Agribusiness

Overlaying Design Matrices for a Parental Model in ASReml-R

Most breeding programs plan several controlled crosses between outstanding parents to detect favorable alleles in their offspring. The progeny are later evaluated in a field experiment, and this information is used to assess the genetic worth of the parents by fitting parental linear mixed models (LMMs) and obtaining best linear unbiased predictions (BLUPs). These BLUPs, which are the _general combining ability_ (GCA), or 1/2 of the _breeding value_ (BV, with BV = 2 ×× GCA) of each parent, are then used to select the best parents for future crosses or operational deployment. In many plant breeding programs, a parent is considered in several crosses. In most cases it is easy to assign the sex of a given individual. However, several commercial plant species are monoecious, which means that a given genotype will bear both male and female flowers. In contrast, dioecious species have distinctive male and female plants. Some examples of monoecious species are corn, squash, banana, and many conifers, particularly those of the genus _Pinus_. In quantitative genetic analyses, monoecious species present a particular challenge, as a given parent can contribute to the estimation of its breeding value (or GCA) as both a male and a female, something that needs to be taken into consideration when a statistical model is fitted. This is done by _overlaying_ design matrices of the factors associated with male and female parents. We will illustrate this here using an example of loblolly pine (_Pinus taeda_) in which some individuals, depending on the availability of pollen or flowers, were used in several artificial crosses as both male and female in the breeding program. The data used here originates from a loblolly pine clonal study published by Resende _et al._ (2012). Parents were crossed in a circular mating design, constituting several full-sib families. Individuals from these families were vegetatively propagated (cloned) and established in a series of field trials. A subset of the full dataset, corresponding to diameter at breast height (DBH, inches) measured at 6 years since planting at the Nassau (Florida, USA) site, is used here. We will be using the adjusted mean values for this trait. In this dataset we have a total of 71 families that originated from 43 parents; however, 20 of those parents were used as both males and females in different crosses. There were no reciprocal or self-pollinated crosses planned, but these can occur in other crops and they might need to be identified and modelled properly. In this dataset, each family is formed by between 1 and 16 individuals (with an average of 12.2). We also have pedigree information for the 43 parents. The first few lines of the phenotypic dataset $\\texttt{PEDPAR\_NASSAU.TXT}$ are presented below: | tree | mother | father | family | DBH | | --- | --- | --- | --- | --- | | 280200 | 20012 | 44112 | 1017 | 9.410 | | 282200 | 20022 | 44090 | 1020 | 11.953 | | 284400 | 44126 | 142170 | 1049 | 10.785 | | 285210 | 50152 | 58040 | 1056 | 9.950 | | 285600 | 142024 | 44112 | 1006 | 10.325 | | 286600 | 44012 | 17766 | 1036 | 11.122 | And the first and last few lines of parental pedigree file $\\texttt{PEDPAR\_NASSAU.TXT}$ are: |   | genotype | mother | father | | --- | --- | --- | --- | | 1 | 14006 | 0 | 0 | | 2 | 14046 | 0 | 0 | | 3 | 14060 | 0 | 0 | | 4 | 14070 | 0 | 0 | | 5 | 14104 | 0 | 0 | | 6 | 14106 | 0 | 0 | | 48 | 142076 | 14114 | 14104 | | 49 | 142170 | 14106 | 14046 | | 50 | 142194 | 14216 | 14060 | | 51 | 202060 | 20030 | 20052 | | 52 | 202096 | 20034 | 20052 | | 53 | 222056 | 22034 | 14006 | | 54 | 222060 | 22020 | 22034 | In the phenotypic data each row contains the id of the individual tree, together with information about their mother and father, followed by the adjusted phenotypic response DBH. In the pedigree file there is information about the mother and father of each of the parents used in the crosses. For example, note that tree $\\texttt{284400}$ has father $\\texttt{142170}$, and this genotype has as parents genotypes $\\texttt{14106}$ and $\\texttt{14046}$. We are interested in fitting a parental model, where our objective is to estimate GCA values for each of the parents. (Note that this is different than an animal model, where we estimate a BV for each of the individuals (parents or offspring).) Our parental base model is: $$ y\_{ijk} = \\mu + f\_i + m\_j + fm\_{ij} + \\epsilon\_{ijk} $$ where, $y\_{ijk}$ is the response for the kth individual originating from the cross between the ith female with the jth male; $\\mu$ is the overall mean; $f\_i$ is the random effect of the ith female, with $f\_i \\sim N(0, \\sigma^2\_f)$; $m\_j$ is the random effect of the jth male, with $m\_j \\sim N(0, \\sigma^2\_m)$; and $fm\_{ij}$ is the interaction or family effect of the cross between the ith female with the jth male, with $fm\_{ij} \\sim N(0, \\sigma^2\_{fm})$; and $\\epsilon\_{ijk}$ is the random residual with $\\epsilon\_{ijk} \\sim N(0, \\sigma^2)$. Note that for the parental effects $f\_i$ and $m\_j$ there is a pedigree available, which is used to obtain the numerator relationship matrix $\\mathbf{A}$, that is incorporated in our analyses. Hence, the vectors of parental effects have the assumptions $\\mathbf{f} \\sim N(\\mathbf{0},\\sigma^2\_f \\mathbf{A})$ and $\\mathbf{m} \\sim N(\\mathbf{0},\\sigma^2\_m \\mathbf{A})$. In the above model, we are assuming that there are distinct variances for females and males, $\\sigma^2\_f$ and $\\sigma^2\_m$, and that these can take any positive value.  We can fit the above model with ASReml-R using the following code: ```plaintext ainv <- ainverse(PED) modP <- asreml(fixed=DBH~1, random=~vm(mother,ainv)+vm(father,ainv)+family, residual=~idv(units), data=PINE) ``` In this code we are generating the numerator relationship matrix $\\mathbf{A}$ using the command $\\texttt{ainverse()}$. The matrix $\\mathbf{A}$ is incorporated into the model using the function $\\texttt{vm()}$. The log-likelihood of the above model fitted to our data is $\\texttt{-744.488}$ and the estimated variance components are: |   | component | std.error | z.ratio bound | $ch | | --- | --- | --- | --- | --- | | vm(mother, ainv) | 0.2774623 | 0.1121623 | 2.473759 P | 0 | | vm(father, ainv) | 0.3815927 | 0.1348447 | 2.829868 P | 0 | | family | 0.0000004 | NA | NA B | 0 | | units!units | 1.8702273 | 0.0930707 | 20.094696 P | 0 | | units!R | 1.0000000 | NA | NA F | 0 | Note the difference in variance components between males (fathers, $\\texttt{0.277}$) and females (mothers, $\\texttt{0.382}$). Finding a difference in variance components by sex is common for plant species and it might be correct depending on the origin of the parents, but also other biological reasons might explain these differences. Also note that the family variance is bounded at almost zero. In our case, we can calculate both the narrow-sense heritability for females and males ($h^2\_f$ and $h^2\_m$) and the dominance ratio ($d^2$), by using the following expressions: $h^2\_f = 4 \\times \\sigma^2\_f / (\\sigma^2\_f + \\sigma^2\_m + \\sigma^2\_{fm} + \\sigma^2)$ $h^2\_m = 4 \\times \\sigma^2\_m / (\\sigma^2\_f + \\sigma^2\_m + \\sigma^2\_{fm} + \\sigma^2)$ $d^2 = 4 \\times \\sigma^2\_{fm} / (\\sigma^2\_f + \\sigma^2\_m + \\sigma^2\_{fm} + \\sigma^2)$ In some cases, particualrly when the estimations of heritability for both sexes might not be very different, these can be combined into a single estimate, as: $$ h^2 = 2 \\times (\\sigma^2\_f +\\sigma^2\_m) / (\\sigma^2\_f + \\sigma^2\_m + \\sigma^2\_{fm} + \\sigma^2) $$ All of the above expressions were obtained in ASReml-R using the command $\\texttt{vpredict()}$ as shown below: ```plaintext vpredict(modP,h2m~4*V1/(V1+V2+V3+V4)) vpredict(modP,h2f~4*V2/(V1+V2+V3+V4)) vpredict(modP,d2~4*V3/(V1+V2+V3+V4)) vpredict(modP,h2~2*(V1+V2)/(V1+V2+V3+V4)) ``` with the results: |   | Estimate | SE | | --- | --- | --- | | h2m | 0.4388000 | 0.1616208 | | h2f | 0.6034797 | 0.1858860 | | d2 | 0.0000007 | 0.0000001 | | h2 | 0.5211399 | 0.1043225 | As expected, our dominance ratio $d^2$ is very small in this particular trait; hence, it could be ignored. Also, the narrow-sense heritabilities are reasonable for this type of study, with a combined estimate of $\\texttt{0.521}$ but with a moderate approximated standard error ($\\texttt{0.104}$). Also, we can obtain the BLUPs for the model terms $\\texttt{mother}$ and $\\texttt{father}$, which in this case will correspond to the GCA values. If these are multiplied by two, we will have the BVs. The GCAs are obtained with the code: ```plaintext summary(modP,coef=TRUE)$coef.random ``` In the output below, we can observe a few of the estimated GCA values for the $\\texttt{mother}$ (top) and $\\texttt{father}$ (bottom). |   | solution | std.error | z.ratio | | --- | --- | --- | --- | | vm(mother, ainv)\_14006 | 0.3600002 | 0.2841548 | 1.2669160 | | vm(mother, ainv)\_14046 | 0.0000000 | 0.5267472 | 0.0000000 | | vm(mother, ainv)\_14060 | \-0.2286267 | 0.4864881 | \-0.4699533 | | vm(mother, ainv)\_14070 | 0.0000000 | 0.5267472 | 0.0000000 | | vm(mother, ainv)\_14104 | \-0.4620406 | 0.4208766 | \-1.0978056 | | vm(mother, ainv)\_14106 | 0.0000000 | 0.5267472 | 0.0000000 | |   | solution | std.error | z.ratio | | --- | --- | --- | --- | | vm(father, ainv)\_14006 | 0.0013612 | 0.2827143 | 0.0048148 | | vm(father, ainv)\_14046 | \-0.5495441 | 0.5510751 | \-0.9972219 | | vm(father, ainv)\_14060 | 0.0000000 | 0.6177321 | 0.0000000 | | vm(father, ainv)\_14070 | \-0.3792472 | 0.3257064 | \-1.1643837 | | vm(father, ainv)\_14104 | \-0.2087355 | 0.5024186 | \-0.4154613 | | vm(father, ainv)\_14106 | \-0.5495441 | 0.5510751 | \-0.9972219 | | vm(father, ainv)\_14114 | 0.1476378 | 0.3462045 | 0.4264466 | Note that for parent $\\texttt{14006}$ the estimates are different as a mother and a father ($\\texttt{0.360}$ against $\\texttt{0.001}$), and their precision will depend on the amount of information a parent has (_i.e._, number of offspring), but also in its relationship with other genotypes on the dataset. So far, we have not combined the information from a given parent when it is used as a male _and_ as a female. Now, it is of interest to _overlay_ the factors $\\texttt{mother}$ and $\\texttt{father}$. To do this in ASReml-R we require two elements: the use of the statement $\\texttt{and()}$ in the model and the specification of the command $\\texttt{equate.levels}$. This is illustrated in the following code for the same data as above: ```plaintext modO <- asreml(fixed=DBH~1, random=~vm(mother,ainv)+and(vm(father,ainv)), equate.levels=c('mother','father'), residual=~idv(units), data=PINE) ``` First, let’s focus on the $\\texttt{and()}$ function. This is used to request that the design matrices associated with $\\texttt{father}$ are _overlaid_ on the design matrix associated with the immediately previous term (here, $\\texttt{mother}$). Second, the expression $\\texttt{equate.levels}$ requests that the levels for the factor $\\texttt{mother}$ and $\\texttt{father}$ are treated as identical. That is, levels that have the same name in the factors $\\texttt{mother}$ and $\\texttt{father}$ will be treated as the same, and levels that are found in only one of the factors will be added to the new design matrix. Both of the above commands are required in ASReml-R to ensure that consistent BV (or GCA) estimates are obtained. In order to illustrate the above overlay of matrices, we will use a simple example, in which we have eight individuals originating from crosses of four parents (P1, P2, P3 and P4). These parents were used as female or male, and in some cases we have reciprocal crosses and selfing. The crossing and design matrices for our base model (without overlay) are shown below: $$ \\begin{matrix}   indiv & female & male \\\\   A & P1 & P2 \\\\   B & P1 & P3 \\\\   C & P1 & P4 \\\\   D & P2 & P3 \\\\   E & P2 & P4 \\\\   F & P3 & P2 \\\\   G & P3 & P4 \\\\   H & P4 & P4 \\\\   \\end{matrix}   \\Rightarrow   \\begin{matrix}   P1 \\:\\: P2 \\:\\: P3 \\:\\: P4 \\\\   \\begin{bmatrix}   1 & 0 & 0 & 0 \\\\   1 & 0 & 0 & 0 \\\\   1 & 0 & 0 & 0 \\\\   0 & 1 & 0 & 0 \\\\   0 & 1 & 0 & 0 \\\\   0 & 0 & 1 & 0 \\\\   0 & 0 & 1 & 0 \\\\   0 & 0 & 0 & 1 \\\\   \\end{bmatrix}   \\end{matrix}   \\:\\:   \\begin{matrix}   P2 \\:\\: P3 \\:\\: P4 \\\\   \\begin{bmatrix}   1 & 0 & 0 \\\\   0 & 1 & 0 \\\\   0 & 0 & 1 \\\\   0 & 1 & 0 \\\\   0 & 0 & 1 \\\\   1 & 0 & 0 \\\\   0 & 0 & 1 \\\\   0 & 0 & 1 \\\\   \\end{bmatrix}   \\end{matrix} $$ Once the LMM model is fitted based on the above matrices (as we did with our previous object $\\texttt{modP}$), we will have a total of four GCAs for females and three for males. If we count the number of ones for each effect, we find that they have between one and three pieces of information to be used in their estimation. Now, if we proceed to overlay the _**female**_ and _**male**_ incidence matrices, we obtain the following results: $$ \\begin{matrix}   indiv & female & male \\\\   A & P1 & P2 \\\\   B & P1 & P3 \\\\   C & P1 & P4 \\\\   D & P2 & P3 \\\\   E & P2 & P4 \\\\   F & P3 & P2 \\\\   G & P3 & P4 \\\\   H & P4 & P4 \\\\   \\end{matrix}   \\Rightarrow   \\begin{matrix}   P1 \\:\\: P2 \\:\\: P3 \\:\\: P4 \\\\   \\begin{bmatrix}   1 & 1 & 0 & 0 \\\\   1 & 0 & 1 & 0 \\\\   1 & 0 & 0 & 1 \\\\   0 & 1 & 1 & 0 \\\\   0 & 1 & 0 & 1 \\\\   0 & 1 & 1 & 0 \\\\   0 & 0 & 1 & 1 \\\\   0 & 0 & 0 & 2 \\\\   \\end{bmatrix}   \\end{matrix} $$ You can observe that there is a single design matrix but only with four columns: one for each parent. In this case, we have more pieces of information to estimate each effect, ranging from three to six. Of special interest is the effect of parent P3, it now uses four pieces of information to estimate its single GCA, whereas before it was being estimated as two effects, each with two pieces of information. There are other interesting things in the above matrix, such as the value 2 associated with individual H, that originated from the cross P4 $\\times$ P4, which corresponds to a selfing of parent P4. Also, individuals D and F are full-sibs, originating from reciprocal crosses, but in this case there is no distinction between their parental effects. Both, selfing and reciprocal crosses can be considered in the fitted linear mixed model as extensions with the aim of evaluating their importance or significance. Finally, we can observe our results from fitting the above overlay model to our loblolly pine data. The estimated variance components are: |   | component | std.error | z.ratio bound | %ch |   | | --- | --- | --- | --- | --- | --- | | vm(mother, ainv) | 0.4000453 | 0.1162417 | 3.441494 | P | 0 | | units!units | 1.8599439 | 0.0917484 | 20.272218 | P | 0 | | units!R | 1.0000000 | NA | NA | F | 0 | In this particular case, we are missing the variance associated with the factor $\\texttt{father}$. However, this is still part of the model. As the matrices were overlaid, we have as an output a single parental effect now called $\\texttt{mother}$, which represents both male and female parents. Also, note that we dropped the term associated with $\\texttt{family}$, as in the previous analysis this was bound to zero. The log-likelihood of this model is $\\texttt{-737.328}$, a greater value indicating a better fit than the obtained from the original model ($\\texttt{-744.488}$), and probably a significant improvement. We can now proceed to obtain our estimate of heritability using the expression: ```plaintext vpredict(modO,h2~4*V1/(2*V1+V2)) ``` which is the traditional formula; however, note that in the denominator we are considering twice the $\\texttt{mother}$ variance as we have a single parental variance component. The results from the above code are presented below: |   | Estimate | SE | | --- | --- | --- | | h2 | 0.601564 | 0.1248922 | As expected, these results are different to those from our previously fitted model because of the way this model is combining the available information. There is an increase in the heritability when we overlay the factors of mother and father compared to when we do not ($h^2 = 0.521$). This increase is expected as we now have more information to estimate each of the effects. Also, we expect a reduction in the standard errors of the estimated GCA values, which are presented below: |   | solution | std.error | z.ratio | | --- | --- | --- | --- | | vm(mother, ainv)\_14006 | 0.5174180 | 0.2116542 | 2.4446388 | | vm(mother, ainv)\_14046 | \-0.5055163 | 0.5609615 | \-0.9011606 | | vm(mother, ainv)\_14060 | \-0.2843599 | 0.5668751 | \-0.5016271 | | vm(mother, ainv)\_14070 | \-0.3430721 | 0.3366609 | \-1.0190434 | | vm(mother, ainv)\_14104 | \-0.4849910 | 0.4781210 | \-1.0143688 | | vm(mother, ainv)\_14106 | \-0.5055163 | 0.5609615 | \-0.9011606 | In this case we have only $\\texttt{mother}$ effects that identify each of the levels of the parent. In contrast with our previous model, parent $\\texttt{14006}$ has a single GCA value ($\\texttt{0.517}$), and its standard error is smaller than before ($\\texttt{0.21}$ compared to $\\texttt{0.28}$). Some GCA estimates will increase or decrease, and their precision might get better or worse depending on how information is combined. In this example, we have explored a parental model where the effects of male and female were overlaid. This resulted, according to the log-likelihood value, in a statistically superior model that combines the data better. But more importantly, this model is more biologically accurate given our knowledge of monoecy of the species under study. ### **Author** Salvador A. Gezan ### **References** Resende, MFR, Munoz, P, Resende, MDV, Garrick, DJ, Fernando, RL, Davis, JM, Jokela, EJ, Martin, TA, Peter, GF and M. Kirst. (2012). Accuracy of genomic selection methods in a standard data set of loblolly pine (_Pinus taeda_ L.) Genetics 190:1503-1510 ### **File to download** [EQ\_LOBLOLLY](https://vsni1.wpengine.com/wp-content/uploads/2020/09/EQ_LOBLOLLY.zip) **Notes**: SAG August-2020

Bees & Elephants

Using mainly the GLM functionality within Genstat, large datasets are quickly and easily analysed with the results factored back into future experimental design.  The conservation of the African elephant provides tremendous opportunities for simultaneously conserving biodiversity and increasing benefits to local communities. Their role as a flagship species of global significance helps maintain biodiversity of the ecosystems they inhabit. In addition, the cultural and aesthetic values of elephants are also important, not only to African societies, but to the world at large. But this needs to be balanced against the fact that as the African elephant range becomes more and more fragmented and elephants get confined into smaller pockets of suitable habitat, humans and elephants are increasingly coming into contact and in conflict with each other. Tracking and recording the actual numbers of elephants in Africa is difficult; data are collated using a wide variety of techniques from ground or aerial surveys to dung counts and informed and other ‘guesstimation’. Overlay the obvious difficulties in the range and distances elephants can travel (global satellite tracking is helping this process) means putting accurate numbers on elephant populations can be, excuse the pun, a mammoth task. That said, counts are achieved and have shown the elephant population in Kenya has gone through various changes. In 1973, the population was about 167,000 declining to just 19,000 in 19891. The African Elephant Status Report 20072 (AESR 2007), recently published by the African Elephant Specialist Group (AfESG), puts the definite elephant count at 23,353, up 1,317 on the 2002 survey results. Add in probable, possible and speculative counts and the 2006 figure is 31,636; a rise of 2,830 on the 2002 figures. Alongside the elephant population growth, the human population in Africa has escalated way beyond anyone’s predictions, reaching an estimated 924 million3 in 2006. This increasing human population is starting to encroach dramatically into traditionally wildlife rich areas forcing large animals like elephants (and lions, buffalos and leopards incidentally) into smaller and smaller areas. Of course, 6 tonne animals like elephants have a huge requirement for food and water and naturally migrate across the landscape searching for sustenance. This is bringing them into direct conflict with people as new villages, roads, schools, fences, bridges and farms are being built over these natural wildlife corridors. The human-elephant conflict is becoming a serious issue in Kenya as people are now killing, spearing or poisoning elephants that come onto their land to eat their crops. So while elephants are major economic assets in generating tourist revenue, crop raiding by elephants is a cause of increasing levels of conflict between local people and wildlife management strategies across Africa. The economic damage to small-scale farmers can be crippling. Unless a cost-effective method of limiting crop damage is found, the pressure on wildlife managers to implement radical methods such as culling, will inevitably become a reality. As Lucy herself says, “When you meet people who are affected by these invading elephants you can only feel the deepest sympathy that they have lost their entire harvest. This causes genuine stress, damage and sometimes even death to these poor rural villagers.” #### **What can be done?** One of the methods that has been tried with variable success is the installation of electric fences to keep wild animals, particularly elephants, out of people’s farms. However, this is very expensive, requires a reliable supply of electricity and cannot be financed by the farmers so they become reliant on donors. Lucy works with a research team called Save the Elephants, which is headed by the elephant expert Dr Iain Douglas-Hamilton OBE; an organisation dedicated to developing a tolerant relationship between elephants and humans. Her research is furthering the aim to find crop-protection methods that can be financed and managed by the farmers themselves. The use of chilli peppers, either as disincentive crop or as a deterrent spray has been pioneered by Osborn (2002) in Zimbabwe with promising, albeit limited, success. Other variations include light-weight fencing hung with cow bells and laced with a potent mix of red chilli and black engine oil, thought to both alarm and irritate the elephants’ huge, sensitive trunks. However, Lucy’s research, based upon Kenya folklore which says that elephants are afraid of bees, would be an innovative and socially appropriate solution. #### **David and Goliath** The project explores the use of traditional, wooden beehives as both an elephant deterrent and a social and economic boost to poverty-stricken rural communities through the sustainable harvesting of honey. Her earlier research has shown that elephants react with obvious alarm and retreating behaviour to bee sounds. Further, recent studies show that elephants will actually avoid trees with beehives. By setting hives in acacia trees and recording how elephants react to them, Lucy hopes to be able to demonstrate that beehives can be used as an eco-barrier protecting fields of crops. When she isn’t persuading the British Army to help her fix her overworked Land Rover, Lucy works from a green canvas tent alongside the beautiful Ewaso Ng’iro river, in the Samburu Reserve.Day to day work involves setting up sample plots and selecting trees for beehives to be hung in. Many plots are tested which means driving through acres of park (hence the overworked Landie) and frequent encounters with elephants. Lucy has employed a local assistant Lukas, from the Ndorobo tribe; well known for their beekeeping abilities, and Lukas has 13 hives of his own which he helps to support his family with. There are also 4 long term elephant monitors, 1 MSc student from Nairobi University studying debarking effects of elephants and 1 other Kenyan researching whether or not lions use the same wildlife corridors as elephants. In addition, a team of researchers, all local Samburu are trained to identify all the elephants in the reserve; incredibly they know about 750 elephants by sight alone #### **Data Analysis** As well as the bee data, data are also collected from observations into factors such as temperature, wind direction and time of day to establish if the elephant behaviours observed are due to these factors, or if the elephants are indeed responding to the presence of the bees. Using mainly the GLM functionality within Genstat, large datasets are quickly and easily analysed with the results factored back into future experimental design. #### **Now, next steps and the future** In this day and age with all the issues of environment and climate change to be able to find a way of assisting farmers without destroying the natural habitat must be of the utmost importance. Here we have an opportunity to be a part of such a programme; and additionally to prove once again to the non-statistician that data analysis and statistics are a crucial part of everyday living. [http://elephantsandbees.com/](http://elephantsandbees.com/)

Nofima

Aquaculture is the name given to the farming of salt water and freshwater fish and marine animals. It is a rapidly growing division of farming across the world; reports from the UN’s FAO suggest that it has been growing more rapidly than any other area of animal food production.  A report published in September 2009 suggested that farm-reared fish accounted for 50% of world fish consumption. This rise in aquaculture production isn’t much of a surprise when you consider the emphasis on the health-giving properties of fish (particularly Omega-3 from oily fish) and the subsequent encouragement for people to eat more oily fish; and it’s certainly good news for the aquaculture producers across the world. However, growth of this level in any industry, whilst exciting and positive in many ways, also brings with it its own complications. The complexities of all types of farming mean that research and understanding is vital in helping the industry to grow safely as well as rapidly. This is particularly important if the current consumption levels of fish continue: the FAO predict that we will need an extra 27 million tonnes of fish by 2030 to meet the demand.  Any farmer will tell you of the importance of vaccination in controlling disease, and this is no different for fish farmers, or specifically Atlantic salmon farmers. Vaccinations against diseases such as furunculosis, vibriosis, cold-water vibriosis, winter ulcer and infectious pancreatic necrosis, which could otherwise decimate a farm, are vital in protecting the fish and farms and controlling these diseases in farmed Atlantic salmon. However, vaccinations can cause reactions at the injection site such as adhesions and discoloration, reduced appetite and growth, and in severe cases a downgrading of the carcass at market. Not only can this have an economic impact on the salmon farms, but also may create a negative perception of the farms with the general public. As with all aspects of farming the public is concerned not just with the food in question, but also of the welfare of the production animals, which means that breeding companies need to be sure of the actual physical health and safety of their fish. As with many aspects of farming and agriculture, all aspects of aquaculture are the subject of scientific research to enable better understanding and improved planning for the future, including prevention of disease and improved fish health. The results from challenge tests have indicated substantial genetic variation in disease resistance to a variety of bacterial and viral diseases (including some of those listed earlier), significant but relatively low genetic correlations among the different diseases and a high genetic correlation between the survival of non-vaccinated pre-smolts (smolts are young salmon as they migrate from freshwater to the sea) and the survival of older non-vaccinated full and half sibs under natural break-outs of the diseases. With this in mind Atlantic salmon breeding companies are looking at both the development of efficient vaccinations and the breeding of fish with higher disease resistance. The results from the challenge test research may suggest that genetic variation in immune systems might lead to genetic variation in innate disease resistance and variation in reactions to the vaccinations. One question researchers in this area need an answer to is whether there is significant genetic correlation between vaccine reactions and innate resistance, as this could mean a change of vaccine dose or a breeding programme to produce fish with the lowest reaction rate to vaccines and the highest natural resistance to diseases. And it is these issues that a recent project, undertaken by researchers from [Nofima Marin](http://www.nofima.no/marin/en), the [Norwegian School of Veterinary Scienc](http://www.veths.no/)e and [Aqua Gen AS](http://www.aquagen.no/En/Specialfolder/Latest_News/) and funded by the [Research Council of Norway](http://www.forskningsradet.no/servlet/Satellite?c=Page&cid=1177315753906&p=1177315753906&pagename=ForskningsradetEngelsk%2FHovedsidemal) (published in the Elsevier journal Aquaculture 287 (2009) 52-58) has looked at. Atlantic salmon were taken from farmed strains and from offspring of wild salmon, and reared at different farms. Data was collected on sex, size (at different stages), adhesion scores and melanin scores of fish at harvest size and survival data from challenge tests of their full- and halfsibs. The data collected was analysed using [ASReml](https://www.vsni.co.uk/software/asreml/) to fit a multivariate linear mixed animal model to obtain estimates for the variance and covariance components for the random effects of the studied traits. A single trait sire and dam model, which included the same fixed effects was used to obtain across year-class heritability estimates (using an alpha version of [ASReml 3](https://www.vsni.co.uk/software/asreml/)). Results from the project indicate that the severity of vaccine injuries in Atlantic salmon could be reduced through selective breeding. Additionally the relatively high correlation that was found between adhesion scores and melanin scores show that there is unlikely to be a need to select against both of these traits. The researchers warned that including an additional breeding trait objective would reduce the genetic gain for other traits, and therefore recommended that other solutions to the vaccine injuries be found, such as improved vaccines or vaccination procedures. The results also indicated a negative genetic correlation between body weight and adhesion or melanin score; however, these estimates are most likely biased towards the negative end of the scale, since vaccine injuries are expected to reduce growth rate for non-genetic reasons.  The study also indicated “no genetic association between resistance to furunuculosis and ISA (infectious salmon anaemia) and vaccine injuries”, which suggest that the vaccine injuries are caused by other aspects of the immune system, not associated with the genetic variation in innate resistance to these diseases.  Research of this kind is extremely important to the aquaculture industry to enable it to continue to develop, expand and improve, not just the industry, but the procedures, processes and systems associated with it. ASReml is widely respected and used in situations such as this. Our thanks to [Dr Bjarne Gjerde](http://www.nofima.no/marin/en/person/bjarne.gjerde) of [Nofima Marin](http://www.nofima.no/marin/en) for his help with this story. \<p>Testing\</p>