A simulation-based method for model evaluation

We wish to evaluate and compare models that are non-nested and fit to data using different fitting criteria. We first estimate parameters in all models by optimizing goodness-of-fit to a dataset. Then, to assess a candidate model, we simulate a population of datasets from it and evaluate the goodness-of-fit of all the models, without re-estimating parameter values. Finally, we see whether the vector of goodness-of-fit criteria for the original data is compatible with the multivariate distribution of these criteria for the simulated datasets. By simulating from each model in turn, we determine whether any, or several, models are consistent with the data. We apply the method to compare three models, fit at different temporal resolutions to binary time series of animal behaviour data, concluding that a semi-Markov model gives a better fit than latent Gaussian and hidden Markov models.

The temporal structure of feeding behavior

Meals have long been considered relevant units of feeding behavior. Large data sets of feeding behavior of cattle, pigs, chickens, ducks, turkeys, dolphins, and rats were analyzed with the aims of 1) describing the temporal structure of feeding behavior and 2) developing appropriate methods for estimating meal criteria. Longer (between-meal) intervals were never distributed as the negative exponential assumed by traditional methods, such as log-survivorship analysis, but as a skewed Gaussian, which can be (almost) normalized by log-transformation of interval lengths. Log-transformation can also normalize frequency distributions of within-meal intervals. Meal criteria, i.e., the longest interval considered to occur within meals, can be estimated after fitting models consisting of Gaussian functions alone or of one Weibull and one or more Gaussian functions to the distribution of log-transformed interval lengths. Nonuniform data sets may require disaggregation before this can be achieved. Observations from all species were in conflict with assumptions of random behavior that underlie traditional methods for criteria estimation. Instead, the observed structure of feeding behavior is consistent with 1) a decrease in satiety associated with an increase in the probability of animals starting a meal with time since the last meal and 2) an increase in satiation associated with an increase in the probability of animals ending a meal with the amount of food already consumed. The novel methodology proposed here will avoid biased conclusions from analyses of feeding behavior associated with previous methods and, as demonstrated, can be applied across a range of species to address questions relevant to the control of food intake.

Clustering of Mycobacterium avium subsp. paratuberculosis in rabbits and the environment: how hot is a hot spot?

Clustering of pathogens in the environment leads to hot spots of diseases at local, regional, national, and international levels. Scotland contains regional hot spots of Johne's disease (caused by Mycobacterium avium subsp. paratuberculosis) in rabbits, and there is increasing evidence of a link between paratuberculosis infections in rabbits and cattle. The spatial and temporal dynamics of paratuberculosis in rabbits within a hot spot region were studied with the overall aim of determining environmental patterns of infection and thus the risk of interspecies transmission to livestock. The specific aims were to determine if prevalence of paratuberculosis in rabbits varies temporally between seasons and whether the heterogeneous spatial environmental distribution of M. avium subsp. paratuberculosis on a large scale (i.e., regional hot spots) is replicated at finer resolutions within a hot spot. The overall prevalence of M. avium subsp. paratuberculosis in rabbits was 39.7%; the temporal distribution of infection in rabbits followed a cyclical pattern, with a peak in spring of 55.4% and a low in summer of 19.4%. Spatially, M. avium subsp. paratuberculosis-infected rabbits and, thus, the risk of interspecies transmission were highly clustered in the environment. However, this is mostly due to the clustered distribution of rabbits. The patterns of M. avium subsp. paratuberculosis infection in rabbits are discussed in relation to the host's socioecology and risk to livestock.

The health of wild red and sika deer in Scotland: an analysis of key endoparasites and recommendations for monitoring disease

Monitoring the health of wildlife populations is important for understanding and controlling the risk of infections to livestock, humans and/or other wildlife. In this paper, we analyse the results of surveys of parasites and non-specific signs of diseases carried out on organs from 638 red and 107 sika deer culled in four regions of Scotland between 1991 and 1997. Infections of the lung by Elaphostrongylus spp. were significantly greater in red than sika deer. Older animals were more heavily infected with Elaphostrongylus spp. and Sarcocystis spp., and infections with Sarcocystis spp. tended to be heavier in more recent years. The results suggest that a combination of key indicator parasite species and non-specific signs of disease may be useful for monitoring the health of wildlife populations at a national scale. However, they also demonstrate that such monitoring needs to be long-term, carried out according to standard protocols and at an appropriate resolution to enable integration with data on other potentially influential environmental factors.

The importance of ‘memory’ in statistical models for animal feeding behaviour

We investigate models for animal feeding behaviour, with the aim of improving understanding of how animals organise their behaviour in the short term. We consider three classes of model: hidden Markov, latent Gaussian and semi-Markov. Each can predict the typical 'clustered' feeding behaviour that is generally observed, however they differ in the extent to which 'memory' of previous behaviour is allowed to affect future behaviour. The hidden Markov model has 'lack of memory', the current behavioural state being dependent on the previous state only. The latent Gaussian model assumes feeding/non-feeding periods to occur by the thresholding of an underlying continuous variable, thereby incorporating some 'short-term memory'. The semi-Markov model, by taking into account the duration of time spent in the previous state, can be said to incorporate 'longer-term memory'. We fit each of these models to a dataset of cow feeding behaviour. We find the semi-Markov model (longer-term memory) to have the best fit to the data and the hidden Markov model (lack of memory) the worst. We argue that in view of effects of satiety on short-term feeding behaviour of animal species in general, biologically suitable models should allow 'memory' to play a role. We conclude that our findings are equally relevant for the analysis of other types of short-term behaviour that are governed by satiety-like principles.

Risk of Disease from Wildlife Reservoirs: Badgers, Cattle, and Bovine Tuberculosis

Livestock face complex foraging options associated with optimizing nutrient intake while being able to avoid areas posing risk of parasites or disease. Areas of tall nutrient-rich swards around fecal deposits may be attractive for grazing, but might incur fitness costs from parasites. We use the example of dairy cattle and the risks of tuberculosis transmission posed to them by pastures contaminated with badger excreta to examine this trade-off. A risk may be posed either by aerosolized inhalation through investigation or by ingestion via grazing contaminated swards. We quantified the levels of investigation and grazing of 150 dairy cows at badger latrines (accumulations of feces and urine) and crossing points (urination-only sites). Grazing behavior was compared between strip-grazed and rotation-grazed fields. Strip grazing had fields subdivided for grazing periods of <24 h, whereas rotational grazing involved access to whole fields for 1 to 7 d each. A higher proportion of the herd investigated badger latrines than crossing points or controls. Cattle initially avoided swards around badger latrines but not around crossing points. Avoidance periods were shorter in strip-compared with rotation-grazing systems. In rotation-grazing management, latrines were avoided for longer times, but there were more investigative contacts than with strip-grazing management. If investigation is a major route of tuberculosis transmission, the risk to cattle is greatest in extensive rotation-grazing systems. However, if ingestion of fresh urine is the primary method of transmission, strip-grazing management may pose a greater threat. Farming systems affect the level and type of contact between livestock and wildlife excreta and thus the risks of disease.

Risk factors for Johne's disease in Scotland--the results of a survey of farmers

The reported incidence of Johne's disease has been increasing in the east of Scotland since 1993. A postal questionnaire survey was sent to 127 farms to identify potential risk factors for Johne's disease in relation to wildlife and farm management practices, and 86 returns were obtained. Of 22 farms which had been assumed to be free of the disease, on the basis of information held by local veterinary centres, seven (32 per cent) reported cases of Johne's disease in the 1990s, indicating that the disease is under-reported. Logistic regression analyses showed that eight of 63 potentially explanatory variables were significant at the 5 per cent level in affecting the likelihood of farms reporting Johne's disease. Of these, large numbers of livestock and rabbits, and access of wildlife to feed stores were the clearest and most consistent risk factors associated with the disease. The application of manure to grazing pasture, the type of water supply for the cattle and the numbers of crows were also related to the presence of Johne's disease but the nature of these relationships was less clear. Only 38 per cent of the farms reported taking any control measures to combat Johne's disease, but three of the control measures were relevant to risk factors identified as significant by the survey, namely maintaining a clean water supply, controlling rabbits and not spreading manure on to grazing pasture.

The use of mixed distribution models to determine bout criteria for analysis of animal behaviour

Feeding behaviour consists of feeding events, separated by non-feeding intervals. Feeding events are often clustered into bouts, which may be called meals. Grouping feeding events into meals requires the determination of a bout or meal criterion, that is, the longest interval accepted as part of a meal. Tolkamp & Kyriazakis (1999a) proposed a three-Gaussian model to estimate meal criteria. The three Gaussians each described the frequency distribution of the log(e)-transformed lengths of a population of intervals. These populations were thought to be: (1) short intervals within meals; (2) intervals within meals during which animals drink; (3) intervals between meals. This model predicted that the probability of an animal starting a meal would first increase, and then decrease with time since the last meal. This contrasts with expectations based on the satiety concept, which predicts that the probability of an animal starting a meal will increase with time since the last meal. This discrepancy is related to the symmetrical nature of the Gaussian distribution. Alternatively, the two-parameter Weibull distribution can take a skewed form and perhaps is more suitable to describe the different populations of intervals. In this study, models consisting of combinations of Gaussian and Weibull distributions were examined for their suitability to describe the observed feeding behaviour of cows. Weibulls did not improve the description of the populations of within-meal intervals, compared to Gaussians. However, the Weibull distribution was found to describe the between-meal population of intervals statistically better than the Gaussian. Additionally, this inclusion of a Weibull, as opposed to a Gaussian, resulted in predictions that were in better agreement with the satiety concept over the entire range of interval lengths observed. A model based on Gaussians to describe the within-meal populations of intervals and a Weibull to describe the population of between-meal intervals is, therefore, proposed. This model leads to biologically more satisfactory estimates of bout criteria than previous models and is likely to be applicable both across species and behaviours.

Satiety splits feeding behaviour into bouts

Animal behaviour is frequently displayed in bouts. Bout analysis aims at finding a bout criterion, i.e. that time between events that separates intervals within, from intervals between, bouts. Methods used for quantitative bout analysis are log-supervivorship and log-frequency analysis. Both models assume that the probability of the start of an event (or a bout) is independent of the time since the last event (or bout) and that, therefore, events as well as bouts occur according to Poisson processes, i.e. purely at random. The frequencies of intervals within, as well as between, bouts are then distributed as negative exponentials. These models are also widely applied in feeding behaviour analysis, where bouts can be meals. However, the satiety concept predicts that after terminating a meal, the animal's feeding motivation will be low. The probability of the animal initiating the next meal is expected to increase with time since the last meal and, therefore, meals will not likely be randomly distributed. A negative exponential is then not the most appropriate model to describe the frequency distribution of intervals between meals. Results of an experiment in which feeding behaviour of 16 cows was recorded continuously for 30 days were used to test the suitability of existing bout analysis techniques. It is concluded that these techniques are inadequate for the description of the observed interval distributions. A new model is proposed that takes account of the observed "shortage" of short intervals between meals. In contrast to existing models, that describe log-transformed frequency distributions of interval lengths, the proposed model describes frequency distributions of log-transformed interval lengths. Compared with existing models, this log-normal model is in better agreement with the biological phenomenon of satiety, it gave a better fit to the observed interval distribution and led to a more meaningful meal criterion.Copyright 1998 Academic Press Limited