Neil J. Walker

Zero-Truncated and Zero-Inflated Models for Count Data

In this chapter, we discuss models for zero-truncated and zero-inflated count data. Zero truncated means the response variable cannot have a value of 0. A typical example from the medical literature is the duration patients are in hospital. For ecological data, think of response variables like the time a whale is at the surface before re-submerging, counts of fin rays on fish (e.g. used for stock identification), dolphin group size, age of an animal in years or months, or the number of days that carcasses of road-killed animals (amphibians, owls, birds, snakes, carnivores, small mammals, etc.) remain on the road. These are all examples for which the response variable cannot take a value of 0.

Culling-induced social perturbation in Eurasian badgers Meles meles and the management of TB in cattle: an analysis of a critical problem in applied ecology.

The Eurasian badger (Meles meles) is implicated in the transmission of bovine tuberculosis (TB) to cattle in the UK and Republic of Ireland. Badger culling has been employed for the control of TB in cattle in both countries, with varying results. Social perturbation of badger populations following culling has been proposed as an explanation for the failure of culling to consistently demonstrate significant reductions in cattle TB. Field studies indicate that culling badgers may result in increased immigration into culled areas, disruption of territoriality, increased ranging and mixing between social groups. Our analysis shows that some measures of sociality may remain significantly disrupted for up to 8 years after culling. This may have epidemiological consequences because previous research has shown that even in a relatively undisturbed badger population, movements between groups are associated with increases in the incidence of Mycobacterium bovis infection. This is consistent with the results from a large-scale field trial, which demonstrated decreased benefits of culling at the edges of culled areas, and an increase in herd breakdown rates in neighbouring cattle.

Bacillus Calmette-Guérin vaccination reduces the severity and progression of tuberculosis in badgers

Control of bovine tuberculosis (TB) in cattle has proven particularly challenging where reservoirs of infection exist in wildlife populations. In Britain and Ireland, control is hampered by a reservoir of infection in Eurasian badgers (Meles meles). Badger culling has positive and negative effects on bovine TB in cattle and is difficult, costly and controversial. Here we show that Bacillus Calmette-Guérin (BCG) vaccination of captive badgers reduced the progression, severity and excretion of Mycobacterium bovis infection after experimental challenge. In a clinical field study, BCG vaccination of free-living badgers reduced the incidence of positive serological test results by 73.8 per cent. In common with other species, BCG did not appear to prevent infection of badgers subjected to experimental challenge, but did significantly reduce the overall disease burden. BCG vaccination of badgers could comprise an important component of a comprehensive programme of measures to control bovine TB in cattle.

Mixed Effects Modelling for Nested Data

In this chapter, we continue with Gaussian linear and additive mixed modelling methods and discuss their application on nested data. Nested data is also referred to as hierarchical data or multilevel data in other scientific fields (Snijders and Boskers, 1999; Raudenbush and Bryk, 2002).

Experimental evidence of competitive release in sympatric carnivores

Changes in the relative abundance of sympatric carnivores can have far-reaching ecological consequences, including the precipitation of trophic cascades and species declines. While such observations are compelling, experimental evaluations of interactions among carnivores remain scarce and are both logistically and ethically challenging. Carnivores are nonetheless a particular focus of management practices owing to their roles as predators of livestock and as vectors and reservoirs of zoonotic diseases. Here, we provide evidence from a replicated and controlled experiment that culling Eurasian badgers Meles meles for disease control was associated with increases in red fox Vulpes vulpes densities of 1.6–2.3 foxes km−2. This unique experiment demonstrates the importance of intraguild relations in determining species abundance and of assessing the wider consequences of intervention in predator populations.

Diagnostic Accuracy and Optimal Use of Three Tests for Tuberculosis in Live Badgers

Background Accurate diagnosis of tuberculosis (TB) due to infection with Mycobacterium bovis is notoriously difficult in live animals, yet important if we are to understand the epidemiology of TB and devise effective strategies to limit its spread. Currently available tests for diagnosing TB in live Eurasian badgers (Meles meles) remain unvalidated against a reliable gold standard. The aim of the present study was to evaluate the diagnostic accuracy and optimal use of three tests for TB in badgers in the absence of a gold standard. Methodology/Principal Findings A Bayesian approach was used to evaluate the diagnostic accuracy and optimal use of mycobacterial culture, gamma-interferon assay and a commercially available serological test using multiple samples collected from 305 live wild badgers. Although no single test was judged to be sufficiently sensitive and specific to be used as a sole diagnostic method, selective combined use of the three tests allowed guidelines to be formulated that allow a diagnosis to be made for individual animals with an estimated overall accuracy of 93% (range: 75% to 97%). Employing this approach in the study population of badgers resulted in approximately 13 out of 14 animals having their true infection status correctly classified from samples collected on a single capture. Conclusions/Significance This method of interpretation represents a marked improvement on the current procedure for diagnosing M. bovis infection in live badgers. The results should be of use to inform future test and intervention strategies with the aim of reducing the incidence of TB in free-living wild badger populations.

Long-term temporal trends and estimated transmission rates for Mycobacterium bovis infection in an undisturbed high-density badger (Meles meles) population.

We describe epidemiological trends in Mycobacterium bovis infection in an undisturbed wild badger (Meles meles) population. Data were derived from the capture, clinical sampling and serological testing of 1803 badgers over 9945 capture events spanning 24 years. Incidence and prevalence increased over time, exhibiting no simple relationship with host density. Potential explanations are presented for a marked increase in the frequency of positive serological test results. Transmission rates (R0) estimated from empirical data were consistent with modelled estimates and robust to changes in test sensitivity and the spatial extent of the population at risk. The risk of a positive culture or serological test result increased with badger age, and varied seasonally. Evidence consistent with progressive disease was found in cubs. This study demonstrates the value of long-term data and the repeated application of imperfect diagnostic tests as indices of infection to reveal epidemiological trends in M. bovis infection in badgers.

Effectiveness of Biosecurity Measures in Preventing Badger Visits to Farm Buildings

Background Bovine tuberculosis caused by Mycobacterium bovis is a serious and economically important disease of cattle. Badgers have been implicated in the transmission and maintenance of the disease in the UK since the 1970s. Recent studies have provided substantial evidence of widespread and frequent visits by badgers to farm buildings during which there is the potential for close direct contact with cattle and contamination of cattle feed. Methodology Here we evaluated the effectiveness of simple exclusion measures in improving farm biosecurity and preventing badger visits to farm buildings. In the first phase of the study, 32 farms were surveyed using motion-triggered infrared cameras on potential entrances to farm buildings to determine the background level of badger visits experienced by each farm. In the second phase, they were divided into four treatment groups; “Control”, “Feed Storage”, “Cattle Housing” and “Both”, whereby no exclusion measures were installed, exclusion measures were installed on feed storage areas only, cattle housing only or both feed storage and cattle housing, respectively. Badger exclusion measures included sheet metal gates, adjustable metal panels for gates, sheet metal fencing, feed bins and electric fencing. Cameras were deployed for at least 365 nights in each phase on each farm. Results Badger visits to farm buildings occurred on 19 of the 32 farms in phase one. In phase two, the simple exclusion measures were 100% effective in preventing badger entry into farm buildings, as long as they were appropriately deployed. Furthermore, the installation of exclusion measures also reduced the level of badger visits to the rest of the farmyard. The findings of the present study clearly demonstrate how relatively simple practical measures can substantially reduce the likelihood of badger visits to buildings and reduce some of the potential for contact and disease transmission between badgers and cattle.

Limitations of Linear Regression Applied on Ecological Data

This chapter revises the basic concepts of linear regression, shows how to apply linear regression in R, discusses model validation, and outlines the limitations of linear regression when applied to ecological data. Later chapters present methods to overcome some of these limitations; but as always before doing any complicated statistical analyses, we begin with a detailed data exploration. The key concepts to consider at this stage are outliers, collinearity, and the type of relationships between the variables. Failure to apply this initial data exploration may result in an inappropriate analysis forcing you to reanalyse your data and rewrite your paper, thesis, or report.

GLM and GAM for Count Data

A generalised linear model (GLM) or a generalised additive model (GAM) consists of three steps: (i) the distribution of the response variable, (ii) the specification of the systematic component in terms of explanatory variables, and (iii) the link between the mean of the response variable and the systematic part. In Chapter 8, we discussed several different distributions for the response variable: Normal, Poisson, negative binomial, geometric, gamma, Bernoulli, and binomial distributions. One of these distributions can be used for the first step mentioned above. In fact, later in Chapter 11, we see how you can also use a mixture of two distributions for the response variable; but in this chapter, we only work with one distribution at a time.