movement pattern in the context of trapping?

Many empirical and theoretical studies indicate that Brownian motion and diffusion models as its mean field counterpart provide appropriate modeling techniques for individual insect movement. However, this traditional approach has been challenged, and conflicting evidence suggests that an alternative movement pattern such as Lévy walks can provide a better description. Lévy walks differ from Brownian motion since they allow for a higher frequency of large steps, resulting in a faster movement. Identification of the 'correct' movement model that would consistently provide the best fit for movement data is challenging and has become a highly controversial issue. In this paper, we show that this controversy may be superficial rather than real if the issue is considered in the context of trapping or, more generally, survival probabilities. In particular, we show that almost identical trap counts are reproduced for inherently different movement models (such as the Brownian motion and the Lévy walk) under certain conditions of equivalence. This apparently suggests that the whole 'Levy or diffusion' debate is rather senseless unless it is placed into a specific ecological context, e.g., pest monitoring programs

A random walk description of individual animal movement accounting for periods of rest

Animals do not move all the time but alternate the period of actual movement (foraging) with periods of rest (e.g. eating or sleeping). Although the existence of rest times is widely acknowledged in the literature and has even become a focus of increased attention recently, the theoretical approaches to describe animal movement by calculating the dispersal kernel and/or the mean squared displacement (MSD) rarely take rests into account. In this study, we aim to bridge this gap. We consider a composite stochastic process where the periods of active dispersal or ‘bouts’ (described by a certain baseline probability density function (pdf) of animal dispersal) alternate with periods of immobility. For this process, we derive a general equation that determines the pdf of this composite movement. The equation is analysed in detail in two special but important cases such as the standard Brownian motion described by a Gaussian kernel and the Levy flight described by a Cauchy distribution. For the Brownian motion, we show that in the large-time asymptotics the effect of rests results in a rescaling of the diffusion coefficient. The movement occurs as a subdiffusive transition between the two diffusive asymptotics. Interestingly, the Levy flight case shows similar properties, which indicates a certain universality of our findings

Experimental data and MATLAB code

This archive contains the experimental data and MATLAB code used in the publication named. Three folders are included containing: raw and processed data files; MATLAB functions for parameter estimation; and MATLAB functions for the generation of power law random walks. The README file provides additional information about these folders and the files contained within

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