Use of novel sensors combining local positioning and acceleration to measure feeding behavior differences associated with lameness in dairy cattle

Time constraints for dairy farmers are an important factor contributing to the under-detection of lameness, resulting in delayed or missed treatment of lame cows within many commercial dairy herds. Hence, a need exists for flexible and affordable cow-based sensor systems capable of monitoring behaviors such as time spent feeding, which may be affected by the onset of lameness. In this study a novel neck-mounted mobile sensor system that combines local positioning and activity (acceleration) was tested and validated on a commercial UK dairy farm. Position and activity data were collected over 5 consecutive days for 19 high-yield dairy cows (10 lame, 9 non-lame) that formed a subset of a larger (120 cow) management group housed in a freestall barn. A decision tree algorithm that included sensor-recorded position and accelerometer data was developed to classify a cow as doing 1 of 3 categories of behavior: (1) feeding, (2) not feeding, and (3) out of pen for milking. For each classified behavior the mean number of bouts, the mean bout duration, and the mean total duration across all bouts was determined on a daily basis, and also separately for the time periods in between milking (morning = 0630–1300 h; afternoon = 1430–2100 h; night = 2230–0500 h). A comparative analysis of the classified cow behaviors was undertaken using a Welch -test with Benjamini-t Hochberg post-hoc correction under the null hypothesis of no differences in the number or duration of behavioral bouts between the 2 test groups of lame and nonlame cows. Analysis showed that mean total daily feeding duration was significantly lower for lame cows compared with non-lame cows. Behavior was also affected by time of day with significantly lower mean total duration of feeding and higher total duration of nonfeeding in the afternoons for lame cows compared with nonlame cows. The results demonstrate how sensors that measure both position and acceleration are capable of detecting differences in feeding behavior that may be associated with lameness. Such behavioral differences could be used in the development of predictive algorithms for the prompt detection of lameness as part of a commercially viable automated behavioral monitoring system

Comparison of the effects of exploitation on theoretical long-lived fish species with different life-history strategies and the implications for management

This article was originally published by ICES on their website http://www.ices.dk/.A stage-based simulation model is used to investigate the effect of exploitation on theoretical populations representing long-lived elasmobranch and teleost species with different life-history strategies. A comparison is made between the effect of exploitation on the elasmobranch ‘k-strategists’ and other teleost species that are ‘r-strategists’. We demonstrate the effects of stage-based exploitation on a typical long-lived elasmobranch population and discuss the implications of this when designing a management plan to ensure survival of the stock

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

A Pearson-Dirichlet random walk

A constrained diffusive random walk of n steps and a random flight in Rd, which can be expressed in the same terms, were investigated independently in recent papers. The n steps of the walk are identically and independently distributed random vectors of exponential length and uniform orientation. Conditioned on the sum of their lengths being equal to a given value l, closed-form expressions for the distribution of the endpoint of the walk were obtained altogether for any n for d=1, 2, 4 . Uniform distributions of the endpoint inside a ball of radius l were evidenced for a walk of three steps in 2D and of two steps in 4D. The previous walk is generalized by considering step lengths which are distributed over the unit (n-1) simplex according to a Dirichlet distribution whose parameters are all equal to q, a given positive value. The walk and the flight above correspond to q=1. For any d >= 3, there exist, for integer and half-integer values of q, two families of Pearson-Dirichlet walks which share a common property. For any n, the d components of the endpoint are jointly distributed as are the d components of a vector uniformly distributed over the surface of a hypersphere of radius l in a space Rk whose dimension k is an affine function of n for a given d. Five additional walks, with a uniform distribution of the endpoint in the inside of a ball, are found from known finite integrals of products of powers and Bessel functions of the first kind. They include four different walks in R3 and two walks in R4. Pearson-Liouville random walks, obtained by distributing the total lengths of the previous Pearson-Dirichlet walks, are finally discussed.Comment: 33 pages 1 figure, the paper includes the content of a recently submitted work together with additional results and an extended section on Pearson-Liouville random walk

Calculating spatial statistics for velocity jump processes with experimentally observed reorientation parameters

Mathematical modelling of the directed movement of animals, microorganisms and cells is of great relevance in the fields of biology and medicine. Simple diffusive models of movement assume a random walk in the position, while more realistic models include the direction of movement by assuming a random walk in the velocity. These velocity jump processes, although more realistic, are much harder to analyse and an equation that describes the underlying spatial distribution only exists in one dimension. In this communication we set up a realistic reorientation model in two dimensions, where the mean turning angle is dependent on the previous direction of movement and bias is implicitly introduced in the probability distribution for the direction of movement. This model, and the associated reorientation parameters, is based on data from experiments on swimming microorganisms. Assuming a transport equation to describe the motion of a population of random walkers using a velocity jump process, together with this realistic reorientation model, we use a moment closure method to derive and solve a system of equations for the spatial statistics. These asymptotic equations are a very good match to simulated random walks for realistic parameter values

Sampling rate effects on measurements of correlated and biased random walks

When observing the two-dimensional movement of animals or microorganisms, it is usually necessary to impose a fixed sampling rate, so that observations are made at certain fixed intervals of time and the trajectory is split into a set of discrete steps. A sampling rate that is too small will result in information about the original path and correlation being lost. If random walk models are to be used to predict movement patterns or to estimate parameters to be used in continuum models, then it is essential to be able to quantify and understand the effect of the sampling rate imposed by the observer on real trajectories. We use a velocity jump process with a realistic reorientation model to simulate correlated and biased random walks and investigate the effect of sampling rate on the observed angular deviation, apparent speed and mean turning angle. We discuss a method of estimating the values of the reorientation parameters used in the original random walk from the rediscretized data that assumes a linear relation between sampling time step and the parameter values

Uncertainty and sustainability in fisheries and benefit of marine protected areas

Over-exploitation of fisheries is a serious and immediate global problem that current management policies struggle to solve. Scientists and managers accept that new strategies based on a long-term approach are required for future fisheries management policies. But to succeed, such strategies are likely to require more than just attempts by management to control annual levels of exploitation. Recent studies show that using MPAs (marine protected areas, marine reserves) can improve yield as well as protect stocks and sustain fishery viability. In this paper, we use a deliberately simple model, which describes an exploited fishery as a nonlinear dynamical system close to a point of bifurcation; small stochastic perturbations can therefore build up to cause fishery collapse. Extending the model shows that a MPA can buffer this stochasticity and alleviate the propensity to collapse. The model illustrates two main points: (i) evaluating fisheries management strategies such as MPAs in a deterministic framework is inherently misleading; at worst it leads to fishery extinction, at best it fails to maximise yield; (ii) management strategies that are designed explicitly to buffer uncertainty in the system can provide a sustainable and productive fishery. Compared with harvest control rules based on uncertain estimates of stock size, our simulations indicate that MPAs can substantially reduce the risk of fisheries collapse for only a very small cost to total yield

Random walk models for the movement and recruitment of reef fish larvae

The factors influencing the movement and recruitment of settlement stage larvae are investigated using random walk models. Individual-based sensing and orientating abilities are included explicitly in the model. We consider 2 simple reef environment models consisting of a simple circular reef with and without a constant cross-current. The sensing ability of the larvae is modelled as either fixed or spatially dependent, together with a fixed orientating ability. The survival probability is found to be highly sensitive to both the sensing and orientating abilities of the larvae, as well as to the properties of the reef environment itself

A Composite Random Walk for Facing Environmental Uncertainty and Reduced Perceptual Capabilities

Theoretical and empirical studies in Biology have showed that strategies based on different random walks, such as: Brownian random walk and Lévy random walk are the best option when there is some degree of environmental uncertainty and there is a lack of perceptual capabilities. When a random walker has no information about where targets are located, different systematic or random searches may provide different chances to find them. However, when time consumption, energy cost and malfunction risks are determinants, an adaptive search strategy becomes necessary in order to improve the performance of the strategy. Thus, we can use a practical methodology to combine a systematic search with a random search through a biological fluctuation. We demonstrate that, in certain environments it is possible to combine a systematic search with a random search to optimally cover a given area. Besides, this work improves the search performance in comparison with pure random walks such as Brownian walk and Lévy walk. We show these theoretical results using computer simulations. © 2011 Springer-Verlag