M. Soller1
INTRODUCTION AND SUMMARY
The native cattle of West Africa, particularly the N'Dama and Baoule breeds possess a remarkable degree of genetic resistance to tsetse-fly transmitted trypanosomiasis. They live and produce profitably in areas in which all other cattle die. This quality makes possible the development of a cattle industry in areas of the humid tropics where grazing is at its best, but where cattle raising has been prevented by the presence of the tsetse fly.
Recent developments in molecular genetics have made available new classes of highly informative genetic markers. These provide the ability to carry out a detailed genetic analysis of almost any inherited genetic trait, identify and map its genetic components and exploit them efficiently in a variety of breeding programs. The aim of the trypanotolerance mapping program is to use these markers and techniques in order to map the genetic loci conferring trypanotolerance. Mapping of trypanotolerance loci is seen as a key step in the development of improved trypanotolerant cattle. It will enable a variety of introgression programs to be carried out that will increase the productivity of the trypanotolerant breeds and allow rapid introgression of trypanotolerance to other breeds.
In this review we will present the evidence for the genetic basis of trypanotolerance, and the rationale and methodology of a trypanotolerance mapping program. Methodologies will be presented first in a general manner, and then with specific application to mapping of trypanotolerance loci. An appendix giving calculations of experimental numbers required for trypanotolerance mapping is also included.
A. TRYPANOTOLERANCE
A.1 The trypanotolerant breeds of West Africa
Numerous studies have shown that many of the West African taurine breeds of cattle are able to survive, maintain body weight, conceive, carry, deliver and suckle a calf without the aid of chemotherapy in areas of tsetse challenge, where the Zebu cannot (reviewed in Murray et al., 1982; Roelants and Pinder, 1984; Roelants, 1986). These animals do become infected with trypanosomes and do respond immunologically, but are characterized by reduced susceptibility to the debilitating effects of the disease. Such animals are said to be “trypanotolerant”.
At present the two major trypanotolerant cattle breeds are the West African Longhorn, (N'Dama) and West African Shorthorn (Baoule). In addition there are indications that some East African Zebu stocks may also exhibit a degree of trypanotolerance (references in Murray et al., 1982). Of these, the N'Dama appears to have the most fully developed degree of trypanotolerance. They are extremely harder animals, also resistant to streptothricosis (of importance in humid areas, Oduye and Okunaiya, 1971). The N'Dama are also the most numerous of the trypanotolerant types. Thus, the N'Dama would seem to be the preferred trypanotolerant type for further genetic analysis.
The superior trypanosomiasis resistance of the N'Dama as compared to the Zebu is expressed by marked differences in weight loss, anemia, survival and productivity following challenge. The superior N'Dama resistance was found regardless of the nature of the challenge, and regardless of whether or not the animals had been previously exposed to trypanosomes. In a three-way comparison of West African Shorthorn, N'Dama and Zebu, the West African Shorthorn were found to be intermediate between N'Dama and Zebu, as judged by clinical condition, anemia and survival (Roberts and Gray, 1973). The trypanotolerance status of the various breeds appears to stand in rough proportion to their historical exposure to trypanosomiasis: The Longhorn ancestors of the N'Dama arrived in Egypt about 5000 BC, the Shorthorn were first introduced into the area about 2500 BC, while it was not until after the Arab invasion (669 AD) that appreciable numbers of Zebu reached Africa (Murray et al., 1982).
A.2 Genetics of trypanotolerance
From reports in the literature and field impressions it is possible to define a graded series of breeds showing increasing degrees of trypanotolerance, as follows: the hypersusceptible Ayrshire < West African Zebu < East African Zebu <West African Shorthorn (Baoule) < West African Longhorn (N'Dama). Furthermore, even the N'Dama does not approach the degree of trypanotolerance found in some of the wild ruminant species (e.g., buffalo). All of this tends to suggest that the trypanotolerance of the most resistant bovine (N'Dama) may be a function of the cumulative action of a number of trypanotolerance loci, i.e., that the trypanotolerance of the N'Dama may have a polygenic basis. However, definitive studies of the total number of loci involved in trypanotolerance have not as yet been carried out in cattle. In mice, between-strain differences in susceptibility to trypanosomes have been found to depend on one or two genetic loci (Murray et al., 1982). None of the mouse strains studied, however, approaches the degree of broad general trypanotolerance found in the N'Dama, and here too, attempts have not been made to determine whether resistance loci of different strains are allelic or complementary, and whether they can be combined together to produce super-tolerant strains.
B. RATIONALE OF THE TRYPANOTOLERANCE MAPPING PROGRAM
It has been found that wherever the Zebu can be raised it will tend to displace the N'Dama or Baoule (Murray et al., 1982). This was initially attributed to the small size of the trypanotolerant breeds as compared to the Zebu. However, studies summarized by ILCA (ILCA/FAO/UNEP, 1979) show that the trypanotolerant cattle are as productive as the Zebu, even under conditions of zero trypanosomiasis risk, and are clearly superior in productivity under conditions of moderate trypanosomiasis risk. The preference of the herder for the larger Zebu cattle under conditions of zero trypanosomiasis risk is probably due to its greater suitability for draught purposes. The Zebu may also be preferred for its greater milk production and well developed herding instinct - the N'Dama tend to disperse on pasture. There is, therefore, interest in developing trypanotolerant types having higher milk production, and other types characterized by larger body size for use as draught animals or for crossing with smaller dams in order to increase calf growth-rate.
Generally, two different approaches can be taken in order to achieve specific livestock improvement objectives. These are: (i) within population selection and (ii) introgression of useful alleles from one breed to another. A priori, both approaches come into consideration as potential routes for improvement of productivity and trypanotolerance in the N'Dama. Introgression alone, however, would appear to be the only feasible means of introducing the trypanotolerance trait into other breeds of livestock.
B.1. Selection within livestock populations
Because of the interbreeding enforced by the nature of their mating system, animal populations generally contain a greater or lesser degree of genetic variation with respect to most traits of economic importance. When genetic variation is present it will generally be possible to design genetic improvement programs based on well proven techniques for within-population selection (Pirchner, 1983). Progress provided by these approaches, however, is relatively slow. At best, programs based on within-population selection in cattle, can be expected to increase milk production at a rate of 1% a year, and growth-rate at the rate of 2% a year. Improvement in practice generally falls far short of these theoretical estimates. In addition, simultaneous selection for two or more traits will decrease genetic progress with respect to any single trait.
B.2 Crossing and introgression
As an alternative to within-population selection with respect to traits such as growth-rate or milk production, one could cross an unimproved, but adapted, native breed such as the N'Dama to European or other breeds that have already been improved with respect to productivity traits, and attempt to select from the segregating intercross-population individuals combining the superior adaptive qualities of the native cattle with the productive qualities of the improved cattle. In practice, the polygenic-quantitative nature of the traits under consideration, their generally low to moderate heritability, and the technical problem of maintaining sufficient adaptive challenge to allow selection for adaptative traits without severe confounding of productivity traits - all the while maintaining a high level of reproduction to allow for adequate selection intensity and short generation interval - render this an extremely difficult and long range approach. Consequently, crossing and introgression have not found useful application in the past, as a means of genetic improvement of animal populations with respect to polygenic traits of economic importance.
B.3 Marker-assisted selection
Recent studies in a wide variety of eukaryote species show that they contain an enormous amount of genetic polymorphism at the DNA level. This polymorphism can serve as a source of molecular markers saturating the genome. The use of molecular genetic markers to assist the breeding process, can allow otherwise inaccessible breeding goals to be achieved in a cost-effective manner and in a reasonably small number of generations. Molecular genetic markers can do this (i) by allowing a detailed genetic map to be generated identifying chromosomal regions having significant effects on traits of interest and (ii) by providing breed specific markers for these chromosomal regions, enabling them to be manipulated efficiently in breeding programs (Soller, 1990; Soller and Beckmann, 1983, 1986, 1988, 1989; Beckmann and Soller, 1983, 1977, 1988). In this way relevant chromosomal regions can first be identified and then, over a small number of generations, combined in a single population or introgressed from one breed to another, by means of repeated intercrosses or backcrosses coupled with selection for the markers characterizing useful chromosomal regions.
A program of this sort would appear to be eminently suitable for genetic analysis and breeding manipulation of trypanotolerance. The genetic aim of such a program would be mapping the loci responsible for the trypanotolerance of the N'Dama. The ultimate breeding aims of the program would be: introducing trypanotolerance to other breeds of livestock; improving economic qualities of the N'Dama by introgression from other more productive breeds without loosing the trypanotolerance trait; and strengthening the trypanotolerance trait in the N'Dama itself by introducing additional trypanotolerance alleles from other trypanotolerant breeds (e.g., Baoule).
Identification and mapping of individual loci contributing to trypanotolerance can also be expected to facilitate the physiological analysis of the trait, by isolating its biological components for individual study. A better understanding of the physiological responses involved in trypanotolerance may have direct relevance to treatment and prevention of trypanosomiasis in cattle, other livestock species and even in man. The availability of information as to the location of trypanotolerance loci in the bovine genome will facilitate the exploration of trypanotolerance loci in other livestock species. Mapping of trypanotolerance loci will also be a first step in their cloning and manipulation through genetic engineering techniques. This could eventually allow rapid transfer of the trypanotolerance trait to other breeds of cattle or even to other species of livestock and would also allow the degree of trypanotolerance in the trypanotolerant breeds themselves to be increased through modification of gene control regions or increase in gene copy number.
All approaches to mapping and identification of individual loci affecting quantitative traits - i.e., traits having a polygenic genetic architecture and subject to environmental sources of variation, depend on linkage disequilibrium between genetic variation at genetic markers and genetic variation at the loci affecting the trait. That is, at specific associations between particular alleles at the polymorphic genetic marker system, and specific positive or negative alleles at the polygenic locus (henceforth termed “Quantitative Trait Locus”, QTL). This association is then detected as a quantitative effect on the trait in question associated with marker genotype. Thus, in devising a program for mapping and identifying the genetic loci contributing to trypanotolerance the two basic factors which must be considered, are: (1) The population and markers investigated for presence of disequilibrium, and (2) The mode of analysis of the data to provide maximum power for detection of association between trait value and marker genotype. In addition, since marker-QTL analysis requires both genotyping of animals with respect to the markers and phenotyping of the animals with respect to the trait of interest, one must also consider (3) The optimum allocation of resources between genotyping and phenotyping. Finally, will come (4) Steps toward reverse genetics: fine mapping, identification and cloning of the QTL
Since the identical reasoning applies to each and every marker locus investigated, the same populations can be used to investigate all marked chromosomal regions. This means that given sufficient markers, appropriately spaced along the genome, a single population will enable the total genome to be mapped for QTL, allowing all chromosomal regions carrying QTL affecting the trait to be identified.
Further consideration will show that the same argument can also be applied to all traits of interest. All that is required is a condition of disequilibrium between marker loci and QTL affecting the trait.
In this review we will first consider the above aspects in a general way, and then with regard to their specific application to loci affecting trypanotolerance.
C. GENERAL ASPECTS OF MAPPING QTL
C.1. Experimental design: populations and markers
Specific designs differ in the type of population within which disequilibrium is sought, and in the relation of the genetic markers used to the trait of interest. There is a fairly close correlation between the two aspects, however, so that choosing a particular population generally implies a particular category of marker, while, conversely, choosing a particular category of marker, generally implies a particular population.
C.1.1 The type of population within which disequilibrium is sought.
Disequilibrium can be sought within three types of populations: population-wide disequilibrium within a large random-mating population; disequilibrium within individual halfsib or full-sib families; and disequilibrium within populations that have recently undergone an episode of wide hybridization, i.e., F-2, F-3 or BC (backcross) populations. These various approaches will differ as to the extent of disequilibrium found, and particularly on the degree to which disequilibrium degenerates as a function of the map distance between the loci involved.
C.1.1.1 Population-wide disequilibrium
Linkage disequilibrium can be generated at a population-wide basis as the result of a number of factors. These include: genetic drift, which will be a function of effective population size, and number of generations that the population has been closed; hybridization (or in-migration) episodes in the past history of the population; and selection (Lande and Thompson, 1990)
C.1.1.1.1 Genetic drift
A number of theoretical studies and simulations show that for populations with relatively small effective population numbers, marked linkage disequilibrium can be generated over a small number of generations between closely linked loci (generally less than 1 cM - centiMorgan - apart).
C.1.1.1.2 Hybridization episodes
The effect of a hybridization or in-migration episode will clearly depend on the difference in allele frequencies at marker and QTL of the populations mixed, on the number of such episodes and the number of generations that have passed since the episodes. Immediately following the hybridization episode, disequilibrium will be found over relatively wide chromosomal regions, but can be expected to decrease rapidly except for closely linked markers. Nevertheless, overall disequilibrium as a result of a hybridization episode can be expected to extend over wider regions than would be achieved by drift alone.
C.1.1.1.3 Selection
Selection at a QTL will increase the frequency of the marker haplotypes specifically associated with the favorable QTL allele. Thus, depending on the initial degree of disequilibrium between marker alleles and QTL a marked degree of disequilibrium can be generated in the population through selection. This will be particularly true when a new positive allele appears at a QTL and is swept up by selection. In this case, the specific marker haplotype within which the new positive allele is embedded can reach high frequencies. Because increase in haplotype frequency can be rapid, the extent of the chromosomal region over which appreciable disequilibrium extends will be rather large, although exact simulations, are not yet available.
In any actual population study, one or more of these mechanisms can be operating to produce disequilibrium at any particular QTL. Thus, there appears to be a reasonable likelihood that a search for linkage disequilibrium between marker loci and QTL can be effective, once marker loci within close range of the QTL are located - offhand I would venture that one would want to be within 1–2 cM of the locus of interest if drift is the major factor, while up to 5 cM might yield interesting disequilibrium if hybridization or mutation/selection have been at play.
C.1.1.2 Disequilibrium within half-sib families
For any linked marker and QTL locus, each individual chromosome represents a specific coupling association between an allele at the marker locus and an allele at the QTL. Thus, to the extent that the two parental chromosomes of a sire represent alternative haplotypes for the marker/QTL linkage association (e.g., MA/ma, where M and m are alleles at the marker locus and A and a are alleles at the QTL), the offspring population will be in strong linkage disequilibrium, with some offspring carrying the MA haplotype from the sire, other the ma haplotype, and others, of course, carrying recombinant haplotypes. Thus, within half-sib families there will be strong linkage disequilibrium between marker alleles and QTL alleles. Experimental designs and analyses for marker/QTL linkage determination based on this principle have been described and implemented extensively (Neimann-Sorensen and Robertson, 1961; Soller an Genizi, 1978; Geldermann, 1975; Soller and Beckmann, 1982, 1983; Weller et al., 1990; Beever et al., 1990; Gonyon et al., 1987; Haenlein et al., 1987; Geldermann et al., 1985). Linkage studies based on this principle can provide good to reasonable power over marker-QTL distances of 10–20 cM.
In many situations, of course, large half-sib families are not available. For such cases, a more general statistic, termed the “relative-pair” analysis, has been developed (Amos and Elston, 1989). In this approach, a particular marker locus is considered in a relative pair (e.g., two full sibs, uncle and nephew etc.). The basic intuition is that if the two marker alleles in both of the relatives are identical by descent from their common ancestors, then any linked QTL will be identical as well. In this case the QTL will not contribute to between pair variance. Conversely, if the two alleles at the marker locus are of different descent in the two relatives, then they may be associated with different alleles at the linked QTL. In this case the QTL will contribute to the between pair variance. Thus, marker/QTL linkage will be detected as a difference in between pair variance in the two cases. This method is of broad generally for use in nuclear family situations, but has very low power unless the QTL effect or number of relative pairs examined, is large.
C.1.1.3 Disequilibrium within immediate descendants of a wide hybridization (F-2, F-3 or BC populations).
Two designs are appropriate here (i) Parent lines differ widely in gene frequencies at marker loci and at QTL, and (ii) Parent line gene frequencies differ widely at the QTL but are similar at the marker loci. Both of these designs can prove good to reasonable power at marker/QTL distances of 10–20 cM.
The choice as to F-1 or BC populations will depend on a number of factors. F-2 populations will have greater power for co-dominant QTL, and are more robust in the face of different degrees and direction of dominance at different QTL. Technically F-2 populations are more difficult to produce, since they require large numbers of F-1 females or utilization of MOETS procedures. BC populations will have greater power for traits exhibiting directional dominance, when the backcross is to the recessive parent, but less power for co-dominant traits, and zero power when the backcross is to the dominant parent. When dominance relationships are appropriate, a BC generation is technically simpler to produce than an F-2, since this requires only a few F-1 males crossed to the predominant females at the experimental location: either of the parental breeds, or even females of some third, non-parental breed.
C.1.1.3.1 Parent lines differ widely at marker loci and at QTL.
The simplest situations of this sort are the F-2 or BC progeny of a cross between lines homozygous for alternative alleles at the marker loci and QTL, i.e., a cross between two lines having the alternative genotypes MA/MA and ma/ma (Soller et al., 1976; Soller and Beckmann, 1986). In this case, except for recombination, the M marker allele in the F-2 produced by crossing these two lines will be in coupling with the A allele, and the m marker allele will be in coupling with the a allele. Alleles at all other QTL differentiating the two breeds will tend to be distributed equally between individuals receiving the M as compared to the m allele at the marker locus. Thus, a comparison of the mean phenotypic value of MM and mm genotypes in the F-2 population should reflect only the quantitative effect of the Aa genotype as compared to the aa genotype.
It should be noted that the observed mean difference between marker genotypes, due to linked QTL, will depend not only on the actual effect of the alleles at the QTL, but also on the degree of recombination between marker locus and QTL - the greater the degree of recombination, the smaller the marker-associated effect (Soller et al., 1976). Thus, the observed marker-associated effects will underestimate the actual quantitative effects of the linked QTL to a greater or lesser extent. Methods for estimating map distance between marker loci and QTL and full effect of the QTL are available (Weller, 1986, 1987; Lander and Botstein, 1989; Knapp et al., 1990; Jensen, 1989).
C.1.1.3.2 Parent lines differ at the QTL, but not at the marker loci
In some instances, two breeds will be close to fixation for alternative alleles at the loci affecting the trait of interest (i.e., at the QTL), but are polymorphic for the same alleles at the marker locus. A simple comparison of quantitative trait value of marker genotypes in the F-2 or BC populations derived from a cross between these two breeds will then have little statistical power (Soller et al., 1976). In this case, it is possible, by considering the marker genotype of the offspring of each particular mating, in relation to the marker genotype of the specific F-1 parents and parental generation grandparents of each F-2 or BC individual, to identify the parental origin of particular marker alleles in the F-2 or BC progeny (Beckmann and Soller, 1988; Mackinnon and Soller, 1991). Quantitative trait value of progeny marker genotypes assigned in this way to specific parental breeds, can be informative for marker/QTL linkage analyses. For the usual diallelic markers, this applies to parental pairs which are homozygous for alternative forms of the marker alleles, and whose F-1 offspring mated with an F-1 derived from a similar mating. This will occur in only a small proportion of random matings, when allelic frequencies in the two populations are similar. The proportion of informative progeny increases rapidly, however, as the frequencies of the two alternative marker alleles differ in the two populations -reaching a maximum for complete homozygosity for alternative alleles (Beckmann and Soller, 1988; Mackinnon and soller, 1991). Also, when polyallelic markers are used the proportion of informative matings and offspring rises rapidly with number of alleles, even when allelic frequencies do not differ between populations crossed. For example, when four alleles are present, even if each is found in equal frequencies in the two populations, almost three-fourths of all random matings will produce informative offspring (Beckmann and Soller, 1988; Mackinnon and Soller, 1991). In some instances a group of closely linked diallelic markers can define a series of alternative haplotypes that can be treated as a series of multiple alleles in mapping studies.
C.1.2 The nature of the genetic marker
Mapping through linkage analysis can be based on anonymous genetic markers or on candidate genes. That is, on genetic polymorphisms chosen for their genetic and genotyping qualities (i.e., chromosomal location, co-dominance, polyallelic nature, suitability for large scale genotyping); or on genetic polymorphisms at genes thought likely, because of their products, to be involved in the physiology or development of the trait of interest.
C.1.2.1 Anonymous genetic markers
A major effort is now underway to provide genetic maps based on polyallelic DNA-level polymorphisms, at 20 cM spacing, for use in genetic mapping of the major livestock species. The availability of such a map means that a general mapping program can be carried out aimed at initial total screening of a genome for marker/QTL linkages. Because of the relatively wide spacing of the markers, however, such a map will be primarily useful for within-family linkage studies (design 1.1.2), or for analysis of crosses between populations close to fixation for alternative alleles at the trait of interest (designs 1.1.3.1 and 1.1.3.2). A set of markers spaced at 20 cM, will be relatively unlikely to detect overall population linkage disequilibrium, since this is generally limited to rather small chromosomal regions (Marko and Soller, 1991).
Once a 20 cM linkage study has identified chromosomal regions which appear to contain QTL affecting the trait of interest, additional genetic markers in the region can be used to confirm the presence of the QTL, and to locate it more precisely on the genetic map. The additional markers in the interesting chromosomal regions can achieve this in two ways. (i) by providing markers that are closer to the putative QTL, and hence provide greater statistical power for the analysis, and (ii) by providing markers that are sufficiently close to the putative QTL to be in population-wide linkage disequilibrium with it, allowing confirmation of the QTL presence by studies of population-wide disequilibrium (design 1.1.1).
C.1.2.2 Candidate genes
The basic hypothesis underlying the candidate gene approach is that genetic variation at genes that are directly involved in the physiology or development of a trait may be responsible for the genetic component of the phenotypic variation in the trait. That is, that QTL affecting a trait are isoalleles of the genes whose protein products are active in trait physiology. A wide variety of methods are now available to uncover DNA-level polymorphisms in the immediate vicinity of cloned genes. These include the now classical RFLP methodologies using the cloned genes as a probe, and newer methodologies based on the polymerase chain reaction (PCR) involving the use of denaturing gels to detect polymorphic point mutations, or to detect length variation due to variable number of repeat units in microsatellite tracts located near the cloned gene.
Genetic polymorphisms in the vicinity of candidate genes, can of course, be used for general linkage detection, just as any other DNA-level genetic marker. In addition, however, on the “candidate gene” hypothesis, these polymorphisms may be in extremely tight linkage to the actual DNA variant that is producing a positive or negative effect on trait value, that is, to the QTL itself. Because of this tight linkage, linkage disequilibrium will have maximum opportunity to develop. Thus, the candidate gene approach is particularly suited to studies based on overall population disequilibrium (design 1.1.1).
C.2. Mode of analysis of the data
The basic mode of analysis of the data will involve (1 t-test or ANOVA of trait value against marker genotypes within one of the experimental designs described above. However, a number of analytical improvements have been proposed which are aimed at increasing experimental power of a given set of data. These include the following: (2) Likelihood ratio tests based on models that more exactly simulate the marker/QTL data structure, (3) Simultaneous consideration of a pair of markers, flanking a chromosomal region (interval mapping), (4) Simultaneous consideration of numerous polymorphic marker loci in the vicinity of a given QTL (multi-point analysis), (5) Joint consideration of all marker/QTL associations in data analysis (simultaneous search), and (6) Joint consideration of all phenotypic information (multi-trait and multi-relative analyses).
C.2.1 t-test and ANOVA
The exact analysis will depend on the design: t-test and one-way ANOVA by marker-genotype will be appropriate for analysis of population-wide data (design 1.1.1), crosses between populations (designs 1.1.3.1 and 1.1.3.2). Power of such analyses is discussed in Soller et al., (1976) and examples can be found in Edwards et al. (1987) and Weller et al., (1988). Within family data (design 1.1.2) is analyzed in a similar manner when the analysis is carried out within a single family only. Examples are given in Beever et al. (1990) and Geldermann et al. (1985). When data are pooled over a number of families more complex analyses involving hierarchal ANOVA (marker genotype nested within families) are required. These analyses and their power are described in Soller and Genizi (1978) and Weller et al. (1990) and examples of such analyses are given in Neimann-Sorensen and Robertson (1961), Gonyon et al., (1987) and Haenlein et al. (1987). In these analyses, each marker is tested separately against the quantitative data. A major weakness of t-test and ANOVA based approaches is that estimates of gene effect at the QTL are biased downwards by recombination between marker and QTL (Soller et al., 1976; Soller and Genizi, 1978; Weller et al., 1990). Recombination will also decrease estimates of the dominance ratio of alleles at the QTL (Soller and Beckmann, 1985; Weller et al., 1988).
C.2.2 Likelihood ratio tests
In actuality, each marker genotype in designs 1.1.2, 1.1.3.1 and 1.1.3.2 will be a mixture of parental and recombinant genotypes, which give it a skewed distribution. The exact distribution will be a complex function of gene effect at the QTL and proportion of recombination between marker and QTL. Consequently, a likelihood ratio test based on the expected distribution of quantitative trait value within marker genotypes taking these factors into account, can be expected to have greater power than t-test or ANOVA, and should also allow maximum likelihood estimates of proportion of recombination between marker and QTL and unbiased estimates of gene effect and dominance at the QTL to be obtained (Darvasi et al., 1991; Weller 1986, 1987; Lander and Botstein, 1989; Knapp et al., 1990; Jensen, 1989). Simulation studies indeed show that power of likelihood ratio tests is increased relative to t-test or ANOVA, with the relative advantage of the likelihood ratio test increasing with increasing proportion of recombination between marker and QTL (Simpson, 1989).
A major difficulty in maximum likelihood estimates is actually obtaining the likelihood solutions. Procedures based on a variety of algorithms have been proposed (Weller, 1986; 1987; Lander and Botstein, 1989; Darvasi et al., 1991; Knapp et al., 1990; Jensen, 1989). A number of experimental studies using maximum likelihood analyses for parameter estimation have been carried out (Weller, 1987; Paterson et al., 1988).
C.2.3 Interval mapping
Lander and Botstein (1989) pointed out that when a pair of markers is used to define a chromosomal region, recombinants in the region can be directly identified. They showed that when the QTL is located midway between the two markers, eliminating marker recombinants from a t-test or ANOVA analysis can increase power of the analysis relative to that obtained with either of the two flanking markers. Here, too, the increase will be greater as map distance between the pair of markers increases. When the QTL is near one of the markers, eliminating recombinants can even decrease power of a t-test or ANOVA, relative to that provided by the nearest single marker (Darvasi and Soller, 1991a), so that when interval mapping is used with t-test or ANOVA it is necessary to carry out a double analysis, once using each marker separately, and again using marker intervals. Because of the correlation between single marker and marker interval data sets, the power and type I error associated with such combined analyses, will not be much different than those associated with the single markers, but exact power calculations are difficult to carry out. When likelihood ratio tests are utilized, both recombinant and non-recombinant progeny are included in the analysis, and the overall power will combine the strengths of both the single marker and marker interval analyses (Darvasi and Soller, 1991a).
C.2.4 Multi-locus analyses
In many situations a significant proportion of progeny will be uninformative with respect to a single marker, even if the marker is polyallelic. This will occur when both parents are homozygous for the marker, or when parents and offspring are all heterozygous for the marker. This will obtain e.g., in F-2 populations out of crosses between inbred lines (design 1.1.3.1, half of this offspring will be of this nature!) and in studies within segregating populations or their crosses (designs 1.1.2 and 1.1.3.2). In these cases, consideration of additional markers in the region will clearly increase the proportion of informative progeny, but will require simultaneous consideration of data from different markers and different families. One possibility will be to consider the group of markers in a given region as a “superlocus” and carry out the analysis on a haplotype basis (Beckmann and Soller, 1988). This will be particularly useful when the markers are tightly linked so that recombination between them is rare. When the markers are spread out over a considerable region so that recombination is not infrequent, it may be necessary to develop extensions of the “interval mapping” procedure so as to utilize all information. This area has been extensively explored in the context of human linkage mapping (Lander and Green, 1987). A number of programs are available which have apparently been applied successfully to QTL mapping in backcross populations (e.g., Paterson et al, 1988). I am not aware, however, of a detailed consideration of this problem in the context of QTL mapping in segregating populations, nor of the extent to which existing programs intended for mapping of Mendelian loci are suitable for this purpose.
C.2.5 Simultaneous search
As QTL mapping procedures are applied and quantitative effects are associated with markers or marker haplotypes, it will become possible to use multiple regression methods to use this information in order to reduce the residual error term (Lander and Botstein, 1989; Knapp et al., 1990). This will increase power for detecting additional QTL, and will also increase accuracy of estimation of QTL effects. This, in turn, will allow further reduction in the residual error, allowing identification of additional QTL and further improvement of estimation of QTL effects. Theoretically, with sufficient markers, and iterations, one could control virtually the entire genetic source of variation in this manner. In practice, recombination and errors of estimation of QTL effects will prevent this ultimate limit from being reached. However, in some situations, particularly for high heritability traits, it may be possible to achieve a major reduction in residual error term in this manner, with consequent improvement in power of the marker/QTL analysis.
C.2.6 Multi-trait and multi-relative analyses.
Information as to genetic status of a given animal with respect to a given trait can come from a variety of sources. These include, measurement of the trait on the animal itself, and also measurements of other traits of the same animal, which are genetically correlated with the primary trait of interest, or which can serve as indicators of environmental factors that affected development of the trait of interest. Similarly, relatives of an animal can provide additional information as to its genetic status with respect to a given trait. Indeed in the granddaughter design (Weller et al., 1990), information on quantitative trait value of sire half-sib progeny groups is used as a basis for estimating trait value of the sire. Sophisticated statistical models are available that can combine all of this information into best linear unbiased estimates of an animals genetic value with respect to a given trait (Gianola et al., 1987; Henderson, 1988; Fernando and Grossman, 1989). Estimates of this sort should be able to reduce residual error terms in marker/QTL linkage evaluations, and contribute to the power of the experiments and the accuracy of evaluation of QTL effects. They would require multiple trait measurements relating to various aspects of a trait and suitable family structure.
C.3. Optimum allocation of resources in marker/QTL linkage mapping
The two basic costs of a marker/QTL linkage mapping exercise are genotyping costs, including costs of DNA sampling and of scoring markers on the DNA samples; and phenotyping costs which include costs of producing and rearing animals and of obtaining measurements of the traits of interest. Optimum allocation of resources among these two different activities will provide maximum power for given total costs. This will involve: (1) optimizing number of markers scored per individual and total number of individuals phenotyped, (2) optimizing the proportion of animals genotyped out of total number of animals phenotyped (selective genotyping), and number of markers scored per individual relative to proportion of animals genotyped, and (3) optimizing the resources devoted to scoring each marker (sequential sampling). When all factors are considered a considerable augmentation in power should be possible relative to scoring all markers on all individuals in some intuitively fixed number of markers and individuals.
C.3.1 Number of markers and number of individuals
In the simplest situation, a given total budget is available for carrying out a marker/QTL linkage analysis. This budget must be applied toward producing, rearing and phenotyping some specified number of animals and genotyping these for some specified number of markers. Elementary statistical considerations of power in relation to experimental size show that power will increase with increase in number of animals phenotyped. However, power is also inversely proportional to average marker/QTL distance, and hence power will increase with increase in number of markers genotyped, since this will decrease average marker/QTL spacing. Thus, optimum power will require consideration of both number of animals phenotyped and number of markers genotyped. It turns out that optimum marker spacing depends on relative costs of genotyping a single marker compared to phenotyping a single individual, but is independent of number of animals phenotyped (Darvasi and Soller, 1991b). That is, for any given cost-ratio optimum marker spacing for maximum power within given total costs will be the same whether many animals are phenotyped (giving high power) or whether few animals are phenotyped (giving low power). Also, costs of genotyping will often decrease with increase in number of markers genotyped, as costs of equipment, management and DNA sampling are prorated over more markers; while costs of phenotyping may increase with increase in number of animals phenotyped, since they may require additional facilities etc. In this case, optimum spacing is determined by the relative marginal cost of the last marker genotyped to the last animal phenotyped.
C.3.2 Selective genotyping
When marker/QTL linkage studies are aimed at analyzing a single trait, Lebowitz et al. (1986) showed that the number of individuals genotyped for given power can be decreased considerably, at the expense of an increase in the number of individuals phenotyped, by genotyping only individuals from the high and low phenotypic tails of the entire sample population. This analysis was based on the change in marker allele frequencies at the tails, as a consequence of linkage to QTL affecting the trait under consideration. Lander and Botstein (1989) later showed that for continuous variables, power for such an analysis can be markedly increased when the analysis is based on the quantitative values of the individuals in the high and low tails of the population studied. They termed this approach “selective genotyping”. Further analysis shows that for experiments intended for genetic analysis of a single trait, it will almost never be worthwhile to genotype more than the upper and lower 25% of the population (that is, 50% of the total population). The contribution of the middle 50% to statistical power is essentially nil (Darvasi, and Soller, 1991c). Beyond this, the optimal proportion selected will depend very strongly on the relative cost of genotyping all markers (including DNA sampling), compared to the costs of phenotyping an individual (including costs of producing and rearing that individual). The question of optimum marker spacing under selective genotyping remains to be considered.
C.3.3 Sequential sampling
In marker/QTL linkage determination, marker information is often obtained in a sequential manner, as DNA samples are extracted from the progeny and genotyped with respect to the markers. In some cases, the entire experimental population will be produced at one time, in others, experimental progeny will be produced and phenotyped in a sequential manner., Thus, it would seem plausible to utilize statistical methods of sequential analysis (Wald, 1947) in order to obtain more rapid decisions as to the presence of a QTL affecting a trait of interest in the vicinity of each particular marker. This will be particularly important in allowing an early decision to discontinue scoring markers in a chromosomal region lacking QTL affecting the trait of interest. In a simulation study, it was found that sequential sampling was able to effect a 50% reduction in sample sizes required for detection of marker/QTL linkage, as compared to non-sequential methods (Motro and Soller, 1991). Sequential sampling methods will be particularly appropriate when carrying out a marker/QTL analysis for a single trait. When multiple traits are involved, it will be necessary to continue genotyping any particular marker until a decision is reached with respect to all traits evaluated. Depending on the number of traits, this will rapidly approach scoring all individuals for all markers.
C.4. Fine mapping of QTL
Fine mapping of QTL serves two important functions: (i) It allows a QTL to be associated with closely linked marker genes, and (ii) It allows a QTL to be associated with possible candidate genes. Association of a QTL with closely linked marker genes can enable estimates of gene effect and dominance at the QTL to be obtained without bias due to recombination. It is also important for purposes of marker-assisted selection and introgression, in order to allow manipulation of QTL through coupled markers, with minimum errors due to recombination. Association of a QTL with potential candidate genes is a basic step towards cloning of the QTL and understanding its physiological or developmental relation to the trait under its control.
Two approaches can be used for fine mapping of QTL (1) Genetic calculations based on consideration of quantitative value of parental types and recombinants, and (2) a search for population-wide linkage disequilibrium. Simulation studies (Darvasi et al., 1991; Weller, 1986) show that map estimates for QTL obtained by genetic calculations have rather wide standard errors. Precision of estimate is limited by the number of recombinants obtained within a given region. Clearly, the more limited the region, the fewer the number of recombinants. In contrast, population-wide disequilibrium is expected only for markers closely linked to QTL, and hence can provide, in theory at least, rather precise estimates of QTL location.
C.4.1 Genetic calculations
Genetic calculations based on algebraic or likelihood expressions can be used to obtain estimates of map distance of QTL from linked markers in crosses between inbred lines or segregating populations or within half-sib families. With a single marker all that can be obtained is the approximate distance of the QTL from the marker. With a series of markers in a chromosomal region, the QTL can be located within a chromosomal region bracketed by a pair of markers, and can be located more precisely within that region, with respect to the bracketing markers.
C.4.1.1 Locating a QTL with respect to a single marker
In F-2 or BC of crosses between inbred lines or in half-sib family groups, when a QTL is located near a marker, progeny having a given marker genotype will be a mixture of QTL genotypes. The proportion of various QTL genotypes in the mixture will depend on the proportion of recombination between marker and QTL. The exact shape of the distribution will also depend on the main effect of alternative alleles at the QTL and on the within QTL genotype variance. On this basis, likelihood expressions for the overall distribution can be written and utilized to obtain maximum likelihood estimates of the parameters values for proportion of recombination between marker and QTL, and main effect and variance at the QTL (Weller, 1986, 1987).
C.4.1.2 Locating a QTL with respect to a series of markers
When a series of markers are spaced along a chromosomal region also containing a QTL, the region can be considered as consisting of a sequence of adjacent subregions, each defined by a pair of bracketing markers. Considering each subregion separately, the offspring will consist of a mixture of parental and recombinant marker genotypes. Considering parental types only, the subregion, containing the QTL can be identified as that subregion for which the difference between alternative parental marker genotypes is greatest. Further analysis (Thoday, 1961; Weller, 1987) showed that a more precise estimate of the QTL within the bracketed region could be obtained by, comparing the difference in quantitative value between marker recombinants to the difference in quantitative value between marker parental types. When the difference between recombinant types is small relative to the difference between parental types, the QTL is located in the center of the bracket. When the difference between recombinant types is comparable to that between parental types, the QTL is located near the bracketing marker having an allele shared by the parental and recombinant types having the greater quantitative value. Likelihood expressions for trait distribution within marker genotypes under the above conditions can also be written and provide maximum likelihood estimates of QTL location with respect to the bracketing markers (Lander and Botstein, 1989; Knapp et al, 1990; Jensen, 1989).
C.4.2 Linkage disequilibrium
Once a QTL has been located to a particular chromosomal region by means of genetic studies the assumption is that any number of genetic markers can be obtained in that region, for a subsequent search for linkage disequilibrium. This seems plausible in view of technical advances toward physical mapping coupled with the abundance and highly polymorphic nature of microsatellite tracts in the eukaryote genome (Beckmann and Soller, 1990). Alternatively, progress toward detailed mapping of the human and mouse genomes together with studies on bovine/human/mouse synteny (Womack and Moll, 1986) will also provide numerous markers in any given chromosomal region.
In principle, given sufficient markers and appropriate populations, linkage disequilibrium could provide at least two further steps down to finer QTL mapping. The first step, following gross mapping via genetic studies, would ideally involve a population that had undergone a hybridization episode a number of generations in the past, so that linkage disequilibrium would be limited to rather closely linked markers. This should be able to provide mapping within, say, 2–5 cM. Assuming further, that within population genetic variation was due to variation at the same loci contributing to between population differences, the final step would require a population that had been closed for many generations, yet which showed appreciable heritability for the trait under consideration. In such a population linkage disequilibrium might be limited to regions of 1 cM or less. Markers in linkage disequilibrium with the QTL in such a population could narrow the potential region of location of the QTL to the point where a search of syntenic regions of human or mouse genome might suggest candidate genes for involvement in trait determination.
A combination of linkage disequilibrium and consideration of candidate gene products might then further narrow the choice down to a single candidate gene for the QTL, concluding the mapping procedure.
D. MAPPING TRYPANOTOLERANCE LOCI
Application of these procedures to the specific goal of mapping the loci responsible for the well-documented between breed differences in trypanotolerance will now be considered. In terms of the genetic resources available for the mapping exercise and of the experimental designs and statistical procedures appropriate for each resource. To the extent that heritable variation in trypanotolerance is also present within the trypanotolerant breeds, it is also possible to consider mapping the loci responsible for this “within-breed” variation.
D.1. Mapping the loci, responsible for between breed differences in trypanotolerance.
There are two genetic resources available for this exercise. The first, and most important, are the trypanotolerant breeds themselves. These can provide the basis for mapping procedures based on crossing trypanotolerant and susceptible breeds and examining the co-segregation of trypanotolerance and markers in the F-2 or BC populations (i.e., designs 1.1.3.1 and 1.1.3.2), depending on the status of marker allele frequencies in the trypanotolerant and susceptible breeds. A second potentially important resource are the mixed populations formed by non-controlled crossing between trypanotolerant and susceptible breeds. These can provide the basis for mapping procedures based on a search for linkage disequilibrium following a hybridization episode.
D.1.1. The trypanotolerant breeds
Of the two major trypanotolerant breeds of West Africa - the N'Dama and Baoule, the N'Dama is commonly considered to have a higher and more consistent degree of trypanotolerance, and hence would appear to be the more suitable candidate for mapping procedures based on marker/QTL linkage analysis in F-2 or BC populations.
D.1.1.1 Experimental design
Initial reports on F-1 trypanotolerance in crosses between N'Dama and Zebu from ITC (Derek Clifford, pers. comm.) and ILRAD (Alan Teale, pers. comm.) suggest that F-1 trypanotolerance is intermediate between that of N'Dama and Zebu, implying that trypanotolerance is a co-dominant trait. In this case the F-2 cross, if technically feasible, would be the design of choice, from the point of view of statistical power and robustness, for given experimental size. However a BC design could also be appropriate if it were technically convenient to produce relatively large numbers of animals for phenotyping.
Initial studies in our laboratory and other reports in the literature indicate that N'Dama and Zebu are segregating for the same marker alleles. For this reason the appropriate design will be that suitable for analysis of crosses between populations that are close to fixation for alternative alleles at the QTL but share alleles at the marker loci (1.1.3.2). This mode of analysis is described in Beckmann and Soller (1988) for an F-2 design and in Mackinnon and Soller (1991) for a BC design.
D.1.1.2 Statistical analysis of the data
Because F-2 or BC animals will be produced specifically in limited numbers for the trypanotolerance mapping program, it is important to obtain maximum power in the analysis of the data. This will require application of a variety of statistical methodologies in a two or three step manner, in order to obtain maximum power within reasonable resources.
As a first step, phenotyping should involve application of a battery of tests to characterize trypanotolerance so that multi-trait analyses (section 2.6) can be used to provide “trypanotolerance value” estimates (analogous to the “breeding value” estimates of classical animal breeding) of individual animal trypanotolerance. This should provide a reduction in the error variance of estimate of trypanotolerance. Analysis of the the data for marker/QTL linkage will then take place at a marker spacing of 20 cM, using likelihood ratio tests and interval mapping (sections 2.2 and 2.3). This will provide initial estimates of chromosomal regions likely to have QTL affecting trypanotolerance. This initial screening would be at a rather high type I error (say, 0.10), in order to avoid eliminating potentially useful regions at this early stage.
In the second stage, additional markers would be scored in the regions of interest, in order to allow multi-locus methods to be employed to increase the proportion of informative offspring for these regions (section 2.4) and also to reduce the average distance between marker and QTL in these regions. Both of these effects would contribute to increased power. The analysis would be repeated, at a somewhat higher type I error level (say, 0.05). Methods for simultaneous search (section 2.5) involving chromosomal regions identified in this analysis as having the most powerful effect on trypanotolerance, would now be implemented, in order to further decrease error variance and increase power. The entire data set would be analyzed again using simultaneous search. Due to the reduction in error variance resulting from simultaneous search procedure, additional chromosomal regions, previously at the borderline of significance, may now show significant association with trypanotolerance. Additional markers would now be scored in these regions as well, to increase the proportion of informative offspring and reduce average QTL marker distance. The entire procedure would now be re-iterated. As additional markers having significant effects on trypanotolerance were uncovered they would be included in the simultaneous search procedure, until new chromosomal regions associated with trypanotolerance were no longer uncovered.
It should also be realized that not all QTL will have equal effects on trypanotolerance. Rather, a distribution of QTL effects on trypanotolerance is expected. The QTL with most powerful effects would be uncovered first. As they were incorporated in the simultaneous search procedure, additional QTL having less powerful effects will be uncovered. Thus, the procedure includes a “bootstrap” element allowing it to progress to greater power through iteration as described above.
In the third stage, the data would be reanalyzed once more, this time at a type I error level of 0.01 to 0.001, in order to provide definitive identification of marker association with trypanotolerance. The very low type I error is necessary because of the large number of markers scored. This increases actual type I errors well beyond those calculated on the basis of a test involving a single marker only.
Appendix I gives power calculations for this procedure on a variety of assumptions.
Because of the relatively large type I error involved in scoring for a large number of markers, it will be useful to confirm tentative marker/QTL linkages on a second set of independent data. These animals would be phenotyped, but genotyped only for those markers found to be associated with QTL affecting trypanotolerance in the first data set.
D.1.1.3 Optimization of experimental resources
Because of the difficulties involved in the production of F-2 animals, experiments based on this design will often involve a fixed number of animals, determined by local considerations, and optimization within this framework. Even in this case, as pointed out in section 3.2, virtually all of the information as to marker/QTL linkage is carried in the upper and lower 25% of the population, so that genotyping can be limited to these individuals. Resources saved in this manner can be more profitably applied to increasing the overall density of marker coverage in the part of the population that is genotyped, or in adding markers to chromosomal regions that show indications of association with trypanotolerance.
Similar considerations apply with respect to sequential sampling (section 3.3) of marker/QTL associations in each chromosomal region. An early decision that a particular region does not carry QTL affecting trypanotolerance can release additional genotyping resources for use elsewhere in the genome. This can allow genotyping additional markers in the more promising chromosomal regions, providing more power where it is most likely to result in a significant marker/QTL association.
In a backcross design, where experimental parameters may be more flexible, some consideration can be devoted to the question of optimum number of markers in relation to optimum number of animals (section 3.1). Also, in this case, selective genotyping can be used to really good advantage, depending on relative costs of genotyping as compared to rearing and phenotyping (section 3.2). Thus, if large numbers of BC animals can be produced, the ability to employ selective genotyping, may allow a BC design to provide equivalent overall power as a fixed size F-2 design, at similar total costs.
D.1.2 Mixed populations due to hybridization of trypanotolerant and trypanosensitive breeds.
In some areas mixed populations formed by crossing of trypanotolerant and sensitive livestock may be found. To the extent that these represent long standing populations, they may be suitable material for a search for population-wide linkage disequilibrium. Such populations could be phenotyped for trypanotolerance, and then selectively genotyped with respect to markers in those chromosomal regions that were identified as being involved in trypanotolerance in the crossing experiments described in the previous section. This would provide confirmation of the marker/QTL linkage mapping results, and possibly a finer estimate of location of QTL affecting trypanotolerance (section 4.2).
D.2. Within population mapping of trypanotolerance loci
Reports from the Trypanotolerance Network indicate the presence of a moderately high heritability for trypanotolerance within the trypanotolerant breeds. It is not at all clear whether the loci responsible for this within breed genetic variation in trypanotolerance are the same as the loci responsible for between breed differences. In principle this question can be resolved by mapping the loci responsible for the within-breed genetic variation. Mapping QTL by linkage analysis within segregating animal populations, however, requires a population structure consisting of large half-sib families as produced, e.g., by artificial insemination in dairy cattle populations. It does not appear as though such families structures are currently available for trypanotolerant cattle. Although relative-pair methods might be applicable, very large sample sizes are required for useful power, unless gene effects at the QTL involved are very large. Thus, the opportunities for linkage mapping within the trypanotolerant breeds may be limited.
Within-breed genetic variation in trypanotolerance, may provide opportunities for mapping by way of linkage disequilibrium. However, this would require that candidate chromosomal regions have previously been identified by mapping experiments involving crosses of trypanotolerant and susceptible breeds, and of course, would be based on the assumption that the same chromosomal regions involved in determining between breed differences in trypanotolerance are also involved in determining within breed differences.
It should be noted that from an ultimate applied point of view, mapping of QTL is important as a means of facilitating marker-assisted selection. Mapping of QTL responsible for between breed differences in trypanotolerance is necessary for marker-assisted introgression of trypanotolerance from N'Dama to other breeds of cattle, and of useful traits from other breeds of cattle to N'Dama. Mapping of QTL responsible for within-breed differences in trypanotolerance is necessary for implementation of marker-assisted selection for genetic improvement of trypanotolerance within the trypanotolerant breeds. There is a major difference, however, in the potential contribution of marker-assisted selection to introgression of traits between breeds as compared to the potential contribution of marker-assisted selection to within breed improvement. Marker-assisted selection is crucial for successful introgression of polygenic traits from one breed to another. Marker assisted selection within breeds is difficult to implement for QTL that are in linkage equilibrium with their linked markers (Kashi et al., 1990). This is due to the fact that in this case, the specific coupling relationship of marker allele and QTL allele must be established separately for each breeding individual by a complex process of progeny testing (Kashi et al., 1990). Thus, within population marker assisted selection would appear to have little to offer to genetic improvement of trypanotolerance under current agricultural practiced in Africa. Indeed, marker-assisted within-breed selection would generally have little to offer in practice toward genetic improvement of a trait with moderate heritability, that is measured at an early age in both sexes, as reported for trypanotolerance. In this case, mass selection would appear to be all that is required for substantial genetic progress within the breed. The potential contribution of marker-assisted selection to within-breed genetic improvement would be greater if linkage disequilibrium between marker loci and QTL were established, so that selection would not require prior establishment of marker-QTL coupling relationships for each breeding individual.
E. CONCLUSIONS
E.1. Why N'Dama? Why trypanotolerance?
There are currently two major applications of marker-assisted selection on the cattle breeding agenda. The first is the proposal to map loci affecting milk production and related traits in the leading European dairy cattle breeds, and make use of marker-assisted selection to increase the rate of genetic progress in these breeds (Soller, 1990). The second is the proposal detailed in this review - to map loci related to trypanotolerance in the N'Dama cattle of West Africa and make use of marker-assisted introgression to introduce trypanotolerance from the N'Dama to other breeds of cattle, and improved production traits from other breeds into the N'Dama.
At first sight it may seem incongruous to propose an esoteric African breed of cattle and a tropical disease in the same high technology context as the ongoing task of improving milk production in the leading dairy cattle breeds of Western agriculture - a task which has engaged the attention of the outstanding scientific animal breeders of the past four decades and continues to involve large numbers of scientists and breeders in many countries. Nevertheless there are cogent technical and agro/economic reasons for the importance attached to this proposal and for the belief that mapping of trypanotolerance loci and their subsequent utilization for marker-assisted introgression, may turn out to be the first major application of recombinant DNA technology to cattle improvement - or to livestock improvement in general!
At a technical level the N'Dama x Zebu cross presents a number of advantages for marker-assisted genetic analysis and breeding. N'Dama and Zebu represent two distinct cattle subraces -Bos taurus and Bos indicus, respectively. For this reason, they are likely to differ in gene frequencies at many loci. This will facilitate mapping of the trypanotolerance loci. In addition, the N'Dama x Zebu cross, so far as trypanotolerance goes, has the advantage of allowing a mode of analysis analogous to that of a cross between inbred lines. This will allow the mapping exercise to be carried out on a relatively small number of F-2 animals -as shown in the Appendix, one or two hundred animals should suffice, as compared to one or two thousands that will be required for mapping loci affection milk production and related traits in dairy cattle populations (Weller et al., 1990).
Furthermore, the N'Dama x Zebu cross will also enable the mapping of loci affecting a number of additional traits of economic and biological importance differentiating these two cattle types. Thus, this cross will provide much new information as to the genetic architecture of economic traits in general in the bovine genome.
At an agro/technical level, application of marker-assisted introgression to trypanotolerance can make a qualitative difference in the levels of livestock productivity in West and Central Africa, a region where chronic shortages of high quality protein are endemic, and where increased productivity will mean increased availability of meat and dairy products for the population, and a source of livelihood for large numbers of individuals. This is in contrast to the situation for Western agriculture, where agricultural surpluses are major economic problems for societies that are determined to maintain a certain minimum proportion of the population on the land and avoid economic crises brought on by surplus/shortage cycles. In these Western societies, much of the increase in economic efficiency which is achieved through increased productivity, is passed on to the consumer in the form of lower prices on the one hand, but then taken away in the form of farm subsidies on the other.
Thus, at a fraction of the cost for mapping productivity loci in dairy cattle, the N'Dama x Zebu cross and the trypanotolerance mapping exercise can be expected to yield great dividends in increased understanding of the bovine genome in general, and in providing solutions to major human problems in Central Africa in particular.
E.2. The trypanotolerance mapping program in relation to the human genome mapping program.
It is important to take into account that the trypanotolerance mapping program, as it is implemented will be taking place simultaneously with the human genome mapping project. Thus, shortly after the trypanotolerance mapping project is completed, it can be anticipated that a complete map of all human genes, and their coding sequences, will be available. Comparative studies of the human and bovine genomes (Womack and Moll, 1986) have shown that large blocks of genes remain united in the same gene order in both human and bovine genomes (a phenomenon termed “synteny”). The presence of synteny means that once a trypanotolerance locus is mapped with respect to bovine genes having known homologues in the human gene map, it will also have been mapped with respect to the complete human genome map. This will allow all human genes in the region to which the trypanotolerance locus has been mapped to be examined for their potential as contributors to trypanotolerance. Candidate human genes can then be used as probes to identify the corresponding bovine genes from a trypanotolerant bovine genomic library. The candidate bovine genes can be examined for ability to confer trypanotolerance in experiments involving transgenic manipulations (possibly in mice - not necessarily in cattle). Thus, mapping of the trypanotolerance loci, in addition to facilitating their breeding manipulation in traditional selection and introgression programs, can also serve as a direct step toward their eventual cloning and manipulation through genetic engineering methods.
F.ACKNOWLEDGEMENT
This review was supported by the U.S.- Israel CRD program of the U.S. AID organization. It is based in part on the Consultation Report entitled: “Toward an Understanding of the Genetic Basis of Trypanotolerance in the N'Dama Breed of West Africa: prepared for FAO, Rome, March 1987 by M. Soller and J.S. Beckmann.
We thank our colleagues at ITC and at ILRAD for sharing with us their experience and knowledge of trypanotolerance and for allowing us the privilege of participating actively with them in the trypanotolerance mapping programs currently underway at these institutions.
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APPENDIX I:
The number of F-2 offspring required for mapping QTL affecting trypanotolerance in a cross between a trypanotolerant breed and a susceptible breed.
The basic assumption is that the two breeds are at fixation (or close to fixation) for alternative alleles at the QTL determining trypanotolerance, but are segregating for the same alleles at the marker loci. Thus, the design to be implemented is that described in section 1.1.3.2 (Beckmann and Soller, 1988). Within this framework, the following factors will determine the power of the experiment:
1. The difference in trypanotolerance measure (henceforth: trypanotolerance) between the trypanotolerant and susceptible breeds (D). This difference will henceforth serve as the unit of measurement for gene effect at the QTL and for variance in trypanotolerance. That is, we set D=1.
2. The number of QTL contributing to the difference in trypanotolerance (k). On the simplistic assumption that all QTL contribute the same amount, the difference between alternative homozygotes (i.e., gene effect) at each locus will be, 2d=D/k=1/k. We will investigate the situation for k=1, k=5 and k=10.
3. The variance of trypanotolerance within marker genotype classes, (s2). This will have three components:
(i) a component due to environmental influences, (s2e). This will be defined in terms of Se and D, i.e., Se=pD=p. We will investigate two situations: p=0.1, which would correspond to the situation where there was a major gap in trypanotolerance between the lowest scoring trypanotolerant animal and the highest scoring trypanosensitive animal; and p=0.2, which would correspond to the situation where the lowest scoring trypanotolerant animal and the highest scoring trypanosensitive animal gave similar scores.
(ii) a component due to segregation at QTL, other than the QTL in linkage to the marker under analysis, (s2g). Assuming co-dominance at the QTL affecting trypanotolerance, this will equal (k-1) (0.5) d2 = (k-1) (0.5) (1/2k)2.
(iii) a component due to recombination between the marker under analysis and the QTL in linkage to it, (s2r). Letting r equal the proportion of recombination between marker and linked QTL, this will equal d2 [(1-r2)2+r2-(1-r)4], e.g., for r=0.1 or 0.05, s2r=0.16/2k2 and 0.08/2k2, respectively.
4. The proportion of recombination between marker and QTL. For a marker spacing of c cM, this will have a maximum value of r=c/2. Under interval mapping, this will increase required numbers by a factors of 1/(1-c/200). We will assume c=20 for the first step of the marker/rker/QTL analysis, and c=5 for subsequent steps.
5. The proportion of informative offspring in each marker genotype class, (I). For a classical F-2, where all offspring marker alleles can be unequivocally allotted to one or other of the parental types, I=0.25. For a Beckmann and Soller (1988) type of analysis, the proportion will be lower and will depend on the type of marker used and the number of markers in the chromosomal region. We will assume I=0.125 (only half of potentially informative offspring, informative in practice) for the first step of the marker/QTL analysis, increasing to 0.20 in the second step, as additional markers are scored in the promising chromosomal regions.
6. The proportion remaining, (S), in the genetic component of the within marker variance, s2g following implementation of simultaneous search procedures. We will assume S=0.5.
7. The proportion remaining, (M), of the environmental component of the within marker variance, s2e, following implementation of multi-trait analyses. We will assume M=0.75.
Thus, considering S and M, we have
s2 (S,M)=s2eM+s2gS+s2r
8. Type I error, (a). We will assume a=0.10 in the first step of the marker analysis, and a=0.01 in the last step. Achieving a=0.001 will require doubling the number of animals as compared to a=0.01.
9. Type II error, (b). We will assume b=0.10.
Considering all factors, and following Soller et al., 1976, we have
N=2(z0.5a+zb)2 / [(2d/s(S,M))2 (1-c/2)I]
The numerator of this expression will equal 17.1, 21.0 and 42.0 for a=0.10, 0.01 and 0.001, respectively.
Parameter | Step 1 | Step 2 | ||
| M | 1.0 | 0.75 | ||
| S | 1.0 | 0.50 | ||
| I | 0.125 | 0.20 | ||
| C | 20 | 5 | ||
| a | 0.10 | 0.01 | ||
| b | 0.10 | 0.10 | ||
| k=1, 2d=1.0 | p = 0.1 | p = 0.2 | p = 0.1 | p = 0.2 |
| S | 0.223 | 0.282 | 0.206 | 0.141 |
| N | 8 | 12 | 5 | 2 |
| k=5, 2d=0.2 | ||||
| S | 0.178 | 0.248 | 0.201 | 0.134 |
| N | 120 | 234 | 43 | 109 |
| k=10, 2d=0.1 | ||||
| S | 0.147 | 0.227 | 0.115 | 0.189 |
| N | 329 | 782 | 143 | 385 |
Comparison of required numbers for step 1 as compared to step 2, shows the importance of adding additional markers to the promising chromosomal regions, and of multi-trait analysis and simultaneous search. The overall impression is that with sufficient markers and statistical sophistication, and F-2 experiment of 150-200 animals would be able to uncover all trypanotolerant loci, if the total number of loci were five or less, and most trypanotolerant loci if the number of loci were six to ten. Sequential sampling and selective genotyping can be implemented as well, in order to allowing genotyping to be focussed on the most informative individuals and the most promising chromosomal regions.
