The optimization and impacts of animal breeding

Animal breeders work with two tools: selection and pairing. When animals are selected for breeding, the frequencies of alleles in that population always change. Some alleles may even be lost, or become fixed, when the allele is the only one in that population. Both of these chances lead to losing genetic material. This loss of material may go unnoticed for a long time, because following alleles in practical breeding is not feasible. To start with, there must be enough genetic variation in the population to allow for any genetic progress.

Selection intensity affects strongly to the progress of breeding. Selection intensity means the percentage of animals chosen for breeding from a particular population. The formula is i = S_P/σ_P, where Sp is the selection difference. i expresses the selection difference measured in units of standard deviation from the population fenotypical mean. Let's say we select sheep based on their weight at 1 year of age. The population mean is 55 kg, and the mean of the chosen animals is 67 kg. Standard deviation is 10 kg. Then i = (67-55)/10 = 1.2. From a selection intensity table (such as this), we see that i of 1.2 means we'll select a bit less than 30 % of the animals in the population. Usually i < 1 is weak selection, and i > 2 is strong selection.The less animals we choose, the more genetic progress we get.

However, the amount of offspring per animal and inbreeding may limit our choices. To keep the population size stable, there are minimum amounts of animals which should be chosen. For cattle, the limits are 50-65 % of females and 0,5-1 % of males. For poultry, 1-2 % of females and 0,5-2 % of males is enough.

Optimizing genetic progression in breeding programmes

The values in The Formula (seen on the left) have connections to one another and to animal properties. Females have less offspring than males, some properties can be measured only from females, and they are sexually mature in different age (difference in L).  The differences can be counted for by calculating the progression as the sum of the genetic value of females and males, divided by the sum of time between generations.

Since different information sources have different weighting factors for females and males, the genetic values are calculated differently. For cattle, cows are evaluated based on their own results. Bulls are evaluated based on the results of their offspring.

Dependencies of the values in the formula are various:

• increasing i by producing more offspring per animal increases L
• using the results of offspring to increase r_TI increases L
• using pedigree information of lower L lowers r_TI
• increasing i by relying on individual evaluations only lowers r_TI

So, to optimize ΔG, every factor must be optimized at the same time!

Pairing strategies and inbreeding

Pairing comes always after careful selection. Three pairing strategies exist: random pairing, assertative pairing and pairing based on kinship.

Random pairing means simply pairing the selected animals randomly. In this strategy, alleles inherit randomly, and the population follow H-W equilibrium (if also random selection is used).

Assertative pairing means that fenotypes of the animals are considered when pairing them. It may be positive or negative. In positive assertative pairing, the animals with the most extreme results in a trait are paired, creating offsprings with extreme results. For example, pairing large bulls with large cows or small bulls with small cows creates either very large or very small calves. Positive pairing temporarily increases genetic variation. Negative assertative pairing, or pairing different animals, is about compensating or fixing trait results. When large bulls are paired with small cows, medium-sized calves are born. However, the calvings will be extremely difficult, so it is important to choose the pairings correctly (small bulls+big cows works much better).

Pairing based on kinship is either avoiding or using inbreeding. Inbreeding means pairing animals which are closer relatives than "cousins". Inbreeding increases the amount of homozygotes, which leads to inbreeding depression. First production traits are affected: milk yield starts to decrease, amount of meat produces decreases and so on. If the inbreeding continues, resessive traits (usually illnesses) became more common, and fertility and survival traits start to decrease as well. The opposite of inbreeding depression is heterosis, which happens when two completely different lines are mated. Heterosis is strongest in the F1 generation, and it increases the amount of heterozygotes. Heterosis may lead to offspring which are better than the average of their parents, thus exceeding breeding expectations.

Note that some level of inbreeding cannot be avoided. Look far enough in any pedigree (even your own), and at some time there will be same names. This is especially true in small or new animal breeds, but works on humans as well. The blog of Discovery magazine states that 1 out of 200 men are direct descendants of the furious fighter (and lover) Genghis Khan!

Long-term impacts of animal breeding

Some of the basic questions of animal breeding is "how far can we go?". Have the cattle populations today reached their production maximum? Is there anything left to improve, and do we have enough genetic variation left? Ethically, one can ask are we doing the right thing? Are we really improving the animals, or just improving their productivity at the expense of their health?

Two extremes. Belgian Blue cows cannot live or give birth normally
due to their extreme size and double muscles. "Teacup puppies" are
very small, and have delicate health with extra risk of bone fractures.

 Genes and traits have correlations. Improving one trait may improve or worsen another trait. While we can estimate ΔG, genetic frequencies change, and mutations happen. Additive genetic variance decreases due to selection (Bulmer-effect). And, we still have only a basic understanding of geneology, with much to learn about interactions between genes and genetic regulation. Estimating the long-term effects on animal breeding is thus just guesswork.

We can try to estimate it using quantitative theories or using selection on populations with short L (mice, microbes, plants). Through genetics we can model changes in allele frequencies, thus estimating changes in heritability and genetic regression. Biology can help us to understand what we are doing to the animal: can it survive with the traits we've created for it, are they useful or harmful? Many examples from dog breeds may come to mind at this point. Due to positive assertative pairing, some breeds are genetically sick. Instead of banning the breed, though, the situation can be corrected by negative assertative breeding and pairing across
breeds. And again, developing traits has its price. Increasing animal's production increases it's need for feed and susceptibility to problems in metabolism. Reducing extreme traits reduces health risks, and pairing across breeds increases variation but decreases the level of racial purity.

Determining feed digestibility

When discussing animal feeds, the terms solubility and digestibility may easily be mixed or misunderstood. Solubility means the degree to which the food breaks down to smaller particles, for example how much of protein breaks into amino acids. The digestibility of a feed determines the amount that is actually absorbed by an animal and therefore the availability of nutrients for growth, reproduction etc. For example, wood, grass silage and straws have the same amount of gross energy, but due to the differences in their digestibility, only  grass silage is useful as a feed. See more terms explained from FAO's site on animal nutrition.

Digestibility of a feed must be originally determined in animal tests. When the base values from solubility and digestibility are thus gained, more tests can be done in laboratories. Lab tests are never equivalent to tests done on living animals, but on the basis of animal welfare, speed, repeatability and cost-effectiveness, they are widely used. This text will cover some basic methods of determining feed digestibility in vivo or in sacco, "in a living animal".

Before any in vivo feed studies, each animal goes through an adaptation phase. For cattle the phase may last 1-2 months, but only 3-5 days for pigs and 1-2 for poultry. During the adaptation, the animal gets used to the new feed, and estimates can be made about its palatability. If the animal will be in a collection pen or crate during the test, it will be there during the adaptation phase too, getting used to the new environment. The actual testing phase lasts from a day to a week or two, depending on the size of the animal.

Total collection

Total collection is a quantitative research method, where the animal is kept in a collection pen or cage. Collection cages used to be very tight, preventing the animal from moving more than a few inches backwards or forwards, but they have now been banned due to obvious animal welfare issues. The crates are designed so that all feces can be collected, and some percentage of it will be analysed. If the balance of nitrogen is studied, then urine will also be gathered and analysed. The animals are fed approximately 90 % of their normal feeding levels, so that there's no leftover feed. All necessary vitamin and mineral supplements are given during the test as usual.

(c) University of Helsinki

Total collection tests can also be done for animals in pasture or in group pens. To get individual results from each animal, the animals are fitted with harnesses or other means of carrying collection bags, which are emptied at least once a day. The harnesses cannot be too heavy or uncomfortable, because stress and pain would immediately affect the animal's behavior and metabolism. A typical collection method for pigs is to glue a plastic bag to its rear end, but it raises concerns of animal welfare.

Total collection method can be used to study the effect of one feed (direct method), of basic feed + test feed (differential method), or of feeds in different amounts, for example 10, 20 and 30% of wheat (regression method). Knowing the chemical composition and dry matter (DM) content of the tested feeds is crucial.


When choosing animals for a total collection test, make sure that

• the animals are of the same age and size
• the feed given is processed identically every day
• the amount of feed eaten is recorded for each individual animal
• feces (and urine) are collected at the same intervals, often enough and without contaminating the samples
• consider the impact of proteins and fat to the digestibility of the feed
• use identical and accurate analyzing methods

Calculating the results

All values are g/kg DM if not stated otherwise. The formulas do not apply for regression method.

Digestibility of the feed:  

(amount of feed eaten - amount of  feces ) / amount of feed eaten

or

1 - (amount of  feces / amount of feed eaten) * 100

Digestibility of different nutrients (multiply with 100 to get the results in percentages):

(Nutrient content in the eaten amount of the feed - Nutrient content in the feces)

 / Nutrient content in the eaten amount of the feed

.
Digestibility of the feed and nutrients when using the differential method:

(amount of test feed eaten - (amount of  feces - undigested basic, non-test feed))

 / amount of test feed eaten

Marker method

Marker method can be used when total collection is not possible or feasible. Marking method includes adding a marker substance to the feed, and then analysing the amount of marker feed in the feces. This method may be conducted with the animal in a collection cage, but is also usable for grazing animal.

The marker substances used in marker method trials must be safe for the animal, travel at the same speed than the feed in the digestive tract, they can not impact the digestibility, mix well with the feed and be stabile. The marker must be detectable and measurable even in very small amounts. Markers can be either liquid or solid, and either added to the feed or insoluble parts of the feed (such as insoluble ash). Common markers used are

• titanium oxide TiO₂
• chromium oxide Cr₂O₃
• ytterbium acetate
• litium
• strontium
• cobalt EDTA
• chromium-mordanted straw (straw covered with chrome, fixed in place with a mordant)

Calculating the results
All values are g/kg DM if not stated otherwise.

Measuring the digestibility in a certain spot in the digestive tract

Fistulated horse (c) Todd Huffman

In some cases, it is important to measure how nutrients are digested in different parts of the digestive tract. This is especially true with ruminants and amino acids. Amino acids which are absorbed in the rumen are used by the rumen microbes, and the animal itself gets only the amino acids which absorb from the small intestine. Even the monogastric pigs can use only the amino acids which absorb from the small intestine, and some trials are done on horses as well.


These trials (animal tests) always need animals with a fistula and/or a cannula. The fistula is usually installed to the rumen or to the beginning/and or end of the small intestine. Sometimes the rumen fistula may be connected to the abomasum with a long tube, enabling collecting samples from the abomasum.

The idea of an animal having a hole in it, and people digging the innards of the animal through the hole is (and should be) very distressing. People who work with fistulated animals may not be the most reliable source, but they claim the fistula causes no discomfort for the animal. Permits for conducting and animal test are needed before the operation. Fistulas are always  made by experienced vets.  Sedation and local anesthetics are always used, and left to heal for two months under direct supervision and care. After healing, the fistula is painless even when used. If the animal is used to being treated (brushed, milked, petted etc), it shows no signs of pain, discomfort or fear when the fistula is opened and a sample is taken. At least fistulated cattle live their lives normally, milking, eating, calving and socializing without problems. However, health and welfare risks exist and must be minimized or removed before proceeding.

In sacco -method (ruminants only)

Fistulated cows (c) David Wilson

In an in sacco -method small nylon bags are filled with the test feed, and inserted into the rumen.  Like in the previous method, in sacco also requires fistulated cows. Being small and light, the nylon bags do not cause discomfort, or affect the rumen functions. It is an reliable way to measure the solubility of certain feeds. Insoluble fibres can be most reliably measured in sacco. The nylon bags are so tight, that no feed particles can escape from the bag or enter it. Only the rumen microbes are able to affect the feed in the bag.

After the bag is taken away from the rumen, it is washed with clean water, and then dried. Single bags are removed after a certain time, and the weight and contents are then analyzed to study the solubility of the feed. Most often bags are removed after 2,4,6,8,10,12 and 48 hours, but for insolubility tests, last samples may be taken as late as after 72 and 96 hours, or even 12 days. Determining the solubility of the tested feed is a matter of comparing the composition and weight of the feed samples before and after the in sacco test.

Apparent vs true digestibility

The digestive tract secretes several substances, which get mixed with the feed and eventually the feces. Most commonly tthey are proteins or other nitrogenous compounds. These animal-based substances, known as metabolical or endogenous secretions, must be considered when analysing digestibility. Apparent digestibility does not consider endogenous secretions, unlike true digestibility. True digestibility for proteins, amino acids and fats is always higher than apparent.

Endogenous excretions include bacteria, enzymes, endogenous peptides, amines, urea, mucus and dead cells of the digestive tract. Measuring the levels of endogenous secretion is difficult, so common factors are used to estimate them. Cattle is estimated to secrete 5 g of endogenous matter per a kilogram of eaten dry matter, while pigs and rats secrete 1 g. 

More information:

FAO: Animal nutrition
University of Florida, dept of Animal Sciences:  Digestibility
E R Ørskov: Methods of estimating nutritive value of fibrous residues

The value, quality and preservation of silage

(c) ukagriculture.com

Silage means forage, which is made of grass or other organic material, and has been preserved with methods based on acidity. Preservation, ensiling or silaging is the process where the spoilage of the forage is prevented by lowering it's pH either with acid or by adding anaerobic, acid-producing fermentative bacteria.

Silage, like any animal feed, has two values: a feed value and a dietary value. Feed value means the energy content and the nutrients of the feed for the animal. Feed value includes the chemical  composition, digestability and the rate of metabolisation. Dietary value is a wider concept, which includes the factors directly or indirectly affecting the metabolisation rate of the silage. These factors are the hygienic quality and the feed value of the silage, plus the animal's need for nutrients and the amount of feed it eats.

Microbial quality of silage concerns the amount of volatile fatty acids (VFA) and the pH of the feed. pH clearly over 4.2 is a sign of failed preservation, and increases the risk of the feed spoiling. pH can rise if unwanted bacteria proliferate in the silage, fermenting proteins into ammonia. VFAs and a high amount of ammonium nitrogen from the total amount of nitrogen also indicate the existence of unwanted microbes. Sometimes microbes (spores of Clostridium, yeasts, molds) can be determined from the feed directly. It is not, however, a routine analysis.

No animal eats just one type of food, but the values of the feeds no dot add up. Different feeds in a diet affect one another. For example, fats decrease the digestability of roughage, but proteins may increase it. These combined effects must be considered when planning for the indoor feeding season. The aim of feed planning is to maximise the "output response", the amount of the feed the animal can use for it's maintenance and production. Maximising the output response must be made cost-efficiently, and without endangering animal welfare and health.

There are several reasons why knowing the quality and value of the forage is important, be it silage, hay or any other feed:

• planning a cost-effective and well balanced diet requires knowledge on the feeds
• giving the right amount of added vitamins etc requires information on the content of the silage
• weather conditions and preservation methods can change the quality of the silage during storage
• dairies must be assured that the feed does not endanger the quality of the milk or any milk products made 
• improving the silage making process is based on knowing the weaknesses and strength of the current process and products

 

Aspergillus-mold on a maize silage.
(c) North Dakota State University

Preservation of silage

Silage is preserved mainly by three different ways: with acid, with acid-producing bacteria or without any additives. Preservation with acid is usually the most effective method, since it lowers the pH faster than the other methods.When the pH decreases, the plants stop breathing and unwanted bacteria dies. Anaerobic preservation is vital for keeping mold and yeast away from the feed, and for promoting the growth of useful lactic acid bacteria. Low amount of moisture also helps to prevent enterobacteria and Clostridium. Silage contaminated with unwanted microbes can endanger the health of the animals and/or the people handling the feed, and affect the quality of products derived from the animal.

There are roughly five classes of preservatives used in silaging, and they vary by function. Some types prevent others: using strong acid to quickly decrease the pH leads to minimal production of lactic acid.

1. Promotes fermentation
   - Lactic acid bacteria, enzymes, sugar (molasses)
2. Prevents fermentation
   - Formic, lactic and mineral acids
   - Nitrite and sulfite salts
   - NaCl
3. Prevents spoiling in aerobic conditions
   - Propionic acid
   - Benzoe and sorbic acid
   - Lactic acid bacteria
4. Nutrients
   - Urea, ammonia, minerals
5. Sorbents (used to absorb the effluent)
   - Straw and beet pulp

 Preservation method may change for silage of different types due to the different buffer capacities of feeds. Grass+legume-silage can resist the decreasing of the pH much better than barley, so different amounts of preservatives are needed. Fermentation factor describes the easiness of preservation for a type of silage. The formula is

dry matter content (%) + 8 * (sugar content/buffer capacity)

A fermentation factor over 45 predicts only a small probability for wrong types of fermentation, i.e. a well-preservable silage.

Fermentation

There are many forms of fermentation, based on which microbes are involved. For silage, fermentation is the process where anaerobic microbes convert sugars (glucose, fructose and saccharose) into lactic acid. The silage must also have enough sugar to maintain fermentation. If the preservation fails, unwanted microbes proliferate, causing faulty fermentation. These microbes produce VFAs, ethanol and especially ammonia, which increases the pH, spoiling the silage even further. Factors affecting the quality of fermentation and thus the whole process of ensiling are

• chemical composition of the feed
• microbiological content
• time of harvest
• weather conditions during harvest
• technique of harvest
• type and amount of preservatives used
• dry matter content of the feed (wet feed needs more preservatives than pre-dried feed)

Fermentation does not only produce something, it also uses nutrients of the feed. The products of fermentation are always less useful for the animal than the original nutrients used. The level of fermentation should thus be kept optimal for ensuring the preservation of the silage, but also losing as little nutrients as possible. The fermentation in the silage ends naturally when there's enough lactic acid to keep the silage acidic. If the silage doesn't have enough sugar or it's pH is too high, the lactic acid fermentation stops and unwanted fermentation begins. The amount of sugar left in the silage can be used when estimating the level and types of fermentation.

The fermentation process.
(c) Engormix

Types of fermentation
The basic rule is that the drier the forage is, the less there's fermentation. The difference between the types of fermentation are also less apparent in dry forage.
 
Limited fermentation may result from using acid or other fermentation preventing preservative. pH is low, sugar content is high and there's only little fermentation end products in the silage. Proteins are scarcely dissolved, so there's little ammonia and soluble nitrogen.
Strong lactic acid fermentation occurs in well-pressed silage or when using preservatives promoting fermentation. pH is low due to high amount of lactic acid, there's only little sugar left and proteins are more dissolved than in limited fermentation. Because the fermentation is caused by lactic acid bacteria, there's not much VFAs (propionate acid, butyric acid and acetic acid).
Faulty fermentation is caused by unwanted microbes. The silage has high pH and lots of VFAs. Proteins are strongly dissolved and mostly transformed into ammonia.

Mathematics of animal breeding

As I mentioned in the post on Basics on animal breeding, this area of animal science is full of equations and mathematical models. This text will shortly list and explain some of these equations, but it will not cover them thoroughly. For a deeper understanding of breeding math, try to get your hands on Richard Bourdon's book Understanding Animal Breeding.

Hardy-Weinberg law

Hardy-Weinberg law (H-W law for short) was formulated by two scientists at the same time, hence the name. It predicts the frequencies of genotypes in a generation based on the allele frequency. The formula is simply

p² : 2pq : q² 

where p is the frequency of the dominant allele, and q is the frequency of the resessive allele (in other words, it's f_AA: f_Aa : f_aa). H-W equilibrium is a status where both the allele frequency and the genotype frequency stay unchanged from generation to another. This can be achieved only in an "ideal population", where there's no random genetic drift, no mutation, no selection, no migration, and all males can reproduce with any female in the population (free reproduction).

Example: In a population of 1000 cows, 175 are white, 600 are spotted and the rest are black. Let's pretend that the genotype for whiteness is bb, Bb for spotted and BB for black. The genotypes hold the following alleles
white: 175 * 2 =  350 b alleles
spotted: 600  b alleles and 600 B alleles
black: 225 * 2 = 450 B alleles
Total:  950 b alleles and 1050 B alleles. Relative frequencies are 0,475 for b and 0,525 for B. Relative genotype frequencies are bb = 0,175, Bb = 0,6 and BB = 0,225.

But does this imaginary population follow the H-W equilibrium? To check that, we count what the genotype frequencies should be according to the law. Now p = 0,525 and q = 0,475. So we should have p² : 2pq : q² = 0,⁵²⁵ : 2*0,525*0,475 : 0,475² = 0,276 : 0,5 : 0,224. Since these are NOT the same as the observed genotype frequencies (0,175 : 0,6 : 0,225), the population is NOT in H-W equilibrium.

Heritability (h²)

Heritability shows how much of the difference between animals is caused by genes. It has two forms: a narrow definition (h²) and a wide definition (H²). Of these two, animal breeding uses h², because it does not include dominance and epistasis, which are not  inherited. The definition of heritability is

h² = σ²_A / σ²_P  
where σ²_A denotes the variance in additive genetic impact and σ²_P the variance in phenotype. So heritability in it's narrow sense shows how much of the difference between animals is caused by differences in their breeding value. It can also be though of as the animal's possibility for genetic progress. The third interpretation for heritability h² is that it is the regression factor for the estimated breeding value (EBV) in relation to the phenotype. So the heritability value is needed when calculating the EBV.

Repeatability (r)

When calculating the EBV, we should always have several measurement results of one trait from one animal. For example, the milk yields for several lactation periods, of the amount of piglets in all of the litters of one sow. This repeatability is the correlation factor between these results, showing a linear continuation in the results for thet trait. Using repeatability one results can be combined into one when calculating the EBV. The formula for repeatability is

r = (σ²_G + σ²_Ep)/ σ²_P
where the sum of genetic variance and permanent environmental variance is divided by the variance in phenotype.

Kinship factor f_x,y

Like it's name suggests, the kinship factor has to do with relationships between two living animals. It predicts the probability that a random allele of one animal is identical by descendent (IBD) with an allele of another animal. That is to say whether that allele is inherited or not. It's important to separate IBD alleles from identical in state (IIS) alleles, where two animals have chemically identical alleles, but they're not inherited. IBD alleles are always inherited from one parent, IIS alleles are just identical but not inherited. IBS is always IIS, but not vice versa!

Kinship factor between a parent and its offspring is always 1/4. Kinship factor is 1/4 also between full sibs. The calculation formula is explained below, the example calculates the kinship between a parent and its offspring.

Additive genetic relationship a_x,y

Additive genetic relationship is simply

a_x,y = 2f_x,y        or formally        a_x,y = Cov(A_x, A_y) / σ²_A

and it shows the conformity between the breeding values (BV) of two animals (x and y). It depends on the probability of common alleles (IBD), and considers only one allele. The probability that one allele of an offspring is inherited from its parent is always 50 %. The probability that full sibs have inherited the same allele (their kinship factor) is 1/4, so their additive genetic relationship is 2 * 1/4 = 1/2 or 50 %.

If the animals considered are inbred, the formula doesn't apply.

Inbreeding coefficient F_x

Inbreeding means mating animals, which are related to one another. For example, mating full siblings or a parent and its offspring. Inbreeding coefficient indicates the probability (in percentage) that both of an animal's alleles are from the same parent (both alleles are IBD). The inbreeding coefficient of an offspring equals the kinship factor of its parents. Since a_x,y = 2f_x,y, f_x,y must be 0,5*a_x,y. Thus, the inbreeding coefficient of an offspring is also 0,5 * the additive genetic relationship between its parents.

Since inbreeding increases the risk of resessive traits and illnesses and narrows the gene pool, it is not recommended to breed animals which would have inbreeding coefficient over 10 %. 

Estimated breeding value

So let's get to the point already! Right, let's do that, and see how to calculate that magical EBV and a breeding value index.

EBV is an estimated breeding value, and it concerns only one trait. It is calculated differently based on what information we have available: one result from the animal, several results from the animal, or results from the animal and it's relatives. The same goes for the b-factor and for the accuracy (r_TI). The best EBV is calculated using regression:

(Â_i- A) = b (P_i - P) 

where (Â_i- A) is the index value, b is the regression factor, P_i is a mean of the animal's results and P is the population mean of those results. If we have only one result from the animal itself, b will be h² squared. 
A common form of the formula, when using results of only one animal, is  just I = b (P_i - P), where I denotes the breeding value index. In this case, b is calculated as

b = (n * h²) / (1 + (n-1) *r)

where  n is the number of results and r is the repeatability factor. Accuracy is still counted as h² squared.

Estimating the breeding value based on the animal's offspring looks like this:

I = 2 * b (P_i - P) where b = (p * h²) / (p-1) * h² + 4

here p is the amount of offspring. The formula is based on the assumption that we have one result from each offspring, and all offsprings are half-sibs. In this case the accuracy depends on the h² and amount of offspring.

Basics of animal breeding

Animal breeding is not just about pedigree dogs, champion cats or winning horses. Breeding aims at improving the genetic level of a certain trait in a population. First, laws, politics and regulations set the framework for animal husbandry. Second, a breeding programme is needed to establish common goals for what the breeders aim at. The programme can be about improving the genetics of the population, or about preserving the genes. What traits should be improved, and how to stress each trait in relation to the others? Third, a system is needed to store the measurable metrics of the traits which the breeders are interested in.

Breeding is based on two techniques: selection and pairing. They're not synonymous. Selection is about choosing which animals to use for breeding. Can one mate animals of different breeds? Which are the best breeds and animals in this situation and in this production environment? For example, one cow might excel in a tie-stall, but be run over in a free-stall barn. Certain cow breeds tolerate cold environments better than others, etc. Pairing happens only after the selection, when the selected animals are used for breeding.  To make these decisions, breeders need information about the animal itself, it's parents, sibs and possibly it's offspring. The gathered data is then used to answer one question: will the offspring be genetically better than their parents?

Breeding is full of equations. The foremost is simply P = G + E. But because genetics are never that simple, the equation is actually

P = µ + G_A + G_D + G_I + E_k + E_s

where P = Phenotype, everything about the animal which can be seen or measured
µ = the mean value of the trait in the population (for example, milk yield)
G = genes, where A denotes additive genetic traits, D dominance and I epistasis
E = environment, which may affect either positively, negatively or not at all to a given trait (for example, illnesses and quality of feed). E_k stands for random errors, and E_s for systematic errors.

As the equation suggests, what we see in an animal is created and modified by it's genes, the mean of the population and the environment. Genetically identical animals (clones) can be very different if they are raised in different environments. Then again a genetically superior animal can produce well even if the environment is less than desirable.

Comparing animals

If we're about to select animals and then pair them, we should be able to compare animals. The selection is based on measurable information, which can be gathered and combined. For a single trait each animal can be assigned a  calculated breeding value, which changes each time more information is gathered from the animal. The more information is available, the higher the accuracy of the breeding value. The formulae for calculating the breeding value (BV) and the accuracy may vary in each country.

Since the environment cannot be calculated into the value, it must be evaluated separately for systematic or random errors. That's why the formula above has two E's (Ek and Es). Systematic errors affect the BV results systematically, i.e. always the same way. Age, gender and permanent environmental conditions are systematic errors. Young animals are smaller than adults, males cannot produce milk, females produce less offspring than males etc. Systematic errors can be predicted and must be corrected when calculating the BV to make the results for all animals comparable. Random errors are errors which cannot be corrected. They just happen, like misspelling the results or a measurement error. Factors affecting the BV are listed below.

Strengthen BV or accuracy	Weaken BV or accuracy
Accuracy of data Corrected systematic errors Data from several offspring Data from parents Data from sibs and half sibs Genomic information Wide range of reference data from other animals in the population	Only a few results Random errors No data from offspring or relatives  No genomic information available Low heritability of a trait No or only little data about the animal population