Modelling the costs of fox predation and preventive measures on sheep farms in Britain

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Abstract

Economic analysis is a useful tool to aid decisions on what to do about wildlife impacts, such as those of vertebrate predators on livestock farmers. The case-study of lamb predation by foxes in Britain is used to develop a theoretical economic model, with the aim of determining a financially optimal solution to minimise the total costs of livestock predation at the farm-level. Total costs include output losses and expenditure on preventive and control measures, in this case indoor housing and lethal fox control. The model is tested empirically with data from a questionnaire survey of sheep farmers and field data on fox population densities in Britain. Regression analyses are used to determine the relationships between lamb losses and expenditure on indoor housing, fox population density and other non-management characteristics. The effect of fox abundance on the cost of fox control is also assessed. Marginal analysis is used to determine the total cost-minimising solution from the farmer's point-of-view, in terms of how many ewes should be housed indoors and for how long, as well as how many foxes should be killed in addition to any lethal control already carried out. Optimal solutions vary according to farm characteristics, including flock size and the regional location of farms. In all cases, to minimise the costs of predation, as many ewes as possible should be housed. However, it is not worthwhile housing them for more than a day after lambing. Efficient fox predation management does not necessarily mean that lamb losses should be reduced to zero, and additional fox control is not worthwhile on the majority of farms. The analysis provides a framework for future evaluations of wildlife impacts and cost-effective management of these problems.

Introduction

The decision of what to do about wildlife impacts involves the allocation of scarce resources amongst competing needs. Economic analysis is therefore a useful tool to aid such decision-making (Stenseth and Hansson, 1981; Mumford and Norton, 1984; Bicknell, 1993). To be worthwhile economically, the benefit of a damage control action should exceed its cost, i.e. the action should be cost-effective (Conway, 1981, Horskins and Wilson, 1999). The use of economic analysis for the management of arthropod and plant pests is well established (Mumford and Norton, 1984; Kropff et al., 1995, Ramirez and Saunders, 1999, Jones and Medd, 2000). However, its use in such decision-making for vertebrates has been neglected (Hone, 1994), probably because they cause less damage than invertebrate organisms (Pimentel, 1986, Van Vuren and Smallwood, 1996) and their impact is difficult to quantify.

Wild predators cause problems for farmers across the world by killing livestock. Livestock losses represent a cost to farmers, as do the measures that are used to prevent them. Therefore the cost of livestock mortality should take into account both the loss, or reduction in output, and the expenditure on extra inputs, including control and prevention costs (McInerney et al., 1992). However, total cost figures alone are of limited use in determining what management action(s) should be taken to help alleviate a wildlife or disease problem (McInerney, 1996, Perry and Randolph, 1999) and an economic analysis of predator control should consider how the marginal benefits of preventive and treatment measures compare with their costs in order to find the most efficient solution to the problem in terms of resource allocation (McInerney et al., 1992, McInerney, 1996).

One common strategy to attempt to reduce wildlife impacts is to reduce population levels. However, the success of this strategy depends on there being an association between a species' abundance and economic losses. Therefore, evaluation of such management strategies requires the specification of relationships between levels of control, species abundance and levels of damage. However, a simple relationship between abundance and damage is unlikely and rare (Hone, 1994). A number of previous studies of the associations between vertebrate predator populations, control and damage have been inconclusive (Robel et al., 1981, Landa et al., 1999), but in Australian studies, a positive association was found between feral pig densities and lamb predation (Choquenot et al., 1997) and fox control resulted in significant reductions in lamb predation by foxes (Greentree et al., 2000).

Prevention of stock predation is a major reason why red foxes (Vulpes vulpes) are deliberately culled in rural areas of Britain (Macdonald, 1984, Produce Studies, 1995, Macdonald and Johnson, 1996, Baker and Macdonald, 2000, Heydon and Reynolds, 2000). Average losses are low, but losses of individual farms can be significant. Heydon and Reynolds (2000) recorded an average of between 0.0 and 0.6% for lamb losses to foxes across the Midlands, East Anglia and Wales, but recorded losses of up to 5.2, 14.5 and 28.6%, respectively in the different regions. Moberly et al. (2003) reported a median of 0.42% of lambs killed by foxes, with a range between 0.06 and 15% (mean=1.17±0.10 s.e.).

A few studies have attempted to estimate the magnitude of the costs of lamb predation by foxes in Britain, calculating these in terms of output loss to farmers, or the market price of the animal multiplied by the number of losses, on a per farm or per region basis (Produce Studies, 1995, Burns et al., 2000, White et al., 2000a, White et al., 2000b). Macdonald and Johnson (1996), on the other hand, asked farmers directly about the total cost of foxes to them, including both lost stock and the cost of protecting against foxes. Based on these studies, White et al. (2000a) calculated that the average cost per farm of lamb losses attributed to fox predation ranged between £53 for lowland areas to £302 in upland Wales. These figures compare with a general estimate of £462 per year by Produce Studies (1995). White et al. (2000b) calculated that the maximum annual financial losses of lambs to fox predation on two farms in Scotland averaged £34 and £121. The annual losses represented between 0.2 and 1.7% of the total revenue from lamb production.

Despite these attempts to quantify the financial losses due to fox predation, there has been no assessment of the cost-effectiveness of management strategies for fox predation and there is a general lack of such studies for livestock predators. In this study, we assess the costs of fox predation on lambs in Britain and develop an economic model to determine a financially optimal solution to the problem of reducing lamb predation by foxes at the farm level. A theoretical model is proposed, which combines elements of decision theory and marginal analysis and relates the costs of predation losses to expenditure on two preventive measures: indoor housing for ewes at lambing and lethal fox control. This model is then tested empirically with data from a questionnaire survey of sheep farmers and field data on fox population densities in Britain. The aim of the analysis is not only to identify a cost-effective solution to the fox predation problem from a farmer's point of view, but also to develop a framework for potential use in the future evaluation of other wild predator control and preventive strategies.

Section snippets

Theoretical model

The profits of a sheep farm are a function of the number of lambs born and lamb losses between birth and weaning, amongst other factors (Kirby, 2000). As lamb losses are made up of predation losses to foxes and losses to other causes, it can be assumed that a sheep farmer aims to minimise lamb losses to foxes per ewe in the total lambing flock so far as is possible. However, a constraint on this is that the farmer also aims to minimise all other sheep husbandry costs, including expenditure on

Data

Data for estimation of the functions were taken from a survey of British sheep farmers and from a fox faecal count survey. In November 1999, questionnaires, with an explanatory letter and Freepost return envelope, were mailed to a random sample of 2000 members of the National Sheep Association in England, Scotland and Wales. The questionnaire included questions on farm and flock size, surrounding land uses, farm location, husbandry practices, fox control and losses of lambs to foxes between

Empirical estimation

A logit model was estimated to predict the probability of fox predation according to farm characteristics, i.e. to estimate Eq. (4). The dependent variable (x) was a binary response variable, coded zero for farms where no lamb predation by foxes occurred and one for farms where lamb predation by foxes was reported. Independent variables coding for farm characteristics and location, surrounding habitats and husbandry techniques, as well as expenditure on housing and fox population density, were

Model output

The theoretical prediction of a negative relationship between lamb losses and expenditure on preventive measures (indoor housing) was supported by the empirical analysis. Losses decline with increasing expenditure (increasing Y and D), but at a decreasing rate, due to diminishing returns to preventive effort, as predicted for livestock disease losses by the loss-expenditure model (McInerney et al., 1992, McInerney, 1996) (Fig. 1). There is a steep drop-off in lamb losses with a low amount spent

Accuracy of data and model output

The results of any statistical model based on empirical data will only be valid for the parameter space on which they were based. We targeted a large, random sample across England, Scotland and Wales, so the data forming the basis for the model should account for most of the range in values across sheep farms in those countries. Compared with the distribution of holdings with breeding ewes in the 1999 MAFF and Scottish Executive June Census, there were more responses than expected from South

Conclusions

This analysis provides a framework for evaluations of livestock predation and management of these problems. It allows for the trade-offs between different preventive measures to be modelled and indicates the best strategies for a farmer in financial terms. The logit model in its current form provides approximate figures and indications of how fox predation could be efficiently managed. However, because of the relatively low R2 value, it does not give output figures that are accurate enough to

Acknowledgements

The authors would like to thank all the sheep producers for their time and effort in providing information for the survey and staff at the National Sheep Association, Malvern, for distributing the questionnaires. We are also grateful to the volunteers who helped with bait-marking trials. Many thanks go to Jim Smart for his help and useful comments on a previous draft of this paper. This study was supported by grants from the Royal Society for the Prevention of Cruelty to Animals and the

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