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Pitfall traps are frequently used to capture ground‐dwelling arthropods, particularly beetles, ants and spiders. The capture efficiency of a pitfall trapping system strongly depends on the number and opening size of traps, how traps are distributed over the sampling area (spatial arrangement) and the movement characteristics of arthropods.We use numerical simulations for a single species to analyse the trap count patterns that emerge from these variables. Arthropod movement of individuals is modelled as correlated random walks, with multiple traps placed over an area, and catches are simulated as individual interaction with traps. We consider four different types of spatial arrangements of traps across a homogeneous landscape: grid (i.e. rectangular array), transect, nested‐cross and randomised. We contextualise our results by considering the locomotion of Pterostichus melanarius, a highly active carabid beetle often serving as a biocontrol agent for the suppression of pest insects and weeds.By simulating the trapping of randomly moving ground‐dwelling arthropods, we show that there is an optimal inter‐trap separation distance (trap spacing) that maximises captures, that can be expressed using exact formulae in terms of trap opening sizes, sampling area and trap number. Moreover, for the grid and nested‐cross arrangements, larger trap spacing to maximise spatial coverage over the whole sampling area is suboptimal. Also, we find that over a large sampling area, there is a hierarchical order for spatial arrangements in relation to capture efficiency: grid, randomised, transect, followed by the nested‐cross. However, over smaller sampling areas, this order is changed as the rate at which trap counts accumulate with trap number varies across arrangements—eventually saturating at different levels. In terms of movement effects, capture efficiency is maximised over a narrow diffusive range and does not depend strongly on the type of spatial arrangement—indicating an approximate optimal mode of arthropod activity, i.e. rate of spread.Our approach simultaneously considers several important experimental design aspects of pitfall trapping providing a basis to optimise and adapt sampling protocols to other types of traps to better reflect their various purposes, such as monitoring, conservation or pest management. [ABSTRACT FROM AUTHOR]

BACKGROUND The distribution of the grey field slug (Deroceras reticulatum Müller) in arable fields is characterised by patches containing higher slug densities dispersed within areas of lower densities. Behavioural responses that lead to the spatial/temporal stability of these patches are poorly understood, thus this study investigated behavioural mechanisms underpinning slug distribution using a new method for long‐term tracking of individual slug movement in the field. RESULTS: A technique for implanting radio frequency identification (RFID) tags (each with a unique identification code) beneath the body wall of slugs was developed. Laboratory tests indicated no consistent detrimental effect on survival, feeding, egg laying or locomotor behaviour (velocity, distance travelled). Movement of individual slugs above and below the soil surface was recorded for >5 weeks (in spring and autumn) in winter wheat fields. Most (~80%) foraged within a limited area; and at the end of the observation period were located at a mean distance of 78.7 ± 33.7 cm (spring) or 101.9 ± 24.1 cm (autumn) from their release point. The maximum detected distance from the release point was 408.8 cm. The remaining slugs (~20%) moved further away and ultimately were lost. CONCLUSIONS: RFID tagging allowed continuous tracking of individual slugs, even below the soil surface. Localised movement of 80% of tracked slugs over 5 weeks offers a mechanism promoting stable slug patches in arable crops. Rapid dispersal of the remaining slugs facilitates exchange of individuals between patches. Precision targeting of pesticides at such stable slug patches may facilitate reduced usage. © 2020 The Authors. Pest Management Science published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The complexity and disorder in the spatiotemporal arrangement of aquatic environments, and the influence of biological systems on this arrangement are investigated. It is shown with the help of results that modeling by reaction-diffusion equations method is considered suitable to examine basic processes of intricate spatiotemporal fish and plankton dynamics.

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. [ABSTRACT FROM AUTHOR]

Characterization of patterns of animal movement is a major challenge in ecology with applications to conservation, biological invasions and pest monitoring. Brownian random walks, and diffusive flux as their mean field counterpart, provide one framework in which to consider this problem. However, it remains subject to debate and controversy. This study presents a test of the diffusion framework using movement data obtained from controlled experiments., Walking beetles ( Tenebrio molitor) were released in an open circular arena with a central hole and the number of individuals falling from the arena edges was monitored over time. These boundary counts were compared, using curve fitting, to the predictions of a diffusion model. The diffusion model is solved precisely, without using numerical simulations., We find that the shape of the curves derived from the diffusion model is a close match to those found experimentally. Furthermore, in general, estimates of the total population obtained from the relevant solution of the diffusion equation are in excellent agreement with the experimental population. Estimates of the dispersal rate of individuals depend on how accurately the initial release distribution is incorporated into the model., We therefore show that diffusive flux is a very good approximation to the movement of a population of Tenebrio molitor beetles. As such, we suggest that it is an adequate theoretical/modelling framework for ecological studies that account for insect movement, although it can be context specific. An immediate practical application of this can be found in the interpretation of trap counts, in particular for the purpose of pest monitoring. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract The factors and mechanisms that enhance population persistence in a fragmented habitat and/or under harsh environmental conditions are of significant current interest. We consider the dynamics of a population in an isolated habitat surrounded by an unfavourable environment subject to different behavioural responses between the individuals. We assume that there are two responses available: one of them is aggression in its extreme form, the other is its contrary when an individual takes flight in order to avoid any contact with its conspecific. We show that a behaviourally structured population consisting of individuals with fixed behavioural responses is intrinsically less prone to extinction under harsh environmental condition than a population where the individuals can ‘choose’ between the two given behaviours. We also show that, contrary to an intuitively expected negative impact of aggression on population persistence, the optimal conditions for population persistence are reached when a considerable proportion of the individuals exhibit aggressive behaviour. [ABSTRACT FROM AUTHOR]

Abstract The dynamics of interacting ecological populations results from the interplay between various deterministic and stochastic factors and this is particularly the case for the phenomenon of biological invasion. Whereas the spread of invasive species via propagation of a population front was shown to appear as a result of deterministic processes, the spread via formation, interaction and movement of separate patches has been recently attributed to the influence of environmental stochasticity. An appropriate understanding of the comparative importance of deterministic and stochastic mechanisms is still lacking, however. In this paper, we show that the patchy invasion appears to be possible also in a fully deterministic predator–prey model as a result of the Allee effect. [ABSTRACT FROM AUTHOR]

The impact of ecological chaos on population dynamics has been an issue of intense discussion over the last decade. While many authors consider chaotic dynamics as a favourable factor facilitating species biodiversity, there is also a strong opinion that chaos may enhance population extinction. In this paper we show that chaotic spatio-temporal dynamics in an ecological community can arise as a response of the community to unfavourable environmental changes. Appearing in that way, chaos can prevent species extinction in a situation when it would be inevitable otherwise. We also show that an essential consequence of chaotic dynamics is that the issue of species extinction is subject to the size of the domain inhabited by the population, the extinction more likely happens in a small domain than in a large one. [ABSTRACT FROM AUTHOR]

Dynamics of human populations can be affected by various socio-economic factors through their influence on the natality and mortality rates, and on the migration intensity and directions. In this work we study an economic–demographic model which takes into account the dependence of the wealth production rate on the available resources. In the case of nonlocal consumption of resources, the homogeneous-in-space wealth–population distribution is replaced by a periodic-in-space distribution for which the total wealth increases. For the global consumption of resources, if the wealth redistribution is small enough, then the homogeneous distribution is replaced by a heterogeneous one with a single wealth accumulation center. Thus, economic and demographic characteristics of nonlocal and global economies can be quite different in comparison with the local economy. [ABSTRACT FROM AUTHOR]

Simple Summary: There is growing public and legislative pressure to reduce the use of pesticides in crop production. It is thought that the gray field slug is not uniformly distributed in arable fields, but that patches of higher slug densities occur, interspersed within areas of lower slug numbers. Targeting molluscicide applications only at these patches, leaving other areas untreated, would substantially reduce the amount of molluscicide used but relies on patches being a feature of slug populations in all susceptible crops, and always occurring in the same places during the periods slug control is needed. This study investigated these requirements in 22 commercial arable field crops from different regions of the UK, and in three different years. Despite a variable proportion of slug populations being found below the soil surface (where they could not be assessed) on different sampling dates, existence of higher density patches were confirmed in all fields, although it was noted that, when too few slugs were active on the soil surface, they could not be reliably detected. When they were detected, they occurred in the same locations in each field. The potential for using these patches in more sustainable slug control approaches is discussed. Exploitation of heterogenous distributions of Deroceras reticulatum, in arable fields by targeting molluscicide applications toward areas with higher slug densities, relies on these patches displaying sufficient spatio-temporal stability. Regular sampling of slug activity/distribution was undertaken using 1 ha rectangular grids of 100 refuge traps established in 22 commercial arable field crops. Activity varied significantly between the three years of the study, and the degree of aggregation (Taylor's Power Law) was higher in fields with higher mean trap catches. Hot spot analysis detected statistically significant spatial clusters in all fields, and in 162 of the 167 individual assessment visits. The five assessment visits in which no clusters were detected coincided with low slug activity (≤0.07 per trap). Generalized Linear Models showed significant spatial stability of patches in 11 fields, with non-significant fields also characterized by low slug activity (≤1.2 per trap). Mantel's permutation tests revealed a high degree of correlation between location of individual patches between sampling dates. It was concluded that patches of higher slug density were spatio-temporally stable, but detection using surface refuge traps (which rely on slug activity on the soil surface) was less reliable when adverse environmental conditions resulted in slugs retreating into the upper soil horizons. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

With the growing number of discovered exoplanets, the Gaia concept finds its second wind. The Gaia concept defines that the biosphere of an inhabited planet regulates a planetary climate through feedback loops such that the planet remains habitable. Crunching the "Gaia" puzzle has been a focus of intense empirical research. Much less attention has been paid to the mathematical realization of this concept. In this paper, we consider the stability of a planetary climate system with the dynamic biosphere by linking a conceptual climate model to a generic population dynamics model with random parameters. We first show that the dynamics of the corresponding coupled system possesses multiple timescales and hence falls into the class of slow-fast dynamics. We then investigate the properties of a general dynamical system to which our model belongs and prove that the feedbacks from the biosphere dynamics cannot break the system's stability as long as the biodiversity is sufficiently high. That may explain why the climate is apparently stable over long time intervals. Interestingly, our coupled climate-biosphere system can lose its stability if biodiversity decreases; in this case, the evolution of the biosphere under the effect of random factors can lead to a global climate change.

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 [Formula: see text] at the beginning and eventually slowing down to the diffusive spread [Formula: see text]. 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.

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.

Dispersal has been the focus of spatial ecology for a few decades. What should be a proper theoretical framework for understanding and modelling of dispersal processes remains a controversial issue though. Integrodifference equations (IDE) model the spatial dynamics of a population with distinct growth and dispersal stages in their life cycle. Depending on the stage observed, the equations take on different forms, only one of which is usually studied in the literature. Here we reveal that while these different forms are mathematically equivalent, the biological conclusions drawn from the different forms may differ considerably. We provide a summary of similarities and differences and point out the greatest potential caveats when applying IDE.