Dr. Wayne C. Jarvis
What are we doing?
As animal breeders, what are our goals and objectives? Why are we mating our animals, and why are we doing it the way we are? Is the goal to produce more alpacas and increase the size of our individual herd as well as the “national herd”? Are we breeding animals to replace our stock? Are we attempting to breed in such a way that the descendants will be “better” than the present generation? What is the “best” alpaca anyway? Is our goal a combination of all of these? If so, which outcome is the most important?
In the first article of this series the three main factors that we must consider in order to produce the next generation of offspring: Traits, Selection and Mating, were introduced. The purpose of this article is to discuss in more detail some of the factors affecting the rate of genetic change touched on in the first article, so that we can progress toward our breeding goals by using these principles of quantitative genetics.
The reader will remember that the key equation that determines the effectiveness of our selection process, states that the rate of genetic change is proportional to selection accuracy, selection intensity, genetic variation and generation interval. Selection accuracy refers to selecting the animals with the best breeding values to be in our breeding program. What the best values are depends on the goals the individual breeder has for future generations. Breeding value (BV) is defined as the animal’s individual value as a genetic parent—i.e. a contributor of genes to the next generation.
Our formula for phenotype:
P = G + E
says that the phenotype for any trait is the result of the combined effects of the genes an animal has inherited and environmental influences it has been subjected to throughout its life. We can refer to the “G” in this equation as the individual animal’s “genotypic value”, but that is not the same as its breeding value (BV) which is that part of the genotypic value that can be transmitted to this individual’s offspring. Some genotypic values are the result of the combination of the effects of many genes, some of which are dominant to others, some of which are additive, and some of these genes can have epistatic effects.
Epistasis means that the genes at one locus can have an effect on genes at other loci.
“A simply-inherited example of epistasis that is relatively easy to understand is coat color in Labrador retrievers. Labs come in three basic colors: black, chocolate and yellow. These colors are determined by genes at two loci: the B (black) locus and E (extension of pigmentation) locus, as follows:
B_E_ => black
bbE_ => chocolate
_ _ee => yellow
The dashes in these genotypes indicate that either allele could be substituted without changing the phenotype. Black Labradors, for example, can be BBEE, BBEe, BbEE, or BbEe. Yellow labs can be BBee, Bbee, or bbee. Note that the expression of genes at the black locus depends on the alleles present at the extension locus. So long as there is at least one E allele at the extension locus, there appears to be complete dominance at the black locus, with black being dominant to chocolate. However, if the genotype at the extension locus is ee, then genes at the black locus become irrelevant—all animals will be yellow”1
In this example then, genes at the E locus are epistatic over genes at the B locus. Epistasis is just one type of gene combination effect. Dominance is another. These effects cannot be passed on by one parent, as they are due to combinations of genes, and the Mendelian process of segregation and independent assortment of genes, that takes place at random when gametes (sperm and egg cells) are formed, prevents the inheritance of any particular combinations of these genes that might be present in the parent.
Because combinations of genes cannot be transmitted, then an animals BV can only represent the independent effects of the genes they have to pass on. Therefore we can say that an animal’s genotypic value (G) is the sum of the independent gene effects that can be passed on (BV) and the gene combination effects that cannot predictably be passed on. We will call that the animals Gene Combination Value (GCV). So in algebraic form we can say:
G = BV + GCV
Substituting into our formula for Phenotype we get:
P = BV + GCV + E
This formula is useful to keep in mind when we look at an alpaca as a potential parent. It tells us that what we can see and measure (the phenotype) is a combination of the genetic factors a parent can potentially transfer to offspring, a genetic component that cannot be transmitted to the offspring, and a component that comes from the effects that the alpaca’s environment has had on it’s growth and development throughout it’s life, which of course cannot be transmitted genetically either.
We cannot directly measure an animal’s genetics. Therefore we also cannot directly measure an animals BV. Instead, we can estimate the breeding value based on performance data. This is what we will call Estimated Breeding Value, or EBV. The more performance data we have, the more accurate this estimate will be. This data can be from the animals own performance records (Individual’s Data); the performance of the animal’s ancestors, and collateral relatives such as siblings and half-siblings (Pedigree Data); and the performance of the individual’s offspring (Progeny Data).
It was stated earlier that the rate of genetic change is proportional to selection accuracy, among other factors, and that selection accuracy was based on choosing animals with the best breeding value for the traits in question. It follows then that the selection accuracy is based on the accuracy of predicting or estimating breeding values (EBV). It is important therefore to understand which performance data provides the most accuracy in predicting breeding values.
It is beyond the scope of this article to explain the statistical and mathematical formulas and processes that are employed to generate the following conclusions. For those who are interested in the mathematics involved in proving my next statements please refer to the genetics and animal breeding texts listed in the references.
The heritability of a given trait affects the overall predictability of an animals breeding value for that trait. The higher the heritability, the more accurate the prediction of breeding value can be from performance records. At any level of heritability however there is a relative value of sources of information in predicting breeding value. Paradoxically the best source of information is an individual’s data, since the animal has 100% of its genes in common with itself, but that is also the most limited source of data. There can obviously be only one individual from which to glean this type of data. The next most accurate source of performance data is from progeny. Progeny of course have only 50% of their genetics in common with the individual and therefore have only one half as much accuracy as far as predicting breeding value from a single offspring as from the individual itself. However, there is the possibility of collecting progeny data from many more than one source, and so even though the value of the data from any one animal is less, the accuracy of prediction from progeny data can exceed that from the individual’s performance record by collecting data from several progeny. For most levels of heritability which we would observe in our alpaca herds, the accuracy of prediction from progeny will exceed that from the individual data by the time we have ten progeny from which to gather performance information. It is not unusual with male alpacas to have many more than ten progeny to evaluate. Full siblings records have nearly the same value as progeny records when it comes to accuracy of prediction of breeding values, however it is much less common in the alpaca industry for us to have ten offspring that are full siblings than it is to have ten progeny from one parent and so practically speaking for our purposes full sibling data is not as valuable as progeny data. Half siblings are numerous, but since they only have 25% of their genes in common with the animal in question they are less valuable in accurately predicting a particular parent’s BV. It would take, depending on heritability, between 20 and 30 half siblings to equal the predictive value of the individual’s own performance, or that of ten of the individual’s offspring.
We can see then that the most accurate single source of information about the breeding value of an individual animal comes from evaluating ten or more of that individual’s progeny. Fortunately we are not required to make our decisions based on one source of information. We can look at all of the performance data of the individual, of his full siblings, half-siblings and of his progeny all together when determining estimated breeding value. It is important however to realize the relative levels of importance that each of these sources of information provide. They are not all equal in value.
Progeny records are the one best source of evaluating and predicting the breeding value of any animal, and for any trait, regardless of its degree of heritability. With enough progeny to evaluate, accuracy of predicted breeding value for a trait can be high even when heritability is low. For example, even when the heritability of a trait is as low as 5% or .05, the accuracy of an estimated breeding value for that trait could be 96% if you had 1000 offspring to look at. With alpacas that is unlikely, but with animals such as beef and dairy cattle where AI is readily available it is not unusual to have records of 1000 offspring of a particular bull. It is not unheard of however for a particular herdsire to have 100 known offspring, and the progeny records of all of those animals would make the EBV of a .05 heritability trait 75% accurate. For a trait that is moderately heritable, say 30%, 100 offspring’s performance records could yield an EBV of 94% accuracy.
In order to make a practical example of that point, let us think of a fleece characteristic of alpacas, such as average fiber diameter. Although heritability calculations for alpaca populations are rare, most breeders believe that fleece characteristics are moderately to highly heritable. If the heritability of AFD is 30%, then measuring AFD on 100 offspring could tell us the breeding value of a particular herdsire with an accuracy of 94% or greater. Therefore, if a hypothetical herdsire Mr. Studly has histograms showing that his average fiber diameter is 10 microns less than the mean fiber diameter of the herd, we could say that his breeding value is –10 microns for AFD, but the accuracy of that EBV would only be 55%. If however we can measure the AFD of 100 of Mr. Studly’s offspring, and the data tells us that his EBV is –10 microns, that estimate would have an accuracy of 94%. You can see from this example how having data on a herdsire’s offspring, or “Progeny Testing”, can give us a much more reliable prediction of how valuable Mr. Studly might really be if we want to breed for lower fiber diameter. Even just 10 offspring’s fiber diameter measurements will give us a much better prediction than Mr. Studly’s histogram does.
The important point to remember is that ALL progeny data must be included for these numbers to be valid. As soon as any one progeny’s record is intentionally left out, then the accuracy of the prediction is no longer what it should be.
Estimated breeding value, EBV, is a way of estimating the genetic value of a parent. However, we often prefer to think of what will the effect of using this particular parent be on the offspring. In other words, how much better than average will Mr. Studly’s offspring be for a particular trait. This is referred to as the Estimated Progeny Difference (EPD) or some geneticists use the term Estimated Transmitting Ability (ETA). Since each parent can only contribute ½ of its genes to the offspring, then on average that parent only passes on ½ of its breeding value to the offspring. So one half of the parents breeding value is the estimated progeny difference.
EPD = ½ EBV
We must understand that a parent doesn’t always pass on exactly one-half of its breeding value to each offspring. He or she always passes on exactly ½ of his or her genes, but the genes that are transmitted are always a random sampling, and are probably different for each and every child. There is no way to predict if a given individual offspring will inherit a poor, average or superior sample of the parents genes.
The better the production records that we have from all possible sources, individuals, siblings and progeny, the more accurate our selection can be. Therefore it is a fact of animal breeding that the breeder who keeps the most precise and detailed records will have the best available information on which to make selection choices and hence will have the best chance to improve the rate of genetic change in his herd.
The next factor in our key equation for affecting the rate of genetic change is selection intensity. This factor of the key equation tells us what percentage of a population is selected as parents. As stated in the previous article, financial considerations and the need to increase the number of alpacas in the national herd make it very difficult for North American alpaca breeders to exercise high selection intensity at this time. As the size of each individual alpaca herd and the overall national herd size increases we will begin to see more selection intensity. We are beginning to see some selection intensity in male alpacas, but the overwhelming majority of all female alpacas are allowed to breed for as long as they are able to produce healthy crias. Therefore a detailed discussion of types of selection intensity and their effects can wait for the day to come when alpaca breeders can decide that they will only allow a certain percentage of their females to reproduce. As we become able to select with higher intensity, we will be able to more rapidly affect genetic change in our herd. Selection intensity, a measure of how picky a breeder is in choosing which animals will be selected to reproduce, is based on one or more selection criteria. Let’s go back to our hypothetical alpaca Mr. Studly. We could suppose for example that AFD again was the trait we wanted to select for. We said Mr. Studly’s EBV for AFD was –10 microns. If all available males have EBVs from –8 to –15 and we choose to breed any male with an EBV of –10 or less we are not excercising a high selection intensity. If on the other hand all available males have EBVs of +10 to –10 microns, and we choose only those with an EBV of –10 microns to breed we are excersising a high selection intensity and will therefore see a more rapid rate of genetic change in the herd.
Another factor in our key equation is genetic variation. In this context genetic variation refers to how much difference there is between breeding values for a given trait within the population being considered. This one is important, but does not require too much discussion to understand. A given population cannot excel beyond the best genetic material present in the gene pool of that population. Genetic variation is not something that is easy to manipulate within a herd. Whatever it is, it is. The only quick way to increase the genetic variation is to bring in animals that are widely different genetically from outside of the population . If these new additions are far superior genetically, then the rate of change toward the superior position can be rapid. If the new additions are inferior genetically then the rate of change in an inferior direction will also be more rapid. Obviously, not a desirable result. This is why it is dangerous to bring in “new genetics” just for the sake of breeding to animals that are not closely related to the original herd. The breeder must be certain of what the expected progeny differences are that these “new genes” will produce. Ideally a new herdsire should be carefully progeny tested before breeding him over your herd.
Generation interval, like heritability and repeatability, is a concept that is very often misunderstood, even by experienced animal breeders. The generation interval within a herd or within an entire species is defined as the amount of time necessary for one generation to be replaced by the next generation for breeding purposes. In the context of the rate at which genetic change in a closed herd occurs, the best definition of generation interval is the average age of all parents in the herd when their selected offspring are born. From a physiological stand point we can speak of minimum generation interval as the least amount of time for a male and female born today to produce an offspring. Let’s say for the sake of discussion that a female born today needs to reach the age of 18 months to conceive, and another 11 months of gestation for the cria to be born, a total of 29 months for the female. Again let’s say for the sake of discussion that a male born today needs to reach the age of 36 months to conceive, and again the cria will arrive after 11 months of gestation, a total of 47 months for this male to produce an offspring. The average age then between 29 months and 47 months is 38 months. Physiologically then we can say that in this example 38 months is the physiologic generation interval. However, the genetic change in the overall herd will not be this rapid unless the parents of these offspring are no longer allowed to breed. It is unlikely that in any livestock breeding enterprise the breeding stock is culled after one offspring. Yet each time that original pair (generation) breeds again the genetics in play are exactly the same as the first time. Therefore if we are to have a realistic number to represent generation interval for genetic rate of change we must average the ages of all breeding stock.
Beef cattle for instance usually have their first calves at age two, but some have their last calves in their teens. If we look at the average age then of beef cattle when their selected offspring are born we find the average age in most herds is four to six years old. We can say then that the generation interval is four to six years for female beef cattle. I hesitate to guess what the average age for female alpacas still producing offspring is in the US today. On any given farm the average age will be different. Generation intervals tend to be less for males as they are more easily replaced since one male can easily service upward of 50 females in a year if so desired. Females are usually kept in our breeding programs for as long as they will produce however, for obvious economic reasons. We must understand however that from a genetic standpoint this is slowing down the rate of genetic change in our herds since it increases the generation interval substantially to have several ten or twelve year old females contributing cria to the gene pool each year. The breeder that can afford to eliminate these females from his breeding program sooner will increase his rate of genetic change, all other factors being equal.
Another way to lower the generation interval is if husbandry practices and/or genetic selection leads to animals that reach maturity and are able to reproduce earlier. This must be considered carefully however since an advantage of decreasing generation interval may be offset by the disadvantage of breeding young and immature animals if it leads to dystocias, reproductive disorders or other detrimental effects on the health of the parent or the cria.
Other Considerations Relative to the Factors of the Key Equation
Having discussed these four factors individually, there are other practical considerations that must be taken into account. Based on what has been written here so far, we would prefer to increase our accuracy of selection accuracy, selection intensity and genetic variation as much as possible while at the same time decreasing the generation interval to its minimum. This would clearly give us the most rapid rate of genetic change. Is it possible to do this? Well, not exactly, because there is often a connection or linkage between two or more of these factors as well as some practical risks involved with attempting to apply the mathematical concepts above with the real practice of breeding animals.
For instance, we said that the best way to increase selection accuracy is through accurate breeding value determinations. We also showed that this accuracy is maximized by having the most abundant progeny data. This progeny testing, however, by its very nature must increase the generation interval because it takes at least one generation to collect the progeny testing data to accurately select the male we want to use over our herd. In other words, it is not possible to have a three year old male alpaca with a highly accurate BV (breeding value) that was calculated from 100 of his progeny if he has just become mature enough to breed!
Accuracy of selection and intensity of selection also have an adverse relationship due to practical considerations. If we want to have highly accurate breeding values to use when choosing a sire then he must have a large number of offspring from which to garner data. The number of females available is limited however, so if we want progeny testing on more males, so that we have more from which to choose and can thus increase our intensity of selection by choosing only the best one(s) to breed, then that means we will have fewer records on each male from which to make our choice. Increasing selection then requires decreased accuracy.
Another problem with intensity and accuracy is that if we are very intense in our section, say choosing only one or two most promising males there is a selection risk that these males may not be as good as predicted and we have used them widely in our breeding program. The same risk as letting a sire have a high breeding impact on our herd based on his beautiful phenotype without having any progeny testing to prove his breeding value.
This article has expanded on the four factors affecting the rate of genetic change as first introduced in “Alpaca Genetic 102”, selection accuracy, selection intensity, genetic variation and generation interval. It has touched on some of the conflicts that naturally occur when trying to optimize all four of these factors.
There are numerous other possible interactions and contradictions between separate factors of our key equation that would lead to a more lengthy discussion than allowed for in a magazine article. Suffice it to say that each breeder must take into account all of these factors, his own breeding goals, the characteristics of his particular herd, his economic considerations and his own comfort zone toward various risk factors in order to devise an educated breeding program. The next articles will discuss some strategies for selection; more detailed understanding of heritability and repeatability and techniques to increase them both; and multiple trait selection concepts.
About the author
Dr. Wayne C. Jarvis, in addition to being an alpaca breeder, lives with his wife and five daughters and three grandchildren at Sixth Day Farm in Holley, NY where they breed Saanen dairy goats, Colored Corriedale Sheep, Registered Cormo Sheep and French Angora rabbits as well as having layer hens, and Guinea fowl. Dr. Jarvis studied chemical engineering, chemistry and biology, including genetics, as an undergraduate, and has been interested in genetics throughout his career as an oral and maxillofacial surgeon treating developmental deformities of the face and jaws. He lectures frequently around the world on bone graft and implant reconstructive surgery for the jaws, implantology, and other scientific topics.
Richard M. Bourdon, Prentice Hall, Understanding Animal Breeding, 2000
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Geoff Simm, Farming Press, Genetic Improvement of Cattle and Sheep, 1998
Malcolm B. Willis, Blackwell Science, Dalton’s Introduction to Practical Animal Breeding, 1991