Optimal use of genetic markers in conservation programmes

Monte Carlo simulations were carried out in order to study the benefits of using molecular markers to minimize the homozygosity by descent in a conservation scheme of the Iberian pig. A selection criterion is introduced: the overall expected heterozygosity of the group of selected individuals. The method to implement this criterion depends on the type of information available. In the absence of molecular information breeding animals are chosen that minimize the average group coancestry calculated from pedigree. If complete molecular information is known the average group coancestry is calculated either from markers alone or by combining pedigree and genotypes with the markers. When a limited number of markers and alleles per marker are considered, the optimal criterion is the average group coancestry based on markers. Other alternatives, such as optimal within-family selection and frequency- dependent selection, are also analysed. © Inra/Elsevier, Paris


INTRODUCTION
Molecular markers are being advocated as a powerful tool for paternity exclusion and for the identification of distinct populations that need to be conserved (1!. Here we focused on a different application, namely the use of markers to delay the loss of genetic variability in a population of limited size. In a previous paper [12] we conclude that a conventional tactic, such as the restriction of the variance of family sizes, is the most important tool for maintaining genetic variability. In this context, frequency-dependent selection seems to be a more efficient criterion than selection for heterozygosity, but an expensive strategy with respect to the number of genotyped candidates and markers is required in order to obtain substantial benefits.
For this reason, we have considered a new criterion of selection: the overall expected heterozygosity of the group of selected individuals. The implementation of this criterion depends on the type of information available, either from pedigree or from molecular markers. A new type of conventional tactics, optimal within-family selection (OWFS) recently proposed by Wang (14!, is also considered.

SIMULATION
The breeding population consisted of N, = 8 sires and N d = 24 dams. Each dam produced three progeny of each sex. These 72 offspring of each sex were candidates for selection to breeding of the next generation. This nucleus mimicked the conservation programme carried out in the Guadyerbas strain of the Iberian pig (11!. The techniques of simulation of the genome, marker loci and frequencydependent selection have been previously described (12!. Here, we introduced a new criterion, the average expected heterozygosity of the group of selected individuals, implemented by three different methods depending on the type of information available: a) average coancestry, including reciprocal and selfcoancestries, calculated from pedigree (GCP); b) average coancestry for the L n markers (GCM), which can be calculated using 1 -L LP7k, where pik is bersome even for a small nucleus. It can be solved using integer mathematical programming techniques, whose computational cost would be feasible in most practical situations but not for simulation work, where the algorithm should be used repeatedly. For this reason we used a simulated annealing algorithm [10] that, although not assuring the optimal solution, was generally shown to exhibit a very good behaviour when dealing with similar problems [5, 8!. Besides the basic situation of no restriction on the family sizes, two types of restrictions were considered: a) within-family selection (WFS) where each dam family contributes one dam and each sire family contributes one sire to the next generation; and b) optimal within-family selection (OWFS): among the N d dams mated with each sire, one is selected at random to contribute N, one son, another one to contribute two daughters and the remaining C N d J -2 B! / contribute one daughter each !14!.
The values of true genomic homozygosity by descent and inbreeding of evaluated individuals at each generation were calculated together with the expected genomic homozygosity of individuals selected from the previous generation and averaged over 100 replicates. The various situations analysed were also compared according to their rate of homozygosity per generation calculated from Ho(t) -Ho(t -1) . __ , , generation 6 to generation 15 as OHo -Ho t -Ho t -1 where Ho (t) is 1( ) ot-1 1) ) W'!'here Ho t is the average homozygosity by descent of individuals in generation. The rate of inbreeding was calculated in a similar way.

No molecular information or complete molecular information
Several cases were considered for two extreme situations: the absence of molecular information or the complete knowledge of the genome. The relative ranking of the methods was maintained for all generations and the results of generation 15 are shown in table L With no molecular information, the true homozygosity values were almost identical to those calculated from pedigrees.
Optimal within-family selection [14] was substantially (about 15 %) more efficient than classical within-family selection. The restrictions on family size distribution are unnecessary if the method of minimum average group coancestry of selected individuals (GCP) is used. The commonly accepted measure of genetic variability of a population is the expected heterozygosity [9] under the Hardy-Weinberg equilibrium (1 -EP 2 ). In the absence of molecular information the average group coancestry measures the expected homozygosity by descent [4] and therefore the best method for choosing breeding animals should minimize the average group coancestry calculated from pedigree [2][3][4]7!. If only full and half-sib relationships are considered, the criterion would lead to the optimal within-family selection method proposed by Wang !14!. When using complete molecular information for selection, the best method was still the same although now the true coancestry for all of the genome was known. In this case, the inbreeding coefficient did not reflect the true homozygosity, and the discrepancy could have been considerable. Furthermore, the rate of advance in the true homozygosity, unlike the rate of inbreeding, does not attain an asymptotic value after a short number of generations but decreases continuously.
The method of minimum average group coancestry using all the molecular information (GCM) reduced the rate of homozygosity by almost a half, although the algorithm utilized did not warrant the attainment of the optimal solutions. The impact of imposing additional restriction on family size was negligible. In a balanced structure, the minimization of average coancestry is mainly attained, as previously explained, by selecting individuals from different families.
Frequency-dependent selection, very easy to apply, can also be efficient as a conventional tactic, although not being theoretically justified and therefore lacking generality. The results of frequency-dependent selection depended on family size restrictions. Without restrictions, the results were almost as bad as when the molecular information was ignored owing to an increasing tendency to co-select sibs [12]. But, after optimal family size restrictions were imposed, the method was as good as the group coancestry method, since the differences were not significant.

Limited number of markers and alleles per marker
The relative utility of the number of markers and alleles per marker is presented in table II, where values of the true genomic homozygosity and inbreeding are given for three situations: average group coancestry criterion (GCM), used either without restriction or with optimal family size restrictions, and frequency-dependent selection with optimal family size restrictions. The cases of complete or null marker information are also presented for comparison.
As the number of markers and alleles per marker increased, the genome homozygosity attained at generation 15 decreased although it was not adequately reflected in the inbreeding coefficient. This also confirmed our previous finding [12] that the value of a marker is related to the number of alleles: two markers with ten alleles are as valuable as six markers with four alleles.
The results also indicated that the use of the method of minimum average group coancestry (or expected heterozygosity) based only on ,molecular data without family restrictions was not a good criterion even with a huge amount of molecular information. The use of this method while applying the optimal restrictions on family sizes emerged from table II as a better criterion (10 % of advantage). Our results, not shown here, also confirmed that slight improvements in the conventional tactics could have an important impact on the maintenance of genetic variability. Thus, OWFS with three markers/chromosome and four alleles/marker was as efficient as WFS with ten markers/chromosome and four alleles/marker (14.80 of genome homozygosity at generation 15 in both cases). Finally, frequency-dependent selection with optimal family restriction, which was previously analysed in more detail (12!, provided good results, and was more easy to implement. Finally, table III shows a comparison of the values for genome homozygosity when using the method of minimizing average group coancestry for markers (GCM) together with restrictions on family sizes with the theoretically optimal method of minimizing average group coancestry based on marker information (GCPM). In order to diminish the high computing cost of the analysis of pedigree involved in the last method, the genome size has been reduced to just one chromosome of 100 cM. Due to this smaller genome size, selection was more efficient and the results of the method of the average group marker coancestry with optimal restrictions were now better than those shown in table II. Results shown in table III also indicated that the method of average group coancestry based on the markers was 20-30 % more efficient. This comparison was only strictly valid for the genome size considered, but it can be safely concluded that the last method could contribute substantially to the efficiency of a markerassisted conservation programme.
Although the conclusions obtained through simulation probably have some generalities, it should be recognized that some theoretical developments on marker-assisted conservation are needed. In recent years, substantial work has been carried out on the joint prediction of inbreeding and genetic gain when selecting for a quantitative trait (see [15], for the latest development of the theory). However, predictions on the rate of advance of the true homozygosity by descent when the selected trait is the heterozygosity itself, measured either by molecular or pedigree information, is lacking.
The use of an optimal method enhances the prospectives of the application of molecular markers in conservation programmes, although the future will depend critically on DNA extraction and genotyping costs. Microsatellite DNA markers have been considered until now as the most useful markers, especially when multiplex genotyping is used, but in the near future other DNA polymorphisms such as SNP could be the most adequate for routine scoring [6]. It is also interesting to emphasize that the adequate use of molecular tools requires increasingly sophisticated methods of Monte Carlo analysis of pedigree and more powerful methods of combinatorial optimization.