Is the maximum-diversity-strategy efficient for the selection of breeds?

Utilisation and conservation of farm animal genetic resources 141

Chapter 6. Selection of breeds for conservation

Box 6.5. he optimum allocation of inancial funds over selected breeds for conservation. he optimal allocation approach proposed by Simianer 2002 and Simianer et al. 2003 makes the following assumptions: he inancial funds available for conservation is most eiciently used if the expected diversity at the end of the considered time horizon t e.g. t = 25 years is maximised. By investing a certain share of the available resources in breed i, the extinction probability z i of this breed will be changed to z i z i , resulting in an increase in the expected diversity at t, i.e. ED t ED t . he conservation efect ∆z i = z i - z i 0 is a function of both the extinction probability of the breed and the amount of funds invested in the conservation of this breed. his cost function ∆ z i = fz i ,b i has to be speciied. Now, let B = {b i } be a vector describing a ixed pattern of allocation of funds to a set of breeds. For each breed with b i 0, the resulting change in extinction probability can be computed using the speciied cost function, ∆ z i = fz i ,b i and a new ED t ED t can be calculated using the reduced extinction probabilities z i z i . his increase of expected diversity is the expected efect of the allocated funds. Under the assumption made above, the optimum allocation of funds can be found using the following algorithm. Divide the total fund into n b equal and small shares of money β. hen follow the iterative procedure: 1. Set b i = 0 for al breeds and start with the irst share β. 2. Compute the expected reduction of extinction probability ∆ z i for each of the breeds under the assumption that β is spent on only this breed. 3. Compute the increase in expected diversity E∆D t | z i , β = ∆z i md i for each breed, where md i is the marginal diversity of the breed. 4. Allocate this share on breed j, for which the increase of expected diversity is highest; update the extinction probability of this breed from the actual value z j by ∆z j to z j and add β to b j . 5. Recalculate marginal diversities for all breeds. 6. Allocate the next share, beginning with step 2, until all shares are allocated. Ater going through the described iterative algorithm, the vector B contains the optimal allocation of the available funding to the set of breeds in the sense that no other pattern of allocation would lead to a higher quantity of conserved diversity. One of the diiculties of this approach is the speciication of the cost function. Based on arguments from population genetics, Simianer et al. 2003 suggested three types of cost functions, which may relect the range of possible functions in typical conservation situations. he authors applied this method to 23 African zebu and zenga cattle breeds, using extinction probabilities of Reist- Marti et al. 2003 Box 6.3 and the Weitzman diversity measure chapter 5. hey found that conservation funds should be spent on only three to nine of the breeds with diferent proportions, depending on the used cost function. Highest amount of funds should be given to those breeds that show a large conservation potential. he optimum allocation approach can also be applied using the marginal utilities of the breeds paragraph 6 instead of the marginal diversities. his would allow considering ▷▷▷ 142 Utilisation and conservation of farm animal genetic resources Jörn Bennewitz, Herwin Eding, John Ruane and Henner Simianer set is formed by breeds that can be considered safe from extinction in the near future. his may encompass breeds that are currently widely used or breeds that already are or will deinitely be subject to conservation due to special traits, etc.. he diversity is estimated that is conserved by these breeds. hen the breeds not in the safe set are added one by one with re-placement to the safe set and the increase in conserved diversity of the safe set+1 is estimated. hose breeds that cause the largest increase in conserved diversity obtain higher priority in the conservation plan. he advantage of this simple approach is that no extinction probabilities need to be speciied; only the breeds for the safe set have to be chosen. his, however, can also be seen as the biggest disadvantage, since the choice of breeds for conservation is totally independent of the breed’s degree of endangerment. 6. Is the maximum-utility-strategy efficient for the selection of breeds? As mentioned in the previous section, the maximum-diversity-strategy is eicient if diversity is the only objective of a conservation plan. If, however, also other features are included sustainable use in rural areas; chapter 2 in the objective, the maximum- diversity-strategy can be straightforwardly extended to the maximum-utility-strategy, as it will be shown next. For further details, including applications, the interested reader is referred to Simianer 2002, Simianer et al. 2003 and Reist-Marti et al. 2006. hese authors also described the use of the optimum allocation scheme Box 6.5 in combination with the utility. he idea of the use of the utility was irst raised by Weitzman 1998. Let us assume that the objective of a conservation plan includes both the sustainable utilisation and the insurance arguments, the latter including neutral diversity and special traits paragraph 2. In this case the utility conserved by a set of non-extinct breeds denoted by K, as in the previous section at a deined future time horizon can be written as Simianer et al., 2003 K ¦ ¦  i B i K j F K D K i j w k w D w U , K K j K j  j K i where U K is the utility of the breed set K, w D is the relative value of a unit neutral diversity, D K is the neutral diversity of the breed set K; w F j is the relative value of feature j e.g. a special trait and j∈K denotes for feature j being present in at least one of the non-extinct breeds, i.e. present in the set K; • • • • also other features included in the conservation objective, e.g. special traits, ixed and variable cost of conservation schemes etc. See Reist-Marti et al. 2006 for an application.