6.4 Cross prediction
There is one further way that it is possible to predict the response to selection in the long term, although not necessarily the rate of response. This approach, based on the genetics underlying the traits, was proposed by Jinks and Pooni, and is currently attracting considerable attention in terms of experimental investigations and in applying it to practical breeding. This will be covered in more detail in the next chapter, but needs mentioning here to keep in view the options available to the breeder in terms of making predictions.
If, to start with, we assume that we have an inbreeding species and wish to produce a final variety that is true-breeding. What we want to know of any population or cross is what is the distribution of inbred lines that we predict can be derived from it, and what is the probability of one of these lines having a phenotype equal to, or exceeding, any target level that we set, in other words, that we would be aiming for with selection.
If we assume that the distribution of the final inbred lines that are derivable have a normal distribution, as is generally the case in practice, then this distribution can be described by the mean and standard deviation. Since they are inbred lines they will have a mean of 
and a standard deviation of 
, we can predict the properties of the distribution of all inbred lines possible and hence we can obtain the frequency 
of inbreds falling into a particular category. In other words, we can simply use the properties of the normal probability integral given in tables to say what is the probability of obtaining an inbred line with expression falling in a particular category. If the probability is low, it will obviously be difficult to actually obtain such a line. If the probability is high, it will be easy to produce.
How do we put this into practice? If we have a set of genotypes for use as parents, which ones do we cross to produce our desired new inbred lines? Do we take 
and 
or 
and 
, etc.? We will need to decide between the crosses before we invest too much time and effort, otherwise we may well be spreading our efforts over crosses that will not easily produce the phenotypes we want. If we take the crosses and estimate 
and 
for each, then we can estimate the probability of obtaining our desired target values. From this we can rank the crosses on their probabilities and then only use the ones with the highest probabilities of producing lines with the required expression of character deemed to be important.
In fact, the approach is even more general in that it can be used to predict the properties of the 
hybrids derived from the inbred lines. It can also be used to predict the probability of combination of characters that is the probability of obtaining desirable levels of expression in a series of characters.
What are the drawbacks to the approach? Firstly, we need to estimate 
and 
, and this involves a certain amount of work in itself, but it is fairly modest.
Secondly, it also assumes that the estimates we use are appropriate to the final environment in which the material is to be grown. In other words, as in the case of heritabilities, if we carry out the experiments in one environment at one site in one year, we are assuming that this is representative of other years and sites. We can, of course, carry out suitable experiments to obtain estimates in more years and sites, but this involves extra time and effort.
The use of cross prediction techniques in selection will be discussed in greater detail in Chapter 7.
It is unfortunate that, in reality, few breeding programmes, both of an academic or commercial nature, seek to gain insight into the topics addressed in this chapter. To some extent this is a consequence of the time and resource constraints under which breeders operate. For instance, many breeders would rather spend resources developing more or larger breeding populations, or running more field trials, than preparing specific populations and analysing the information they provide. Nevertheless, we argue that most, if not all, breeding programmes would benefit, achieve greater genetic progress and therefore develop superior varieties, if just a small fraction of their efforts was devoted to gaining insight as noted above.
Think questions
- Given values for the variance of the mean of the
, and variance of the 
, estimate 
and explain what this tells us about the genetic determination of the trait.
Given below are the variances of the mean from two parents (
and 
), the 
, and both backcross families (
and 
). Estimate 
and explain what the value means in genetic terms.
- List the six assumptions necessary for a straightforward interpretation of a Hayman and Jinks' analysis of diallels.
Below are shown values of array means, within array variances
and covariances between array values and non-recurrent parents 
from a Hayman and Jinks' analysis of a 
complete diallel in dry pea. The trait of interest is pea grain yield. Regression of 
against 
resulted in the equation: 
, with standard error of the regression slope equal to 
. An analysis of variance of 
showed significant differences between arrays, while a similar analysis of 
showed no significant differences between arrays. What can be deduced regarding the inheritance of pea yield from the information provided? If you were a plant breeder interested in developing high-yielding dry pea cultivars, on which two parental lines would you concentrate your breeding efforts? Briefly explain why.Parent name 
Array mean ‘Souper’ 34.1 19.3 456 ‘Dleiyon’ 99.9 79.3 305 ‘Yielder’ 21.0 11.2 502 ‘Shatter’ 99.4 68.4 314 ‘Creamy’ 49.6 39.4 372 ‘SweetP’ 59.1 48.8 361 ‘Limer’ 61.8 49.2 393 - Below is shown an analysis of variance of plant yield from a
half diallel (including parents). The analysis of variance is from a Griffing's analysis (Model 2). 
combining ability, 
combining ability, 
obtained by replication, 
of freedom, and 
of square.
Source df SS GCA 5 4,988 SCA 15 6,789 Error 21 5,412 Discuss the results from the analysis, given that the six parents were: (a) specifically chosen, and (b) chosen completely at random.
- It is desired to determine the narrow-sense heritability for flowering date in spring canola (B. napus). Both parents and their offspring from ten cross combinations were grown in a properly designed field experiment. At harvest, yield was recorded for each entry, and using these data the average phenotype of two parents (i.e.
) was considered to be 
, the independent variable, while the performance of their offspring was considered as 
, the dependent variable. A regression analysis is to be carried out by regression of the offspring 
onto the average parent 
. The following data are derived: 
. Estimate the slope of the regression line (b), test whether this slope is greater than zero, and estimate the narrow-sense heritability from the regression equation.
How would the relationship between the regression and the narrow-sense heritability differ if the regression were carried out between only the offspring and the male parent?
- Four types of diallel can be analysed using a Griffing's analysis. Describe these types.
Families from a
half diallel (including selfs) were planted in a two-replicate yield trial at a single location. The parents used in the diallel design were chosen to be the highest yielding lines grown in the Pacific-Northwest region. Data for yield were analysed using a Griffing's analysis of variance. Family means, averaged over two replicates, degrees of freedom and sum of squares (SS) from that analysis are shown below. Interpret the results from the Griffing's analysis. What differences would there be in your analytical methods if the parents used had been chosen at random?Parent 1 Parent 1 62.0 Parent 2 Parent 2 71.0 69.5 Parent 3 Parent 3 55.5 52.5 50.5 Parent 4 Parent 4 72.5 80.5 56.5 76.5 Parent 5 Parent 5 70.5 66.5 36.5 71.0 64.5 Source df SS GCA 4 6,694.058 SCA 10 825.676 Replicates 1 8.533 Error 14 317.467 Total 29 7,845.733 From the same diallel data (above), within-array variances
and between-array and non-recurrent parent covariances 
were calculated. The values of 
and 
for each parent along with the mean of 
, mean of 
, sum of squares of 
, sum of squares of 
and sum of products 
are shown below.
1 98.0 102.0 2 66.3 53.2 3 161.8 207.4 4 50.3 65.2 5 71.4 83.1 Mean of
; mean of 
. From these data, test whether the additive – dominance model is adequate to describe variation between the progenies. What can be determined about the importance of additive versus dominance genetic variation in this study? From all the results (Griffing, and Hayman and Jinks, above), which two parents would you use in your breeding programme and why? - Given the variance from two parents (
and 
), the 
and 
families, estimate the narrow-sense heritability 
and explain what the value means in genetic terms.
- A new oil crop (Brassica gasolinous) has been discovered that may have potential as a biologically renewable fuel oil substitute. This diploid species is tolerant to inbreeding and is self-compatible. A preliminary genetic experiment was designed to examine the inheritance of seed yield (Yield) and percentage oil content (%Oil). This experiment involved a
half diallel (including selfs). The four homozygous parental lines are represented by the codes AAA, BBB, CCC and DDD. The half diallel array values (averaged over two replicates), array means, general combining ability (GCA) values, mean squares from the analyses of variance (Griffing style), 
and 
values (Hayman and Jinks' analysis), variance of array means 
and parental variances 
, and the one-way analyses of variance for 
and 
are shown below for each character.
Yield AAA 40.5 BBB 38.5 29.5 CCC 37.0 28.0 19.5 DDD 32.5 20.5 18.5 10.0 AAA BBB CCC DDD Array means 37.1 29.1 25.8 20.4 %Oil AAA 20.5 BBB 20.5 25.0 CCC 23.0 26.0 30.5 DDD 24.5 27.5 31.0 36.0 AAA BBB CCC DDD Array means 22.1 24.7 27.6 29.8 Source df Yield %Oil GCA 3 796.5 180.6 SCA 6 90.5 30.1 Replicate blocks 1 0.4 0.1 Replicate error 9 51.5 5.7 
and 
valuesYield %Oil 
AAA 46.2 171.3 15.6 50.7 BBB 218.2 376.7 36.3 75.0 CCC 297.7 436.7 58.3 98.0 DDD 344.3 472.3 97.3 132.3 
and 
valuesYield %Oil 
196.9 44.4 
687.6 180.7 Yield %Oil Source df 
Between 3 8,760 28.0 628 7.68 Within 4 133 17.0 115 4.77 Without using regression, estimate the narrow-sense heritability
for seed yield, and explain this value in terms of genetic variance. Explain the analyses for Yield and outline any conclusions that can be drawn from these data. Explain the analysis for %Oil (percentage of seed weight that is oil) and outline any conclusions that can be drawn from these data. Which one of these four genotypes would you choose as a parent in your breeding programme? Explain your choice. Describe any difficulties suggested from these analyses in a breeding programme designed for selecting lines with high yield and high percentage of oil. 
and 
families were evaluated for plant yield (kg/plot) from a cross between two homozygous spring wheat parents. The following variances from each of the four families were found:
Calculate the broad-sense
and narrow-sense 
heritabilities for plant yield. Given the heritability estimates you have obtained, would you recommend selection for yield at the 
stage in this wheat breeding programme, and why?- Griffing has described four types of diallel crossing designs. Briefly outline the features of each of Methods 1, 2, 3 and 4. Why would you choose Method 3 over Method 1? Why would you choose Method 2 over Method 1?
A full diallel, including selfs, was carried out involving five chickpea parents (assumed to be chosen as fixed parents), and all families resulting were evaluated at the
stage for seed yield. The following analysis of variance for general combining ability (GCA), specific combining ability (SCA) and reciprocal effects (Griffing's analysis) was obtained:Source df MS GCA 5 30,769 SCA 10 10,934 Reciprocal 10 9,638 Error 49 5,136 Complete the analysis of variance and draw conclusions from the analysis. If it was actually the case that the parents were chosen at random, how would this change the results and your conclusions?
Plant height was also recorded on the same diallel families and an additive – dominance model found to be adequate to explain the genetic variation in plant height. Array variances
and non-recurrent parent covariances 
were calculated and are shown alongside the general combining ability (GCA) of each of the five parents, below:Parent 
GCA 1 491.4 436.8 
2 610.3 664.2 
3 302.4 234.8 
4 310.2 226.9 
5 832.7 769.4 
Without further calculations, what can be deduced about the inheritance of plant height in chickpea?
- A
half diallel design (with selfs) was carried out in cherry and the following seed yields of each possible 
family were observed:
Small reds Small reds 12 Big yields Big yields 27 36 Jim's delight Jim's delight 21 35 27 Jacks' best Jack's best 28 27 26 21 From the above data, determine the narrow-sense heritability for yield in cherry.
- A crossing design involving two homozygous pea cultivars was carried out, and both parents were grown in a properly designed field experiment with the
and 
families. Given the following standard deviations for parents (
and 
), the 
, and both backcross progeny (
and 
), determine the broad-sense heritability and narrow-sense heritability for seed size in these dry peas. What can be concluded from the values of heritability you obtain?
Family Standard deviation Variance 
3.521 12.39 
3.317 11.00 
6.008 36.10 
5.450 29.70 
5.157 26.59 - It is common in plant breeding programmes to carry out diallel analyses to determine the genetics of specific parents and their progeny. With particular reference to diallel interpretation, explain the terms fixed and random parents, and how choosing one or other would influence the analyses of a Griffing ANOVA.
Griffing's analysis of diallels is a statistical analysis based on the following model:
Describe the meaning of the terms in the
and 
in the Griffing model, above.Below are the mean seed yields (kg/plot), averaged over four replicates, of the parents and offspring from a
half diallel, with selfs.Sunrise Sunrise 16.4 Premier Premier 14.3 11.1 Clearwater Clearwater 18.3 15.2 17.6 Hyola.401 Hyola.401 13.2 10.7 16.2 15.3 Using these data, determine the
value of each parent and estimate the 
value in the cross Hyola.
. - A newly appointed barley breeder was interested in the inheritance and heritability of yield in spring barley. He chose five cultivars from a range that were grown throughout his target region and intercrossed them in all possible cross combinations (excluding reciprocals) including selfs, and he completed a Hayman and Jinks' analysis. Some of the results are shown below.
Cultivar Mean yield 
Premier 62 1.8 −8.1 Sunrise 44 64.1 51.5 Reaper 39 43.8 38.0 Lifeline 66 7.1 9.4 Star 39 71.0 51.1 Mean 37.56 28.38 The regression equation of
onto 
is: 
, and the standard error of the slope is 0.103.The variance of parents
is 42.37, and the variance or array means 
is 16.77.Complete the Hayman and Jinks' analysis of variance, determine whether the additive – dominance model is appropriate, calculate the narrow-sense heritability, and describe what can be determined about the inheritance of yield in spring barley.