This sexed semen article is a copy that was published in the Texas Dairy Review in June 2010 where you can find here. I thought it would be of interest to my readers. It might be a little out of date, but I think I can add extra post in the future about the subject of Sexed Semen. – Enjoy!
Sexed semen has been one of the newest technologies available to dairymen for reproduction of their herds in the past few years. The mechanically-engineered Gender Enhanced Semen (GES) has been around since the early 1980s but did not hit the commercial market until the early 2000s. Once it was released, dairy producers were anxious to use the marketing tool to increase heifer population and ultimately enable their dairies to produce more milk.
But, is the industry headed down the right path with the use of sexed semen? While the majority of dairymen, scientists, and big A.I. companies may say “yes” because of its obvious benefits, others are not so sure and feel it adds to the overwhelming problems and contradictions already present in the dairy industry.
Competing without sexed semen
Eric Danzeisen, partner with Wout Vander Goot, of Sierra Desert Breeders, based in Tulare, California, began their AI breeding service in 2007 and have found they can successfully compete in the AI market without selling sexed semen. Within three short years, they have rapidly grown their core customer base, even during the recent economic recession.
“We are doing as well or better than some other AI breeding companies. We don’t sell sexed semen because of our concerns,” Danzeisen said. “We saw what happened with BST after it was the big rage and then dwindled away. We don’t know if that will happen with sexed semen or not but it’s a concern we have considered.”
Old fashioned AI
Danzeisen and sales representative Josh Verburg said they can attribute most of their business success to long hours and hard work. “You just have to get out there and look at the genetics if you want to sell good semen to dairymen. We don’t just look at numbers on a piece of paper—we check out the genetics the old-fashioned way – through the best cow families and looking at milking daughters.”
Danzeisen and Verburg said personalized service and fashioning their business away from the popular trend of sexed semen, sets them apart from other AI companies. They are convinced that conventional AI breeding has proved its effectiveness over its many years of use but since sexed semen is relatively new, no one really knows what can happen with it in the future.
Overuse of sexed semen
The breeder specialists said problems in the dairy industry become even more apparent with the overuse of sexed semen. In the latest episode of spiraling milk prices, dairy industry experts across the nation claim the biggest part of the price problem is due to too much milk on the market.
“That fits the popular trend of growing your milk production,” Danzeisen and Verburg said. “But, when you add more and more heifers to the mix, and keep adding them, it becomes an overall production problem for dairymen that works against them, instead of for them.”
Economics show too much milk diminishes negotiating power that results in milk prices bottoming out, as seen at the end of 2008 through 2009. Cooperatives maintain they cannot get good milk prices when processors have an overabundance of the product—and claim the responsibility lies with its producers. Meanwhile, the value of the world’s most unique and nutritious commodity becomes insignificant.
No stopping point
“This popular dairy philosophy of ‘more is better’ provides no stopping point,” Danzeisen said. “My producers feel they have to grow to keep up with modern trends to compete in the market and it would be next to impossible to get a producer to limit his own production when his peers or neighbors will not.”
Danziesen sees this as the same mindset for the overuse of sexed semen and “more” can be detrimental to the overall financial health of producers and the entire industry.
Contradictions in financial reward
One dairy producer mentioned to Danziesen the incredibly high cull rate among some producers. But, to cull cows, only to go out and buy more sexed semen to increase a herd, is not a good business decision. This is especially true, the producer added, when considering it takes about $1800 to grow out a heifer yet it is only worth about $1100 on the market. Where is the financial reward in this?
Another contradiction is Cooperatives Working Together (CWT), when a few years ago it initiated an effort to curtail milk production. “Dairy producers pay .10 cents per hundredweight into the program to kill cows, yet, they turn right around and buy sexed semen to grow more heifers which means more milk—the very thing they are trying to get rid of,” Verburg said.
“Killing 280,000 cows last year and producing approximately 300,000 new heifers at the same time, does not make sense,” he added.
Control in world market
Danziesen pointed out that as the U.S. enters a world milk market, American genetics are very much in demand. “Third world nations are now constructing basic, and in some cases, huge infrastructures to compete with our milk markets. It is crucial to minimize the effects of American genetics through sexed semen worldwide.
“If we have added 300,000 new heifers, how many more heifers were produced worldwide with the best genetics in the world?” Danzeisen asked.
In today’s industry, producers are aware of the importance of exhibiting a good public image. As seen with the public’s outrage of BST, it is becoming clear the public is moving toward natural and organic products and does not take well to products that are mechanically engineered.
“As AI breeders, we realize there are more benefits to sexed semen than not. But, it isn’t natural to sort semen to get exactly what you want and it hasn’t been around long enough to see if the public will accept this practice once they discover it,” Danziesen said.
Since some cooperatives in the past required producers to quit using BST, Danziesen wonders if they will ask producers to quit using sexed semen. “Not just because of the public, but also because of the overpopulated heifer industry.”
Experts have said sexed semen is not a “band aid” for poor reproductive performance and advise producers to focus on keeping their herds healthy and disease-free.
Drawbacks against rewards
Thomas R. Overton, associate professor, DVM, MPVM, Dairy Production Medicine at the University of Georgia, College of Veterinary Medicine, addresses sexed semen in his article, “Economic considerations of sexed semen on your dairy,” (2007).
He outlines the genetic improvements sexed semen provides but also points to its drawbacks and the risks that should be weighed against potential rewards.
In part, he said while the use of sexed semen may increase the proportion of live female calves born yearly, more pregnancies are needed to return cows to the next lactation than are needed to produce the necessary herd replacements. “Producing more heifers than are needed by the dairy industry is not desirable,” Overton said.
He said the downside to sexed semen technology for increased replacement heifers is: every cow should not produce a heifer calf; only the best cows should be producing daughters for maximal genetic gain; there is an extra cost for sexed semen; and, there can be problems with reduced fertility.
Too many heifers, less value
Like too much milk, Overton said too many heifers in excess of industry needs will have less value. He added the use of sexed semen is risky if the producer is only trying to capture value from high heifer prices.
Overton said a major advantage to sexed semen for herd expansion is it increases biosecurity. But, he advises producers to consider filling rates for barns and pens, meaning many expanding herds will still need to buy cows. He said producers should plan for the extra heifers and determine if there is enough room for the increase.
Extra cost considered?
“Hutches, pens, labor, capital, feed supplies, and storage facilities are some of the many areas that can become overwhelmed if heifer numbers increase by 70% (from a 50% heifer ratio to an 85% ratio),” he said.
Danzeisen and Verburg concur dairy producers should be aware of the consequences of using sexed semen. “It might make financial sense to do so on your dairy farm, but taking two steps forward yesterday might have actually depleted your bank account today.”
In the past 10 yrs. the dairy industry has made significant strides in efforts to get cows pregnant, we’ve seen reproduction improve from various factors whether it has come from improved cow transition, nutrition approach, management practices, or environment it certainly has been a focus in our herds. I am all too aware of the focus of pregnancy rate of the lactating herd with my former career in the AI Industry, until the advent and commercial acceptance of sexed semen there was little pressure put on heifer breeding. The metric that I saw used the most was, “What % was pregnant at vet check?” If this number was quite high ~90%+ then little was done to look into how we were doing in terms of heifer reproduction.
Now this is not to say that there were not producers, consultants, etc. paying attention in more detail to heifer reproduction but I’d say the focus changed almost instantly when sexed semen was commercially adopted by a couple major studs in 2005. Heifer conception rate became a metric in the cross-hairs as the costs of the heifer breeding program increased with the cost of sexed semen and the fertility drag resulting in more services and days-on-feed to get heifers pregnant. The graph below shows how a small increase in conception rate can impact a population of heifers/cows getting pregnant efficiently.
Group A Group B
Starting Head Count: 1000 Starting Head Count:1000
Conception Rate: 55% Conception Rate: 65%
# Preg/Service Animals still open # Preg/Service Animals still open
- 550.0 450.0 650.0 350.0
- 247.5 202.5 192.5 157.5
- 111.4 91.1 86.6 70.9
- 50.1 41.0 39.0 31.9
While conception rate is a very good metric in looking at reproductive results in both heifers and cows we need to focus on more metrics in our heifer breeding program. Heat detection cannot be overlooked in our heifer program, we also need to have properly trained AI Technicians, quality facilities to be able to heat detect, highly fertile service sires and proper immunization. (Chebel et al. 2010) With the above being mentioned, I’d like to focus on the “how to” in having a successful heifer AI program. Once determining the age or weight that you want your heifers to be bred at we need to focus on how we can get the heifer bred in a timely matter.
At this time I believe there are three solid options to begin with (these protocols can also be used in conjunction with one another):
- Chalking/Observation protocol
- PGF-2a induced protocol
- 100% Timed AI protocol.
The chalking/observation protocol is a common practice in the western US and involves locking the breeding age heifers daily and placing a strip of chalk on the tailhead to utilize for estrous detection. Advantages: Easy to implement if have facilities to lock heifers & low cost. Disadvantages: Does not submit heifers to insemination that do not show heat.
The PGF-2a protocol is simply determining the heifers you want bred and administering a dose of PGF-2a and observing for heat utilizing observation, chalk, or some other heat detection device such as a Kamar® patch. The animals not showing heat and thus not being inseminated can be given another shot 1 or 2 weeks (to be determined with your veterinarian) later to induce a heat on those remaining animals. Advantages: Easy to set up, get inseminations in tight window which can allow for quicker flow through breeding pen if short on space. Outcome can yield tight distribution of average age at 1st calving. Disadvantages: Requires giving shots, additional record keeping, and some additional cost.
The final protocol mentioned is a 100% Timed-AI program. In the past ovsynch protocols have not performed well on virgin heifers because heifers have 3 follicular waves vs. lactating dairy cows having 2 and the program not being set up to work with 3 follicular waves. The 5 day program with the CIDR has addressed the follicular wave pattern of heifers and is the program of choice if you want to time AI your heifers.Advantages: Heifers get bred in a tight window, faster flow through breeding pens, great option if you do not have facilities to lock heifers daily or have heifers on pasture. Disadvantages: Shot compliance is mandatory; need accurate record keeping, and additional cost.
The chart below shows a comparison of conception rate between two groups and the outcome on age fresh just due to conception rate differences. Keep in mind this is assuming 100% heat detection, if we factored in heat detection rate and open heifers at vet check this distribution would be even wider.
Group A Starting Age: 13.00
Starting Head Count: 1000
Conception Rate: 50%
Serv# #Preg/serv #Anim open % open % calv at age Age @ 1st calf
- 500.0 500.0 50% 50% 22.0
- 150.0 350.0 35% 15% 22.7
- 105.0 245.0 25% 11% 23.4
- 73.5 171.5 17% 7% 24.1
- 51.5 120.1 12% 5% 24.8
- 36.0 84.0 8% 4% 25.5
- 25.2 58.8 6% 3% 26.2
- 17.6 41.2 4% 2% 26.9
Group B Starting Age: 13.00
Starting Head Count: 1000
Conception Rate: 60%
Serv# #Preg/serv #Anim open % open % calv at age Age @ 1st calf
- 600.0 400.0 40% 60% 22.0
- 120.0 280.0 28% 12% 22.7
- 84.0 196.0 20% 8% 23.4
- 58.8 137.2 14% 6% 24.1
- 41.2 96.0 10% 4% 24.8
- 28.8 67.2 7% 3% 25.5
- 20.2 47.1 5% 2% 26.2
- 14.1 32.9 3% 1% 26.9
All these programs need the following to maximize their efficiency:
- Heifers moved in a timely manner, preferably once a week or every other week move in heifers qualified by age/weight for breeding and move out pregnant animals.
- Consistent pregnancy checks, if checking cow herd weekly check heifers as well. Don’t go more than two weeks without pregnancy check.
- High level of accurate heat detection.
- High fertility service sires.
Heifer breeding protocol suggestions (s):Please visit with your veterinarian on which alternative or variation of protocol would work best for your herd.
- Chalk heifers and heat detect. Vet check weekly or every other week. Administer PGF-2a to open heifers and missed heats/heifers not showing heat since last vet check.
- Chalk heifers and heat detect. After 2-3 days (allow technician adequate time to get chalk on heifers) in breeding pen administer PGF-2a to all heifers not bred. Continue daily chalking and insemination of heifers showing heat. 2 weeks after 1st PGF-2a shot give another shot to all heifers not bred. Vet checks same as above and PGF-2a open heifers.
- Follow protocol of Option#2 except on open heifers utilize 5d CIDR Cosynch to insure open heifers are being bred.
- Set up all heifers qualified to be bred on 5d CIDR Cosynch protocol, chalk & heat detect daily and inseminate those heifers coming into heat. Re-enroll open heifers at vet check onto 5d CIDR program.
The group at Progressive Dairy Solutions wants you to use whatever program you find best for your operation that results in getting your virgin heifers pregnant is a very efficient manner allowing you to keep rearing costs low and produce a constant flow of fresh 1st lactation animals into your milking herd.
Ricardo Chebel 2010. New Strategies for Synchronization of Dairy Heifers and Economic Considerations.
by Tony Timmons
Wout and I want to give everybody that we came in contact last week at the World Dairy Expo a big Thank You for coming by our booth and what a great week it was! We met more people than we even expected! Everything seemed to go perfect from the mid 70 degree weather to our booth being busy to having our first board meeting! 😉 We already know we will not miss next year – booth and all!
We got most of our to-do list done. Having a booth got us lots of leads on both future customers and bull prospects. We appreciate all the people who came to the expo looking for us. They came prepared with pedigrees in hand and all! We also want to give a big thank you to our representatives and a few customers who helped us work our booth including our Sersia France relationship with having a dedicated representative helping us out a lot – it is very much appreciated!
Wout and I just got done talking and we definitely felt much more noticed by the other A.I. studs this year than last year! Many more dirty looks than ever before – not all though, Genex and CRV both were very nice to us giving them both credit for the mutual respect. I think more people know who we are now because of a combination of Social Media outlets and also the awesome job Progressive Dairyman does in their advertising reach in letting people know we are around and mean business! 🙂
One of our biggest highlights of the week was sealing a deal with Mitch Breunig of Mystic Valley Dairy with the purchase of a Goldwyn half brother to Toystory and another great bull we won’t mention quite yet! We are hoping to have semen available by early February just in time for the World Ag Expo in Tulare!
As I’m driving up to JLG today to get another truck load of semen I have been looking back at what has happened in the past five years where this whole idea of starting a semen company was just an idea. We knew that opportunities were right in front of us, but I want to list a few things today that I never really thought would happen in my wildest dreams!
1. Meeting so many new people
2. Exporting semen consistently
3. Booth at World Dairy Expo
4. Breeders excited to work with us
5. Very very dedicated customers
6. Having so many bulls in multi breeds
7. Comp wondering what we are up too
8. Lots of dedicated reps working hard
9. Supporting so many families!
10. Having so much fun
My advise to anyone: Even in a tough economy don’t let anything stop you from living your dream!
Have you ever wanted to learn the basics of Embryo Transfer? Well, you get your chance October 18, 19 and 20th of 2011 at Red Knob Farm in Peach Bottom, PA! It is put on by our NE distributor Precision Diagnositics LLC by
Doug Speicher and Nate Cossaboom. These highly trained individuals are the best to learn from!
This is for anyone interested! “We always get a mix of people at our course”, commented Nate Cossaboom in the Progressive Dairyman article. “We have veterinarians, veterinarian students, experienced dairy and beef farmers, and A.I technicians taking the course.” This year we even have somebody flying out from Washington State!
Learn something new or use it as a refresher course. Space is limited and the time is near. Give Doug or Nate a call for more details!
I have a suggestion for the daughter proven proofs that they should implement right away to make everything more transparent.
They need to have a genomic % influence number on the proof. This should be easy to do and it will give us a better understanding how much genomics are influencing the daughter proven proofs of individual bulls. For example if a bull has 40 daughters in the milk proof it should show a 90% genomic influence number (or whatever it is) or if another bull has 10,000 daughters it should show that the genomic influence is only 3% (or whatever it is). As of today we have no clue how much genomics influence the daughter proven proofs. I keep hearing that the numbers are coming out very close to the genomic numbers…..ok, but if the genomic numbers are influencing those numbers by 75% of course they are going to be similar! They should have a genomic influence number for both the milk and type proofs. This would give genomics more credibility for many people and give everybody a better understanding on how much genomics influence all the numbers. I hope somebody takes a look at my suggestion!
ABS Global, Accelerated Genetics, Alta Genetics, Bull Bred, Central Valley Breeders, Creative Genetics, CRI, CRI Genex, CRV, El Toro Genetics, Genex, Genex CRI, Holland Genetics, Joe Berry, Select Sires, Semex, Sexing Technologies, TAG, TAG Genetics
I am going to rank our top 5 competitors from my point of view from time to time. I will also have a honorable mention list in alphabetical order. This will give my readers what I see in the semen market business on the ground. It also gives me a record of what I was thinking at certain periods of time. I really don’t have any numbers to back up my thoughts just my perspective in the market.
Coming in on number 1 is Alta Genetics! I’m still trying to diagnose exactly why I see them as our biggest competitor. I think it is a combination of a good technician force and salesmen with great personalities. They have a decent lineup and are over coming the low fertility stigma that they had 5-10 years ago with lots of advertising about fertility.
Number 2 competitor is Select Sires! Unlike Alta Genetics I think I know why they are at the top of the list. I believe they do have the best line up in the business and their salesmen are more knowledgeable about genetics than any other company. I think Select is much more open in telling their reps what is really going on in the business and they don’t hide any real information from their employees. I think as time goes on they will always be in the top 3 competitors for many years to come. All around solid company with line up and employees.
Third place winner is ABS! I wouldn’t exactly call it winning… They dropped like a rock! 18-24 months ago they were number 1 and unbeatable with their solid technician force….until they all left! It was amazing to see big groups of technicians leaving at different times and at different locations. I think it all started to change when they took the company public a couple years ago? They have a pretty good lineup and will continue to have good bulls for a long time. It is going to take a lot of dedication and hard work to build up what they had. I am already seeing very bad mistakes and taking the wrong roads….
Number 4 goes to non other than the Bull! He is still a tough guy to beat no matter what! He is still in nearly half of all the pens in the West Coast! He actually should be number 1 if you are looking at pure number of pregnancies bred by the bull. He is slowly dying off, but it is a slow death! The milk and feed price is sure helping him disappear! It is costing lots of money to feed that bull to breed some cows who are longer in milk! Lots of those pregnancies are not desired like they used to be…..so the battle continues!
Creative Genetics made the list! The reason they made the list is because we started marketing bulls in their niche market. They have created a great market for themselves. We are getting into this market because of long term goals and what we see to be the future in the market place in the next 20+ years. I think Creative Genetics will only grow to be a stronger competitor as time goes on.
Accelerated – Do they only sell semen over seas?
CRI – They keep trying, but don’t see much action or semen in tanks.
CRV – Huge pocket book is stimulating our economy!
El Toro – Because Bill is a great guy and a hard worker!
Joe Berry – Solid customer base, and he made the honorable mention list!
Semex – Continued growth around here….We don’t sell in Canada
Sexing Technologies – Almost #5 They let every one have sex semen besides us!
TAG – See in advertising, great bulls, but not many results…hope they grow.
Productive Life! It is what every dairyman wants out of his cows! It is the reason why we are in the business we are in! But what is it exactly? I can not find any one spot where they show the calculation in this “number”….so I am going to keep an ongoing blog on this subject. My goal is to better understand what Productive Life is in a bulls proof….Here you go!
Simple definition of Productive Life (PL)
Productive life measures how long dairy cows survive in a herd after they calve for the first time. It is based on calving dates, culling or death dates, and days in milk (based on dry dates) in each lactation for cows on DHI test. Cows receive credit for each month in milk, including time beyond 305 days of lactation, starting with their first calf and continuing until they die or are culled from the herd, regardless of age. This approach differs from genetic evaluations for milk production, which include only the first five records, even if cows continue to make additional records. Each month in production receives a slightly different weight based on a standard lactation curve, so that months around peak yield receive more weight than months in late lactation. The heritability of PL is low at 0.085, and cows express this trait only once in their lifetime.
PL is a difficult trait to improve through selection because of low heritability and expression of the trait late in life. Genetic evaluations for PL in AI bulls rely on genetically correlated traits when progeny are too young for complete lifetimes. Traits used for predicting PL on younger cows include yield traits, fertility, somatic cell score, the calving difficulty traits, and the three type composites shown in Table 1. Proofs are expressed in months of PL.
If you seem to be scratching your head…I will simplify it for you with the calculations!
Now for the calculations that I found:
Development of Diminishing Credits for PL
The diminishing credits approach to redefine PL imposed no restriction on age or lactation length of the cow. The credits were based on population lactation curves across 999 d of lactation. Test-day data, available at AIPL-USDA for Holstein cows that had calved from 1997 to 2003, were used to obtain the suitable prediction formulas for lactation curves for the population. After editing, there were 903,579 lactation records of 305,202 cows with lactation lengths varying from 5 to 999 d. Initially, descriptive statistics such as means and frequency distributions of DIM were investigated Journal of Dairy Science Vol. 89 No. 8, 2006 for each parity to determine the variability in length of extended lactations of Holsteins. Three parity groups were defined as first, second, and third or greater (up to 9 lactations) based on the differences in shape of the lactation curves. Curves may differ for very old cows, but few records were available to estimate these shapes.
Lactation curves for each parity group were fitted to the average daily yield of cows that remained in milk for each given day of lactation. Lactation curves described in the literature (Wood, 1967; Rook et al., 1993; Dijkstra et al., 1997; Pollott, 2000) and the multiphasic curves of Grossman and Koops (1988) were tested using the PROC NLIN procedure in SAS (SAS Institute, 2000). However, the fit was poor for production beyond 305 d, as seen earlier by Grossman and Koops (2003). During the later stages of extended lactations, the observed yields exceeded the predictions. This is in part due to the prediction curves in this study being based on only the cows still in milk at each day of lactation. Therefore, the following empirical model (a modification of the model of Dijkstra et al., 1997) was used to estimate the curves for each of the 3 parity groups:
Yi,t= β0,i + β1,i e[β2,i(1 − e−β3,i t)/β3,i −β4,it]
where Yi,t is the average test-day yield on the tth day in milk (t = 1, 2, . . ., 999) for the ith parity group (i =1, 2, 3), and β are curve parameters.
Cows must produce at a certain level to cover costs, and only when they exceed these costs can they produce a profit. Analogous to this concept, a baseline (β5) was imposed for all parities, and only the yield above the baseline (Yi,t − β5) was credited in PL. Introduction of a baseline altered the credits assigned to each day of lactation and consequently improved the statistical properties of the PL derived. The baseline (β5) of 13.62 kg (= 30 lb) was a compromise that slightly improved heritability of PL and was used for all parity groups. The USDA recently changed from a mature equivalent basis to a 36-mo equivalent in adjusting for age. Thus, we chose the average daily yield during the first 305 d of the second parity (Y2,305= 35.09 kg) as the base milk yield for deriving credits. The credit for the tth day in milk of the ith parity group (ωi,t) was equal to the yield deviation from the baseline on the tth day in milk (Yi,t − β5), proportional to Y2,305 − β:
ωi,t = Yi,t − β5/Y2,305 − β5 =
β0,i + β1,ie[β2,i(1−e−β3,it)/β3,i − β4,it] − β5 / ∫ 305 1 β0,2 + β1,2 e[β2,2(1−e−β3,2t)/β3,2 − β4,2 t] dt /305 − β5
ωi,t> 1.0 for Yi,t > Y2,305
ωi,t= 1.0 for Yi,t = Y 2,305
ωi,t <1.0 for Yi,t < Y2,305.
Moreover, the credits given for each day a cow is in milk were always positive, because the baseline used was lower than the asymptotes of the 3 lactation curves. For the second lactation, a cow will earn a total of 305 d of PL credits if she has exactly 305 DIM. Finally, the PL with diminishing credits for a cow was defined as the summation of the credits earned for the DIM in all her lactations.
Note: You can find more details HERE on this ONE calculation of PL.
Full Model for Indirect Prediction
An indirect estimate of PTA for PL (uˆind) was obtained from PTA for milk, fat, and 14 linear type traits using the following equation (3).
uˆind = Cov[uPL,u]¢[Var(u)] –1u
where uPL = transmitting ability for PL, u = vector of true transmitting abilities for production and type traits, and uˆ= vector of multiple-trait BLUP predictions of u. The method is approximate in the current situation because PTA for linear type traits are calculated using a multiple-trait BLUP, but PTA for milk and fat are currently calculated using a single-trait BLUP. The REL of uˆ ind was calculated using the following expression:
RELind = Cov[uPL,u]¢[Var(u)]–1[Var(uˆ)][Var(u)]–1Cov[uPL,u]/Var(uPL)
max(RELind) = Cov[uPL,u]¢[Var(u)]–1Cov[uPL,u]/Var(u PL) ,
which occurs when Var(uˆ ) = Var(u) (i.e., with an infinite amount of data on traits in u) .
Direct and indirect PL predictions were combined in a weighted mean as follows;
uˆcomb = wdiruˆ dir + winduˆind
wdir = (1 – RELind ´c)/(1 – RELindRELdir ´ c2) ,
wind = (1 – RELdir ´c)/(1 – RELindRELdir ´ c2) ,
c = 1 + [DEboth/DEdirDEind]´Ö[(4 – hdir) (4 – ) / ( ) ]
and DE = daughter equivalent (14). Note that c, which is a measure of the lack of independence between direct and indirect evaluations, is a function of direct and indirect trait heritabilities and of the proportion of progeny evaluated for type and production traits that also have direct culling data available. The quantity c can be derived as 1 + [Co(edir,eind) /Cov(udir,uind)](DEboth /DEdirDEind) . The covariance of direct and indirect daughter means equals the genetic covariance multiplied by (DEboth/DEdirDEind) , and we assumed that direct and indirect daughter means are regressed toward the parent average by REL dir and RELind/max (RELind) , respectively. Only daughters with both direct and indirect observations contribute to the error covariance. The c term represents the covariance of the daughter means divided by Co(udir,uind) . If genetic and phenotypic correlations are assumed to be equal, then [Cov(edir,eind)/Cov(udir,uind) ] equals the square root of [(4 hdir) ( 4 – ) / ( )], which is equal 2hind2hdir2hind2 to 26.3 for direct and indirect trait heritabilities of 0.085 and 0.25, respectively. The weights, wdir and wind, are then determined as follows. We know that the covariance of a genetic effect with its BLUP predictor equals REL times genetic variance, which is also the variance of the predictor. Therefore, Cov(uˆdir,uPL) = Var(uˆ dir) = RELdirVar(uPL) , and Cov(uˆind,uPL) = Var(uˆ ind) = RELindVar(uPL) . Furthermore, Cov(uˆdir,uˆ ind) RELdirRELindcVar(uPL) . Then, w = Cov[(uˆdir,uˆ ind),uPL]¢[Var(uˆ dir,uˆ ind)]–1. Simple rules for inverting 2´2 matrices allow the weights to be reexpressed as wdir=(1 – RELind ´ c)/(1 – RELindRELdir ´ c2) and wind = (1 – RELdir ´ c)/(1 – RELindRELdir ´ c2) . Finally, approximate REL of the weighted average was calculated as RELcomb = (RELdir + RELind–2RELindRELdir ´ c)/(1 – RELindRELdir ´ c2) .
Note: You can find more details HERE on this ONE calculation of PL.