Testing for density dependence

Summary The robustness and sensitivity of a test for density dependence in an animal population against departures from the assumed null and alternative model is assessed via simulation. The test is shown to be nonrobust and insensitive to departures from the assumed models.     

Flow- and substratum-mediated movement by a stream insect

1. In streams subject to frequent hydrologic disturbance, the ability of benthic invertebrates to disperse within the channel is key to understanding the mechanisms of flow refugium use and population persistence. This study focuses on crawling invertebrates, the effects on movement of abiotic factors (specifically, flow near the stream bed and bed micro‐topography) and the consequences for dispersal. 2. In a large flume, we observed individual cased caddisflies, Potamophylax latipennis, moving in fully turbulent flows over a precise replica of a water‐worked surface. From maps of movement paths, we quantified crawling behaviour and entrainment, and the influence of bed micro‐topography. We manipulated discharge and tested its effect on movement, linear displacement and areal dispersal. The highest discharge treatment was a disturbance to the caddis; the lowest discharge was not. Crawling behaviours were used to parameterise random walk models and estimate population dispersal, and to test the effects of abiotic factors on movement. 3. Bed micro‐topography influenced crawling in several ways. Caddis spent most of their time at the junctions between proud particles and the adjacent plane bed. The frequency distribution of turn angles was bimodal, with modal values approximating the angle required to travel around median‐sized particles. Larvae generally crawled downstream, but crawling direction relative to the flow was skewed by bed micro‐topography and was not directly downstream, unlike drift. 4. Caddis crawled for most of the time and discharge affected almost every aspect of their movement. As discharge increased, caddis crawled less often, more slowly and over shorter distances; they also became entrained more frequently and over greater distances. With increased discharge, caddis spent proportionately less time at the junctions between proud particles and the adjacent plane bed, and more time on the tops and sides of proud clasts. This is curious as most entrainment occurred from the tops and sides of clasts and entrainment is generally considered to be disadvantageous during disturbances. 5. Linear displacement (drift and entrainment combined) was downstream, but the relation between total displacement and discharge was complex. Total displacement decreased at intermediate discharge as crawling decreased, but increased at high discharge as entrainment and drift played a greater role in movement. 6. Within‐stream dispersal via crawling contained elements of both a correlated random walk (we observed directional persistence in turn angles) and a biased random walk (we observed downstream bias in move direction angles) and was best described as a biased correlated random walk. Dispersal was inversely related to discharge, suggesting that the ability of P. latipennis to crawl into flow refugia on the streambed is reduced at high flow.     

Analysis of a one-dimensional random walk with irreversible losses at each step: applications for protein movement on DNA

We analysed a one-dimensional random walk between two points when the migrating particle could be irreversibly lost (dissociated) from the system at each step of the process. We show that in the case of losses at each step the average number of steps made by the particle that reaches the final point does not obey quadratic dependence on the distance between the starting and the final points: for long distances this dependence is linear. This is because losses "select" for shorter pathways between the starting and the final points. We applied this analysis to protein translocations within long DNA molecules.     

Modelling nematode movement using time-fractional dynamics

We use a correlated random walk model in two dimensions to simulate the movement of the slug parasitic nematode Phasmarhabditis hermaphrodita in homogeneous environments. The model incorporates the observed statistical distributions of turning angle and speed derived from time-lapse studies of individual nematode trails. We identify strong temporal correlations between the turning angles and speed that preclude the case of a simple random walk in which successive steps are independent. These correlated random walks are appropriately modelled using an anomalous diffusion model, more precisely using a fractional sub-diffusion model for which the associated stochastic process is characterised by strong memory effects in the probability density function.     

Hierarchical patch dynamics and animal movement pattern

In hierarchical patch systems, small-scale patches of high density are nested within large-scale patches of low density. The organization of multiple-scale hierarchical systems makes non-random strategies for dispersal and movement particularly important. Here, we apply a new method based on first-passage time on the pathway of a foraging seabird, the Antarctic petrel (Thalassoica antarctica), to quantify its foraging pattern and the spatial dynamics of its foraging areas. Our results suggest that Antarctic petrels used a nested search strategy to track a highly dynamic hierarchical patch system where small-scale patches were congregated within patches at larger scales. The birds searched for large-scale patches by traveling fast and over long distances. Once within a large-scale patch, the birds concentrated their search to find smaller scale patches. By comparing the pathway of different birds we were able to quantify the spatial scale and turnover of their foraging areas. On the largest scale we found foraging areas with a characteristic scale of about 400 km. Nested within these areas we found foraging areas with a characteristic scale of about 100 km. The large-scale areas disappeared or moved within a time frame of weeks while the nested small-scale areas disappeared or moved within days. Antarctic krill (Euphausia superba) is the dominant food item of Antarctic petrels and we suggest that our findings reflect the spatial dynamics of krill in the area.Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at .     

The effect of cell sedimentation on measuring chondrocyte population migration using a Boyden chamber

The Boyden chamber assay provides a convenient method of assessing cell migration and measuring cell motility coefficients at the population level. Previous models of this assay completely ignore cell sedimentation in the suspension, assuming that all cells have already settled on the filter surface before commencing migration within the filter. However, ignoring cell sedimentation could lead to poor data interpretation because the time required for cells to settle through the suspension is close to the incubation period of only a few hours. This study models the Boyden chamber assay by incorporating the cell settling process to account for the cells remaining in the upper well when other cells migrate in the filter. The simulations in this study elucidate the experiments in the literature that test the haptotactic and chemotactic responses of rabbit chondrocytes to type II collagen. This study determines the cell population random motility, as well as the haptotaxis and chemotaxis coefficients, by fitting the experimental data. Results show that the chemotactic motility coefficient is 100 times greater than the haptotactic coefficient, and the equilibrium collagen-receptor dissociation constant is about 10-fold the haptotactic counterpart. Diffusion causes the soluble collagen gradients in the chemotactic case to decline over time, while the coated collagen gradients in the haptotactic assay are likely to remain fixed. As a result, the chemotactic case exhibits a lower number of migrated cells than the haptotactic assay. This study also demonstrates the influences of the dimensionless parameters that control cell behavior in the Boyden assay, providing a reference for future experiment designs.     

Analytical and numerical tools for diffusion-based movement models

I present a general diffusion-based modeling framework for the analysis of animal movements in heterogeneous landscapes, including terms representing advection, mortality, and edge-mediated behavior. I use adjoint operator theory to develop mathematical machinery for the assessment of a number of biologically relevant quantities, such as occupancy times, hitting probabilities, quasi-stationary distributions, the backwards equation, and conditional probability densities. I derive finite-element approximations, which can be used to obtain numerical solutions in domains which do not allow for an analytical treatment. As an example, I model the movements of the butterfly Melitaea cinxia in an island consisting of a set of habitat patches and the intervening matrix habitat. I illustrate the behavior of the model and the mathematical theory by examining the effects of a hypothetical movement barrier and advection caused by prevailing wind conditions.     

Superdiffusion in a Model for Diffusion in a Molecularly Crowded Environment

We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in a percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times but anomalous diffusion at intermediate times. The effective exponents for square distance vs time usually are below one at these intermediate times, but they can also be larger than one for high barrier concentrations. Thus, we observe sub- and superdiffusion in a crowded environment.     

Modelling baculovirus infection of insect cells in culture

Conclusions Infection of insect cells with baculovirus is a potentially attractive means for producing both viral insecticides and recombinant proteins. The continuation of mathematical modelling studies such as those reviewed in this paper are essential in order to realise the full potential of the system. Through mathematical models it is possible to predict complex behaviours such as those observed when infecting cells at low MOI or when propagating virus in a continuous culture system. A purely empirical analysis of the same phenomena is very difficult if not impossible.The present three models are — despite their complexity and the effort that has gone into developing them — all first generation models. They summarise, to a large extent, our present quantitative understanding of the interaction between baculovirus and insect cells, when looked upon as a black box system. The binding and initial infection processes are still quantitatively poorly understood and further work in this area is much needed. On the longer term, a second generation of models is likely to consider interior processes such as viral DNA and RNA accumulation in much more detail using a structured model of the infection cycle.     

Risky movement increases the rate of range expansion

The movement rules used by an individual determine both its survival and dispersal success. Here, we develop a simple model that links inter-patch movement behaviour with population dynamics in order to explore how individual dispersal behaviour influences not only its dispersal and survival, but also the population's rate of range expansion. Whereas dispersers are most likely to survive when they follow nearly straight lines and rapidly orient movement towards a non-natal patch, the most rapid rates of range expansion are obtained for trajectories in which individuals delay biasing their movement towards a non-natal patch. This result is robust to the spatial structure of the landscape. Importantly, in a set of evolutionary simulations, we also demonstrate that the movement strategy that evolves at an expanding front is much closer to that maximizing the rate of range expansion than that which maximizes the survival of dispersers. Our results suggest that if one of our conservation goals is the facilitation of range-shifting, then current indices of connectivity need to be complemented by the development and utilization of new indices providing a measure of the ease with which a species spreads across a landscape.     

Random movement pattern of the sea urchin Strongylocentrotus droebachiensis

We describe the fine-scale movement of the sea urchin Strongylocentrotus droebachiensis based on analyses of video recordings of undisturbed individuals in the two habitats which mainly differed in food availability, urchin barrens and grazing front. Urchin activity decreased as urchin density increased. Individuals alternated between moving and being stationary and their behaviour did not appear to be affected by either current velocity (within the range from 0 to 15 cm s^− 1) and temperature (2.3 to 6.0 °C). Movement of individuals at each location was compared to that predicted by a random walk model. Mean move length (linear distance between two stationary periods), turning angle and net squared displacement were calculated for each individual. The distribution of turning angles was uniform at each location and there was no evidence of a relationship between urchin density and either move length or urchin velocity. The random model predicted a higher dispersal rate at locations with low urchin densities, such as barrens habitats. However, the movement was sometimes greater or less than predicted by the model, suggesting the influence of local environmental factors. The deviation of individual paths from the model revealed that urchins can be stationary or adopt a local (displacement less than random), random or directional movement. The net daily distance displaced on the barrens, predicted by a random walk model, was similar to the observed movement recorded in our previous study of tagged urchins at one site, but less than that observed at a second site. We postulate that the random dispersal of urchins allows individuals on barrens to reach the kelp zone where food is more abundant although the time required to reach the kelp zone may be considerable (months to years). Urchins decrease their rate of dispersal once they reach the kelp zone so that they likely remain close to this abundant food sources for long periods.     

Relative movement patterns of a tephritid fly and its parasitoid wasps

The extent of within-patch dispersal by a tephritid fly and its four major parasitoids was examined over three field seasons. Hosts and parasitoids were marked using acrylic paint and observed as they oviposited into the flowerheads of marsh thistle, Cirsium palustre. The average recapture rate pooled across all species was 22%. The four parasitoids showed consistently greater rates of movement than the host in all three years. In nearly all comparisons, male dispersal was less than female dispersal. There was no evidence that parasitoids moved longer distances after visiting low quality rather than high quality patches. In the one season it was studied, no correlations between movement and insect size were observed. The relevance of these observations to host-parasitoid population dynamics is discussed.     

Modelling the wave movement of a multisegment biomechanical system

Modeling of wave motion of human body's multi-segment biomechanical system by examination of forced transverse oscillations of one-dimensional bar system with distributed parameters is performed in javelin throwing. Energy flow value under different changes of model parameters is investigated. The experimental data showing wave front motion and transformation of spectral density of oscillations from segment to segment of the thrower's body are discussed. Share of the energy transferred along the body's segments in the total energy of javelin release is 70-72 per cent according to theoretical estimates for concrete model parameters, and 63-75 per cent according to the experimental data for 8 attempts.     

Movements of carabid beetles (Coleoptera: Carabidae) inhabiting cereal fields: a field tracing study

Summary The individual movements of four carabid species were investigated by tracing beetles in the field using a portable radar system (harmonic radar). The field-inhabiting a Pterostichus melanarius Illiger, P. niger Schaller and Harpalus rufipes De Geer were traced in cereal fields. The movements of P. melanarius Mnd P. niger were also tracked in a wood and then compared with the movements of the forest-species Carabus nemoralis Müller. P. melanarius and P. niger displayed directed movements in cereal fields, although P. niger moved faster than P. melanarius. The movement pattern of H. rufipes in the field, and C. nemoralis and P. malanarius in the wood can be described as a c correlated random walk. In cereal fields, P. melanarius burrowed actively into the soil, and P. niger searched out crevices. In contrast, none of these two carabids burrowed in the forest soil, whereas C. nemoralis did. No statistically significant difference was observed between the movements of hungry and satiated beetles, although starved beetles tended to disperse shorter distances per move and turned back more often (especially P. niger). The significance of the various movement patterns exhibited by the species studied for their reproduction and survival on arable land is discussed.