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Bateson's Second Welfare Equation -(7.3.06)

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Bateson and Bradshaw - The Welfare Equation
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It is now widely accepted that hunting with hounds has a welfare cost.  The practicable alternative to hunting, namely stalking with high powered rifles, also has a welfare cost since not all deer are killed outright and some may escape wounded.  In assessing which culling method is more humane, it is necessary to take into account the additional numbers, of deer that would be shot if hunting were to stop altogether.  If hunting with hounds were to cease and the numbers of deer previously killed by the Hunts were instead killed with rifles (in order to maintain cull rates), under what conditions would the welfare benefits of reduced hunting be outweighed by the welfare costs of increased, shooting?  In this note we summarise the principal ways in which the question may be answered, extracting the arguments from a longer essay on welfare and conservation (Bradshaw and Bateson1999a).

When the overall welfare costs of culling before the end of hunting are the same as those afterwards, it is possible to derive a simple analytical equation {see the Box at the end of this document), the conclusion from which was originally given in the report to the National Trust (Bateson, 1997).   If all hunts resulting in a kill exceeded an acceptable welfare threshold and the welfare costs of hunting by hounds were the same as those of every gunshot wound.  Banning hunting by hounds would have a welfare benefit in all cases except those in which every stalker's shot, led to a wounding.  If wounding carries a higher welfare cost than hunting and the probability of wounding is estimated at 5%, the average welfare costs of wounding would have to be 20 times as bad as those of hunting by hounds for a ban on hunting with hounds to have no welfare benefit.  If, as seems likely, some deer escape from the hunts suffered a welfare cost, then the welfare cost of wounding would have to be correspondingly higher since the stalkers only need to shoot as many as the Hunts kill in order to maintain a stable population.

The advantage of the simple formulation used to derive these conclusions is that the numbers required to obtain an answer are already available and it is not necessary to calculate the units of welfare cost.  A wounded deer may have to suffer its state much longer than a deer that is being hunted by hounds.  It is certainly difficult to assert with any confidence just how much worse than hunting is a lingering death after the lower jaw of a deer has been shattered with a rifle bullet.  We have offered some estimates of the relative welfare costs obtained from the physiological measures of hunted deer and seriously wounded deer (Bradshaw and Bateson, 1999b,  Bateson, 1997).  This comparison suggested that the welfare costs of extended hunting and wounding are the same at the moment of assessment.  However, the time dimension is left out in such comparisons and must be considered.

If the time spent suffering by each individual deer is treated as a separate data point comparisons may then be made between the median number of suffering hours for hunted deer and stalked deer.  Clearly, the wounding rate of the stalkers would have to exceed 50% of the total shot for the median number of hours suffered to exceed zero, if we assume that a cleanly shot deer without any suffering and all those that are wounded, eventually die from their wounds.  If all deer that are hunted suffer somewhat, whether or not they escape. then the difference in suffering caused by stalking and bunting is obvious. The wounding rate by the stalkers would have to be far higher than any estimate that has been suggested so far for cessation of hunting to have no welfare benefit.
This approach bas been criticised on the intuitive grounds that many animals suffering for a
short time could be regarded as equivalent to a few animals suffering for a long time.  The quantification is difficult, however, since it does not follow that an animal that takes a long time to die from its wounds, has suffered in the same way throughout that period. Moreover, one animal suffering for 21 days from a shattered jaw before it died from starvation would distort the picture for the population as a whole, particularly if the great majority experienced no suffering at all when they were culled.  Unfortunately, we do not know with any degree of certainty the frequency of such occurrences.  Such evidence as is available suggests that severe wounding leading to protracted deaths are very infrequent.  Nor do we know the duration of suffering of any wounded deer.  The uncertainty of knowledge also applies to the hurting side of the equation.  One hunted animal that incurred severe muscle damage before escaping might experience a sharp reduction in its welfare for days and might eventually die.  So might an animal that was totally depleted of carbohydrate after being hunted all day in winter:  Any severely stressed animal might also have a suppression of its immune system, increasing its vulnerability to disease.  In the US study of White-tailed deer some animals died as much as 26 days after they were rocket netted and marked (Beringer, 1996).  Death might result from a multiple cascade of events following stress shock or over-heating.  Red deer may well overheat as a result of being chased.  Nobody knows how often, they die after escape from a hunt, but absence of evidence is not the same as evidence or absence.

Even if some guesses are made for the values of the missing data, a further difference between stalking and hunting must be taken into account.  Stalkers are advised to kill calves running with their mothers because of the danger that the calves will be alienated from the herd and die of starvation.  The staIker’s commonly accept this advice.  The Hunts rarely kill calves accompanying hinds. Some estimate of the differences in suffering involved here ought to be included, though the guess-work here is as great as in all other aspects of the general approach.
Faced with the difficulty of obtaining reliable empirical evidence, judgements about the welfare balance arrived at on the basis of the total numbers of suffering hours are liable to be made on the basis of a few anecdotes and are bound to be extremely unreliable.  One  animal wounded in the jaw and taking 21 days to die swings the conclusion massively in one direction. Two animals taking the same amount of time to die from the ill effects of hunting swings it in the opposite direction.  The exercise seems pointless.

If the simple welfare equation which we originally proposed is not used, precision may never be given to calculations of the frequency and duration of welfare costs arising from the various methods of culling.  If so, a decision to ban hunting hinges on a qualitative assessment that, leaving aside a few rogue cases, the welfare costs of hunting are greater
than those of stalking.  Alternatively, it hinges on a straight moral judgement.  It is relevant
in this context that the central cost of cruelty in much of the legislation concerning the welfare of domestic and wild animals rests on the notion of humans causing unnecessary  suffering, and further, that the regulations governing the treatment of domestic animals stipulate that animals should not be subjected to “any avoidable suffering” (Radford, 1996).

If it is widely accepted that hunting with hounds inevitably causes suffering, as now seems to be the case,  then anybody who hunts does so in the knowledge that  they cause suffering.  By contrast. a stalker shoots an animal in the expectation that death will be instantaneous.  If the animal is wounded by a shot, that is a mistake; it was never the: stalker's intention to wound.  This is perhaps the most marked moral distinction that may be made between the two methods of culling.  The difference is accentuated because hunting with hounds is regarded as better sport when the chase is long, whereas stalkers will strive to improve their technique in order to minimise the risk of wounding.  The suffering of hunted deer is in the context of culling both unnecessary and avoidable, given that a more efficient culling methods exist.

This last point may be more compelling to independent people than any further attempt to formalise the welfare equation. However, the central issues in the stag-hunting debate that relate to animal welfare and conservation remain to be addressed.  The preceding discussion was based on the assumption that the majority of culling will be carried out by competent marksmen using high velocity rifles.  What happens if an increase in shooting deer,  resulting from a cessation of hunting with hounds, entailed an increase in the use of shotguns, or greater activity on the part of incompetent marksmen?  In general, these are problems that need to be addressed both by changes in the legislation governing the type of weapon used to shoot, red deer (The Deer Act 1991) and the requirements, placed upon
those who carry out the shooting (The Firearms (Amendment) Act 1991).  A system of issuing tags for carcasses. such as already used in France and, at the time of writing is proposed for Scotland. would inhibit the activities of illegal poachers, and serve to regulate the numbers of animals culled each year.  If crop damage is one of the main concerns then,  compensation schemes are required.  Such changes in legislation have long term implications for improving welfare, but will not prevent short term conservation problems relating to local populations.


Bateson, P. (1997) The behavioural and physiological effects of culling red deer. London:
The National Trust.
Beringer J., Hansen, L.P., Wilding, W.,  Fischer. J. & Sheriff,  S.L (1996)  Factors
affecting capture myopathy in white-tailed deer.  Journal of Wildlife Management,  60. 373-380.
Bradshaw, E. L. & Bateson. P. (l999a), Animal welfare and wildlife conservation. In Behaviour and Conservation, ed.,  L. M. GoslIng and W. ], Sutherland, . Cambridge: Cambridge University Press.
Bradshaw E. L. & Bateson. P. (l999b) Welfare Implications of culIing red deer (Cervus elaphus), Animal Welfare, submitted.
Radford. M. (1996) Partial protection: animal welfare and the law.  In Animal rights; the changing debate., ed., R. Garner pp. 67-91. Basingstoke:MacMillan Press.

A simple analytical equation.

The annual welfare costs of culling red deer before a cessation on hunting with hounds may be formalised as follows:

Tb = Wh.Ph.Nh + Ws.Pb.Ns
Tb = total annual welfare cost before cessation.
Wh = average welfare cost to chose deer that suffer unacceptable welfare cost when hunted with hounds
Ph = probability of hunting leading to unacceptable welfare cost
Nh = total number of deer killed per year with hounds
Ws = average welfare cost to each wounded animal.
Pb = probability of being wounded by stalking.
Ns = total; number of deer shot per year

Ta = Ws.Pb (Nh+Ns) where:
Ta = total annual welfare cost after cessation.
Pa =.probability of being wounded by shooting.

In this simple case, it is assumed that no deer escaping from a hunt suffers a welfare
cost and every deer that is wounded by shooting. eventually dies from its wounds.
When the total culling rate is constant, cessation of hunting by hounds, has no effect on
the total welfare cost at the point f indifference..(i.e. Tb = Ta).

Wh.Ph.Nh + Ws.Pb.Ns  = Ws.Pb. (Nh = Ns).
Dividing through by Ws.Pa.
Wh.Ph.Nh/Ws.Pa + Pb.Ns/Pa = Nh + Ns

If the proportion wounded by stalking is unchanged by cessation of hunting, then let:

Pb + Pa +Ps

This then simplifies the equation:
Wh.Ph.Nh/Ws.Ps = Nh
Dividing through by Nh and rearranging the equation:
Ps/Ph = Wh/Ws

This is at the point of indifference where no change in deer welfare occurs after a hunting with hounds ban.   If every hunt that leads to a kill is deemed to involve a welfare cost then a cessation of hunting with hounds would be beneficial when:

Ps < Wh/Ws

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