2. Traits of goats can be considered either to be qualitative (simply inherited) or quantitative. Most economically important traits are quantitative.

3. Genetic Parameters Quantitative traits of goats are those which are influenced by genes at many different loci (gene sites on a chromosome), each contributing a relatively small amount to the total expression of the trait. A second characteristic of quantitative traits is that their expression is influenced to some degree by the environment in which the goat performs.

4. The phenotype of a goat is the observable expression of some trait, e.g., pounds of milk produced in a lactation. The phenotype (P) for a trait can be defined as the sum of the goat's genetic merit for that trait (G), the influence of the environment (E) on the record, and the population mean for the trait (M). If one looks at phenotype of several goats for a given trait, one can also determine their average performance and a certain variation from animal to animal called variance. The sum of the variances due to genetic and environmental influences makes up the total phenotypic variance, from which the standard deviation can be extracted; i.e., the standard deviation is the square root of the variance.

5. Average performance and standard deviation describe a trait in a given population. If a trait is normally distributed along a bell-curve, then 500f the trait's records will lie between -0.67 and +0.67 standard deviations and 950f the records between -1.96 and +1.96 standard deviations in a particular population (Figure 1). The ratio of the additive genetic variance over the phenotypic variance is the important parameter called heritability (h+/-), which can take on values from 0 to 1. A value of 0 means more of the variation in the trait is genetic, and a value of 1 means all the observed variation is genetic. Few economically important traits in goats have values exceeding 0.5. General characterizations for selecting traits are:

8. The true breeding value (BV) of goats is never known and they are compared on estimates of BV, which are subject to the variance or error in estimation. Accuracy denotes how well the BV of a goat has been estimated. The more information available on an individual, either in terms of repeated records or information on relatives, the more accurate the estimated BV's (EBV), and the less likely the comparison of individuals is in error.

9. The EBV's can be used to rank goats comparatively for selection. In the example, the goat (A) producing 1100 lb of milk was 25 lb genetically superior to the breed average doe. Another doe (B) producing 900 lb milk is 25 lb inferior to the breed average (-100 x 0.25). Thus, goat A is 50 lb milk genetically superior to goat B.

10. The EBV of an individual represents its own genetic merit but greater interest lies in the merit of that individual's progeny. ''How much of an in dividual's breeding value or superiority will be transmitted to its progeny?'' is the question. The concept of Estimated Transmitting Ability (ETA) equals one half the EBV of an individual goat, since one half of her genes are represented in her progeny; the other half being supplied by the other parent. Genes obtained by one particular progeny from its parent are a random sample. A progeny may receive in the extreme a sample of the parent's best or its worst genes only. This explains why poor progeny sometimes may result from good parents and good ones from poor parents.

11. The genetic parameter closely related to heritability is repeatability (r). It is also a ratio of variances, namely the variance for permanent environmental influence (e.g. injury) plus the total genetic variance, not just the additive, over the phenotypic variance. Repeatability is equal to or greater than heritability by definition. Repeatability can be used to predict the future performance of a goat based on her past performance.

12. This Most Probable Producing Ability (MPPA) can be calculated as: P'+r(P-P') when the goat has one record. The doe (A) producing 1100 lb (P) in the population averaging 1000 lbs (P') has an MPPA of 1050, if r=0.50. When the goat had n records the calculation for MPPA is:

13. All domestic livestock have several traits of economic importance, and their relationships to each other are critical for selection programs. A correlation describes the relationship between two traits. There are phenotypic, genetic, and environmental correlations. A correlation can have values between -1.0 and +1.0, with zero meaning no relationship. The nearer the correlation is to +1.0 or -1.0, the closer the relationship is between the two traits. A positive correlation (+) indicates high measures of one trait tend to occur with high values of the second and low values for the first with low values for the second. A negative correlation (-) indicates a tendency for high values of one trait to occur with low values of the second. For example, milk and fat yields of goats are positively correlated. As pounds of milk per lactation increase so do the pounds of fat produced. However, milk yield and milk fat percentage are negatively correlated. As pounds of milk increase, the percentage of fat in the milk of goats tends to decrease.

14. Genetic correlations are important in selection and have two biological causes: pleiotropy and linkage. Pleiotropy is the result of one gene contributing to the phenotype of more than one trait. Linkage means a gene (or set of genes) is in close proximity on a chromosome to a gene for a second trait. Being close together on the same chromosome, they are passed on to the progeny together and cause the genetic correlation. Thus selection for one trait will alter also the performance of the population for all other traits which are genetically correlated to the trait under direct selection. That change in a correlated trait is called a correlated response. Some correlated responses can be beneficial in terms of improving the total productivity of goats; however, others may be detrimental. Genetic correlations as well as phenotypic correlations may be used in indexing animals for simultaneous selection of more than one trait.

15. Selection Response The first step in the selection process is to define the goals of the program, e.g., which trait or traits are desired in selection. The appropriate records need to be collected on the selection candidates and their relatives. From these records, the BV's of the individuals are estimated and the goats ranked from best to worst. The breeder must now decide how many goats are needed for both sexes, and selection is then simply keeping the top ranked animals. Fewer bucks are required to maintain the population than females, therefore the intensity of selection for males can be much greater. This points out that more progress can be made by concentrating efforts on buck selection.

16. A selection differential is the phenotypic average difference of the selected parent animals (Ps) from the population average (P'). Selection intensity (i) is the selection differential expressed in terms of phenotypic standard deviations (s); i.e. the ratio of (Ps-P') over s. Selection is used in predicting genetic response due to selection because it can be related to that percent of the population saved as parents (see Table 1). If the top 100f goats available are used for selection, their mean phenotypic superiority due to selection intensity is 1.75 standard deviations above the population mean. If the top 70are selected then the selection intensity will be only 0.5 standard deviations above average.

17. Table 1. Selection intensities (i) for different percentages of individuals selected to be parents from a large population.

18. The parameter of heritability is used to calculate selection response. The square root of heritability is called accuracy (h). The formula for selection response after using a certain superior male in a goat herd is one-half of the product of accuracy, times selection intensity, times the additive genetic variance for the trait. The reason for ''one-half'' is, of course, that only half of the sire's genetic superiority is passed on to his progeny. Selection response is the genetic change due to selection in one generation. Many times, interest lies in the genetic change per year. To obtain this estimate, one must divide by the generation interval (t), which is the average age of the parents when their progeny are born. For example, if the heritability of yearling weight is 0.49, then the accuracy is the square root or 0.7. The generation interval of goats is two years. According to the above formula, the answer in the case of 10 election intensity (equal to 1.75 standard deviations) would be 1/2(0.7) (1.75)/2=0.31 standard deviations selection response per year for strictly male selection only. If however, 700f all females selected is the selection intensity program, then the selection progress becomes, according to the same formula, 1/2(0.7) (0.5)/2=0.09 standard deviations selection response per year above herd average. If both programs are combined, the answers are combined and the selection response for yearling weight becomes 0.4 standard deviations progress per year in average.

19. Selection for more than one trait based on independent culling levels is accomplished by ranking candidates for both traits and requiring the selected animals to meet a minimum standard in both traits. This process is repeated each year with only minimum standards adjusted for progress made by selection.

20. Figure 2 shows independent culling plotted for a large number of animals for two traits. Goats in the upper righthand quadrant meet the standards for both traits and are chosen to become parents of the next generation. Two points in Figure 2 are goats A and B for the two traits. Goat A is superior to the population for trait 1 but falls just below the culling minimum level for trait 2; so this animal would be culled. Goat B has a performance level just above the standards for both traits and is kept as a parent. It can be seen that Goat A could probably be a more appropriate parent than B. Their difference in performance for trait 2 is minimal while goat A is far superior to B for trait 1.

21. Compromises have to be made for goats which are superior for the one trait but just below borderline for the other trait. This has led to the procedure of Selection Index which allows ranking animals simultaneously for two or more traits in one single index.

22. A selection index is calculated from the sum of trait means each multiplied by appropriate factors which weigh their relative importance genetically and economically. An index provides the opportunity for multiple trait selection. For example, a goat breeder considers trait 1 two times as important as trait 2. Hence, trait 1 would have a weighting factor double that of trait 2. In figure 2, goat A would now be selected rather than goat B because of the index method. Selection index, under certain assumptions, can maximize selection response for both traits.

23. Breeding Systems Random mating is a system where an individual goat has an equal opportunity to be mated with any other individual of the opposite sex. The mating of two particular goats occurs essentially by chance in that no breeder decision was made to join them as mates.

24. Assortative mating is based on phenotypic performance or characteristics. Mating individuals of like performance is positive assortative mating, e.g., large goats to large mates and small to small. Mating individuals of unlike performance is negative assortative mating, e.g., large goats to small mates. Positive assortative mating tends to cause more variation in the total population of progeny than would occur from random mating, and negative assortative mating tends to reduce the variation. Assortative mating is practiced for type (conformation) traits. For example, ''corrective'' mating for progeny of a doe with certain physical weaknesses to a buck with strengths in those attributes would be negative assortative mating. Perpetuating strengths of a given line by selecting a buck also strong in those characteristics would be positive assortative mating. Assortative mating deviates from random mating in that decisions by the breeder based on phenotypes exclude or reduce the possibility of some matings.

25. The concept of relationship is important in deciding on certain breeding systems. The basic principle involved in determining relationship is that a parent passes one half of its gene complement to its progeny. Hence, in a noninbred population, a parent is related to its progeny by 0.5, meaning 500f their genes are in common or they have a relationship of 50 Other types of relationships in noninbred populations are calculated as products of this 0.5 or (1/2). For example, the relationship between paternal half-sibs (progeny of the same sire mated to different dams) is 25as can be seen in the following diagram:

dam 1 > progeny 1 < sire > progeny 2 < dam 2

Each progeny receives a sample half of the sire's genes. The portion of genes that progeny 1 received from its sire, which are replicates of the same genes received by progeny 2, is (1/2) times (1/2) or 0.25

26. The relationship of a goat (C) to its grandparent (A) is also 25 because:

Parent goat B received one half of its genes from grandparent A and in turn passes one half of its genes to progeny C. The relationship is (1/2) times (1/2) or 0.25 x 025

27. The relationship between C and its great-grandparents (E) would be one half of 0.25 or 12.5

28. A quick method of calculating relationships between two individuals in a noninbred population is to set each ''arrow'' between related individuals equal to (1/2) and multiply. This is equivalent to raising (1/2) to the nth power, (1/2)n, where n represents the number of arrows or generation steps. The relationship of goat D to goat E having a common grandparent (A) would be:

29. The degree of inbreeding of a particular individual equals one half the relationship of its parents. This value is called the inbreeding coefficient (F). The progeny resulting from mating a sire to his daughters has an F of 0.25, while mating two paternal half-sibs results in a progeny inbred 12.5

30. The consequence of inbreeding is increased homozygosity or likeness of genes. If an individual goat has two unlike genes at a particular trait locus it is called heterozygous. However, an inbred animal has more loci in homozygous states than the average noninbred animal. For a particular trait, there is a higher number of homozygous individuals in an inbred population than in a non-inbred one. Over time with inbreeding, certain genes which were present in the initial population may get lost in subsequent generations. Within an inbred line, the tendency towards fixation of few genes reduces the amount of genetic variation. In the absence of selection, genes are lost or fixed at random. The variation between inbred lines increases, however. Inbreeding can be used to create diverse lines.

31. An advantage of an inbred goat as parent is the increased uniformity in its progeny. Uniformity does not imply superiority, which is a function of genetic merit. An inbred animal may or may not be superior. Since inbreeding increases homozygosity in a population, it follows that this includes undesirable recessive genes. Hence, with inbreeding, the risk exists that one would generate a higher incidence of homozygotes for lethal, sublethal, and undesirable genotypes than ocurs in random mating populations.

32. A second negative aspect of inbreeding is inbreeding depression, which is reduced performance related to increased homozygosity. The traits most influenced by inbreeding depression are in general those which have low heritabilities. Unfortunately, this includes such traits as viability and reproductive performance. A realistic threat associated with intensive inbreeding is producing a population of goats unable to survive or reproduce well enough to maintain the population.

33. Inbreeding occurs from breeding programs designed to mate relatives and in small herds where introduction of outside breeding stock is rare. The rate of change per generation in the average level of inbreeding is not large enough in most herds to be of concern. For example, if one uses 5 bucks selected from within a herd of 50 does, the level of inbreeding increases by 0.0275 per generation. However, in small herds where, for example, two bucks may be used on 20 does, the increase is 0.069 per generation. A progeny from two unrelated, inbred parents has an inbreeding coefficient F of zero. If a breeder feels his herd is getting too inbred, he can relieve the problem in the subsequent generation by using unrelated breeding stock. A breeder can also bring an unrelated, even though highly inbred sire into his herd without suffering the consequences of inbreeding depression in the progeny of that buck, because the progeny of two unrelated, although inbred, parents has an inbreeding coefficient of zero.

34. Line breeding maintains a high degree of relationship of individuals to a superior ancestor but has less severe consequences than inbreeding.

Assume goat A was a buck used on several does in a herd generating daughters B and C. These daughters are mated to unrelated bucks and produce a son D and daughter E. The goats D and E are related to A by 25, but to each other by 6.25

35. Assuming it was recognized that A was a truly superior buck. If his descendents were mated each generation to unrelated animals, the relationship of A to that progeny would continue to decrease by one half each generation. Progeny Z is related to great grandparent A not by 12.5but by 25, because there are both parents D and E related to Z. Since D and E are related by 6.25, progeny Z has an inbreeding coefficient of 3.15 The recapture of some of A's gene combinations is not certain but possible. The probability can be increased through line breeding or increased inbreeding with its other consequences.

36. The opposite mating system is designed to increase heterozygosity. Crossing of lines within a breed or the crossing of breeds are examples of such strategies. The fundamental assumption is that the genes at the various loci differ in the two parent lines or breeds. For many traits, the crossing of lines or crossbreeding results in progeny whose performance exceeds that which was expected from their parents' performance. This deviation is called heterosis or hybrid vigor and can be calculated as the difference from the expected.

37. For example, assume we cross two goat breeds, one averaging 800 lb of milk per lactation and the other 1000 lb. The expected progeny performance would be 900 lb milk while the actual performance of the crossbred progeny was 950 lb, indicating 5.6 2.256835e+199terosis ((950-90 Progeny exceeding their expected performance for a trait are not necessarily superior to both of the parental lines for that trait. Furthermore, crossbreeding influences all traits so that if complementary breeds are used, the total merit of the crossbreds may exceed each parental breed.

38. Heterosis is associated with dominant gene action. Assume that trait (A) has three possible genotypes with the following relative phenotypic values.

Gene (A) is dominant to its recessive allele (a) and the genotypes (AA) and (Aa) have the same phenotypic values. At a second trait locus (B) assume the values for the three genotypes are:

There is no dominance at this locus since (Bb) is the average of the values of the two homozygous states. At a third trait locus (C) it is assumed that the following values exist:

There is incomplete dominance since Cc has a value exceeding 50 but less than 100.

39. Given these three loci and their relative values, one can now demonstrate heterosis from crossing two breeds of goats that have the following of the above genotypes:

The relative phenotypic value of each breed is the sum of the values of their genotypes at each of the loci. Breed 1 would have a value of 100 and breed 2 a value of 200; with an average for both parents of 150. Any crossbred progeny will be heterozygous at all three loci. Hence, their value will be the sum of their heterozygote values: 210. Heterosis for this particular crossing is 40(210 - 150/150 =0.4). If all three loci had no dominance, then the heterozygote values at each locus would all be 50, and the value sum for the crossbred progeny would be: 150. Hence, with no dominance, the percentage heterosis is zero

40. Heterosis is essentially the opposite of inbreeding depression and is also related to heritability. Those traits with low heritability usually show the greatest percentage of heterosis. These include viability and reproductive performance, both important characteristics in a total production system.

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