(b) Quantifying LD (including via r-squared)
138 To recap from my principal reasons and some of the evidence led before me, polymorphisms (such as SNPs) that have alleles that are co-inherited on the same chromosome with a causative polymorphism, that is, a polymorphism that has a direct effect on phenotype, are also referred to as being in potential linkage disequilibrium (LD) with the causative polymorphism. LD is measured as a correlation.
139 LD between two polymorphisms is influenced by several factors, but can be thought of as a function of the time that the respective polymorphisms arose in a given population and the distance between the polymorphisms on the chromosome.
140 As Professor Taylor said in terms of time, the greater the period of time between the respective polymorphisms arising, the lower the level of LD in the population, on average. For example, if a first mutation (polymorphism) arose several thousand years ago in a given bovine population, and the second polymorphism arose only ten years ago in that population, then the two polymorphisms would generally be in very low LD with each other because they will differ greatly in their frequency. Conversely, if two mutations arose at the same time (or close in time) in a population, then, subject to the distance between the two polymorphisms, there would generally be far greater LD between the two polymorphisms because they will be similar in frequency. Similar allele frequencies are required for strong LD between two loci but does not ensure that this will always be the case. Conversely, two loci that differ greatly in their allele frequencies cannot be in strong LD.
141 In terms of distance, the closer the distance between the two polymorphisms on the chromosome the higher will be the LD, on average. This is because the closer together on a chromosome two polymorphisms are, the lower the likelihood of recombination between the sites, and therefore the greater will be the likelihood that allelic combinations on the chromosomes present within the population will be preserved.
142 As Professor Taylor said, these matters were well understood by those in the field of quantitative genetics well before the priority date. This understanding is consistent with what is said in the specification at [0199]: "The degree of LD varies considerably throughout the genome and is function of time, recombination events, mutation rate and population structure."
143 According to Professor Taylor, he and others like him that work in the field of quantitative genetics refer to LD in terms of 'strong' or 'high' LD. And he said that despite the terms 'strong' and 'high' being relative descriptors, they convey a meaning and information. He understood 'strong linkage disequilibrium' to mean, inter-alia, that inherently the two SNPs have very similar allele frequencies in a given population.
144 Now LD may be measured. And there were various techniques available to do so before the priority date. The extent of LD could be calculated using algorithms and statistical methods that were well known to Professor Taylor and others in the field of population genetics at the priority date.
145 Now well before the priority date, LD had been commonly measured in terms of a D or D' value, although r2 which is the squared correlation of alleles at two loci was also utilised. But due to limitations with the D and D' statistic, r2 has become the more commonly used statistic. As explained in McKay SD et al., "Whole genome linkage disequilibrium maps in cattle" (2007) 8(74) BMC Genetics 1-12, of which Professor Taylor was an author, and albeit after the priority date (at 6):
It has been suggested that when large differences exist between marker allele frequencies, due to the presence of a rare allele, these two measures of LD are divergent. D' estimates historical recombination through allelic association whereas r2 measures the squared correlation coefficient between locus allele frequencies and is strongly influenced by the order in which the mutations arose (genealogy) and not necessarily the physical distance between loci. In the context of QTL mapping, r2 is the preferred measure of LD, because it quantifies the amount of information that can be inferred about one (perhaps nonobservable quantitative trait or disease) locus from another, and can therefore be used to estimate the number of loci needed for association studies. For this reason we have used r2 as the primary measure of LD in this study.
(Citations omitted.)
146 But according to Professor Taylor, r2 was also used and preferred by some in the quantitative genetics field before the priority date. In a review on LD in humans in Pritchard JK and Przeworski M, "Linkage Disequilibrium in Humans: Models and Data" (2001) 69 Am J Hum Genet 1-14, the authors referred to their use of "one popular measure of LD between pairs of biallelic markers, commonly denoted by r2". So at 1 and 2 they state:
Models and Measures of LD
LD refers to the nonindependence of alleles at different sites. For example, suppose that allele A at locus 1 and allele B at locus 2 are at frequencies πA and πB, respectively, in the population. If the two loci are independent, then would we expect to see the AB haplotype at frequency πAπB. If the population frequency of the AB haplotype is either higher or lower than this - implying that particular alleles tend to be observed together - then the two loci are said to be in LD.
A wide variety of statistics have been proposed to measure the amount of LD, and these have different strengths, depending on the context. The measurement of LD is a large and complex topic and will not be reviewed in detail here; but see the work of Devlin and Risch (1995); Jorde (2000) and Hudson (2001). Most of the measures of LD that are in wide use quantify the degree of association between pairs of markers. In part, they differ according to the way in which they depend on the marginal allele frequencies. In the present article, we use one popular measure of LD between pairs of biallelic markers, commonly denoted by r2 (elsewhere, r2 is also denoted by Δ2). We also discuss a multilocus approach, based on an underlying population genetic model, that we feel has some advantages as a summary of the overall amount of LD in a region.
Consider two biallelic loci on the same chromosome, with alleles A and a at the first locus and with alleles B and b at the second locus, where the labeling is arbitrary. The allele frequencies will be written as πA, πa, πB, and πb, and the four haplotype frequencies will be written as πAB, πAb, πaB, and πab. Then,
In some of the figures, we plot √r2, because this can make it easier to see the data points. For brevity, we will refer to √r2 as "r".
In practice, one typically has a sample of m chromosomes from the population. Then, estimates of r2 ( ̂r2) are usually obtained by plugging the sample frequencies ̂πA, ̂πB, ̂πAB, etc., into equation (1).
Besides estimating the amount of disequilibrium between pairs of markers, it is also natural to test the null hypothesis of independence between marker pairs (i.e., linkage equilibrium). This can be done by a x2 test, and it turns out that, for biallelic markers, ̂r2 is the standard x2-test statistic divided by the number of chromosomes in the sample (Weir 1996, p. 113). As shown later in the present article, r2 also arises naturally in the context of association mapping.
The actual value of the disequilibrium coefficient r2 (or any other measure of LD) between two loci is drawn from a probability distribution that results from the evolutionary process. This process can be described in terms of a population genetics tool called the "coalescent" (for reviews, see, e.g., Hudson 1993; Nordborg 2001). When we draw a sample of chromosomes from a population, all the chromosomes are related by some unknown ancestral genealogy, known as a "coalescent tree". Genetic markers that are very close together on a chromosome have either the same or similar genealogies, and this induces dependence between the alleles at different markers. Markers that are farther apart may have different ancestral genealogies, because of recombination. For this reason, the strength of LD between pairs of markers decreases as a function of the genetic distance between markers.
The expected value of r2 is a function of the parameter p ≡ 4Nec, where c is the recombination rate between the two markers and where Ne is the effective population size. For large p, E(r2) ≈ 1/p (reviewed by Hudson 2001). Below, we will show simulations of the distribution of r under various models.
147 Further, according to Professor Taylor, software programs were also available around 2002 to calculate LD using several different measures including D, D' and r2. Two programs that he was aware of were Popgene and Merlin. Software programs became more widely available from the mid-2000s.
148 Generally, as the specification described at [0199], LD varies as a function of distance and time. But Professor Taylor said that the degree of LD can be and could be at the priority date readily measured at any time by any of the methods mentioned.
149 Contrastingly, Professor Visscher gave evidence that although he understood r2 values of LD before December 2002, there was no consensus within the field as to the appropriate metric to use to measure LD in cattle. Let me elaborate at this point a little further on r2 before continuing with the discussion concerning LD.
150 A reference to an r value is sometimes referred to as the Pearson correlation coefficient, developed by Karl Pearson. Simply put, it is the covariance of two variables divided by the product of their standard deviations. Related to the use of this coefficient is what was described by some of the experts before me on both the appeal and the amendment application as the Fisher transformation. Because the sampling distribution of the correlation coefficient for highly correlated variables may be significantly skewed, the Fisher transformation converts the skewed distribution of the sample correlation coefficient into a Gaussian distribution. So, the sampling distribution of the correlation coefficient untransformed as I understood it did not conform to the central limit theorem. Solution? Perform the Fisher transformation. Such a transformation thereby enables you to test a hypothesis i.e. to accept or reject the null hypothesis as against the hypothesis of interest, or to provide confidence intervals. Now an r value can range from -1 to +1. It is a measure of the strength of the linear relationship between two variables. A figure of 0 indicates that there is no linear correlation. A figure of 1 indicates a perfect positive linear correlation. A figure of -1 indicates a perfect negative correlation. The value of r may be squared to r2. Values of r2 obviously range between 0 and 1. The closer the value of r2 to 1 the higher the correlation.
151 Contrastingly, R2 is sometimes referred to as the coefficient of determination. The metric is classically used when carrying out a linear regression analysis involving ordinary least squares where one is positing a linear model to explain the relationship between a variable of interest (the dependent variable) and another variable(s) (the independent or explanatory variable(s)). Take a population or sample of interest where you measure the dependent variable and are able to calculate or infer the mean of the variable and the variance from the mean or its standard deviation (the square root of the variance). Now say the dependent variable (y) is plotted on a graph against the explanatory value (x). Say a line of best fit is calculated through the data points using the ordinary least squares method involving a modicum of differential calculus, so that an equation for the line is produced (y = a + bx); I will leave out the error term for the moment. Assuming that the line is a good fit (that concept glosses over a number of issues including avoiding serial correlation, heteroscedasticity etc.), for any measurement of x you can use the equation to predict the y value. But in the real world the observed value of y will usually fall either side of your regression line. So there is a variance of the observed values of y from what the regression line would predict; this is reflected in the residual or error term (c), so that the "true" equation should be y = a + bx + c.
152 Now very simply put, what the R2 metric does is to compare and relate the variance of the dependent variable (y) against its mean on the one hand, with the variance of the dependent variable (y) against the regression line (y being regressed on x). If the variance of the dependent variable against the regression line is much smaller than its variance against the dependent variable's mean, then the linear model provides a good basis for explaining the variance of the dependent variable from its mean. In simple terms, R2 is calculated as follows:
or (equivalently)
153 The R2 metric is measured between 0 and 1. The higher the R2 value, the greater the variance in the dependent variable from its mean is explained or "determined" by the explanatory variable; hence the expression "coefficient of determination".
154 Let me make some final points concerning R2 and r2. First, R2 is used in linear regression models as a measure of predictive power. The relationship between specified values of an independent variable(s) (x) and the means of all corresponding values of the dependent variable (y) is modelled for predictive purposes. R2 is the measure of that predictive power. Contrastingly, r2 is used to determine the degree of association or correlation between two variables. It is used to determine the strength of the linear relationship, the present context that I am considering in dealing with LD (I am not at this point discussing predicting phenotype from genotype but the narrower question of the LD between a limb (a) SNP and a limb (b) SNP). Second, it is well accepted that R2 and r2 are not mutually exclusive concepts. Indeed, it can be shown that r2, where you have one independent variable (x) (cf x1, x2… xn) is a special case of R2 making necessary assumptions.
155 Let me return to the question of LD.
156 As should be apparent from what I have just said, LD when measured by r2 is on a continuum from 0 to 1. An r2 value of 0 is indicative of no LD. In other words, the polymorphisms are in linkage equilibrium and therefore knowledge of the identity of an allele at one location tells you nothing more about the identity of an allele at the location of the other polymorphism than was already known based on its frequency in the population.
157 An r2 value of 1.0 is indicative of 100% LD between the polymorphisms. This indicates that knowledge of the allele present at one of the polymorphisms allows you to conclude the presence of the allele at the second polymorphism with 100% accuracy for every chromosome in the population. Consequently, the genotypes of individuals within the given population can be coded in a manner that is identical at both polymorphisms. That is, every animal in the population that is AA, AB or BB, at the first polymorphism will be AA, AB and BB, respectively, at the second polymorphism.
158 Now as I have said, values of r2 are between 0 and 1 and indicative of the degree of LD between the polymorphisms. Professor Taylor understood 'medium' or 'moderate' LD to equate to an r2 value between approximately 0.3 and 0.7. He understood 'low' or 'weak' LD to equate to an r2 value greater than 0 but less than 0.3. Contrastingly, although Professor Visscher agreed that the terms "strong" and "high" were relative descriptors of LD, there was no consensus before the priority date (or indeed now) as to any particular value to be ascribed to these relative terms. And he considered Professor Taylor's attempt to quantify "low", "moderate" and "high" LD as arbitrary as there were no generally accepted values described as such in the field.
159 Now Professor Taylor said that he and others like him that worked in the field of quantitative genetics well understood at the priority date that there was no need for 100% LD between two polymorphisms such as a SNP and a causal polymorphism, which might itself be a SNP or an insertion or deletion event, in order to detect SNPs that are associated with traits in association analyses. For example, in the trait association research that he has done, the SNPs on the BovineSNP50 assay (which queries 54,001 SNP genotypes in an individual) have an average spacing of about 45,000 bases and have an average r2 value of about 0.2. Moreover, he said that polymorphisms that directly cause trait variation in this context could lie no further than 22,500 bases from a tested marker, and the r2 value between the tested marker and causal variant would, on average, be greater than 0.3. He also explained that the BovineSNP50 assay has been extensively used world-wide for association studies in cattle.
160 Professor Taylor also said that for association studies such as those described in the specification he understood a higher r2 value to be desirable, as the objective of association studies is to generate diagnostic markers that increase the likelihood of correctly identifying the genotype of cattle at polymorphisms that directly cause variation in traits. He said that whilst any degree of LD is better than a random association (i.e. r2 = 0) and is sufficient to improve the accuracy of predictions of cattle genotypes at a polymorphism that directly affects a trait, in practice association studies by their nature and as described in the background section of the specification require higher levels of association to detect causal polymorphisms that might have more modest effect sizes and to increase the degree of predictability of genetic potential in animals for breeding and management decisions.
161 For these reasons, according to Professor Taylor, in the context of association studies, despite the fact that there is no explicit disclosure in the specification of a particular r2 value, he understood the reference to LD in the specification to be, practically, a reference to a need for 'high' or 'strong' LD, and for that to equate to an r2 value of 0.7 and above. I must say that I have little reason to doubt his evidence or his understanding, which if necessary I am prepared to accept would be the reading and understanding of a person skilled in the art. Further, in [0201] of the specification, there is a reference to LD between the limb (a) and limb (b) SNPs. Professor Taylor's understanding of the extent of LD that I have just discussed also applies to the extent of LD between the limb (a) and limb (b) SNPs referred to in [0201].
162 Further, Professor Taylor noted that the proposed amendments require that the SNPs in both limbs (i.e. limb (a) and limb (b)) must be significantly associated with a trait. He also noted that the limb (b) SNP retains the requirement to be within 500 kb of the limb (a) SNP.
163 Now Professor Taylor accepted that although the requirement for the respective SNPs to be within 500 kb of each other does not necessarily mean that the two SNPs will be in LD with each other, this distance limitation in the claims, particularly when considered in combination with the requirement that both SNPs must be associated with the same trait, would strongly suggest that the two SNPs were in moderate or strong LD. He pointed out that this is illustrated in Example 3 where the inventors took a sample of the associated SNPs from Example 2 and tested whether additional linked SNPs were associated with the same traits. By analysing the association of SNPs located at varying distances from one of the 2,510 SNPs, the inventors estimated that LD extended about 500 kb. Example 3 provides reasonable (although not conclusive) evidence of LD between the associated SNPs.
164 I must say that I found Professor Taylor's analysis and opinions on this point and the preceding points persuasive.
165 Now Professor Visscher accepted that if two SNP variants are located close to one another on the genome, the same sets of alleles at each locus tend to travel together from one generation to the next non-randomly and the markers can be considered to be in LD. Where there is essentially complete LD between the two SNPs, trait variation explained by one SNP will be similarly explained by the second SNP. But as the distance between the two SNPs increases, the association of the alleles becomes more random. As with association, the LD measured between two loci also varies between breeds, the population tested and is affected by the population size. For example, the larger the population size the greater the accuracy of the measurement.
166 Professor Visscher accepted that LD can be measured in different ways including the Pearson coefficient of correlation (r), a squared coefficient of correlation (r2), or a standardised relative measure of disequilibrium (D) compared to its maximum expressed as D'.
167 And as he said, LD is not an all or nothing state. In his view it is necessary to specify the strength of the association, which is somewhere between 0 and 1 for both the r2 and D' values. Using r2 as the measure, zero indicates that two loci are not in LD and therefore a marker at one location tells you nothing about another location. A value of 1 indicates that there is complete LD between two loci and therefore both markers provide the same information in relation to variation in a trait. Further, he said that the precision of estimation will vary with sample size.
168 Now Professor Taylor accepted that the precision of estimation of r2 values, as with any statistical measure, will depend on sample size. Moreover, the hypothesis that r2 is greater or less than certain threshold values such as 0.7 can be statistically tested using the data that were generated to estimate the r2 value. He said that it was understood that a reasonable sample size was required in order for the null hypothesis to be rejected when it is not true.
169 Professor Taylor said that he agreed with Professor Visscher that LD is not an all or nothing state and that the strength of the association ranges from 0 through to 1. This was well understood by him and other population geneticists. But he said that the proposed amended claims specify the particular strength of the required association through the requirement for the LD to be either equal to or greater than an r2 value of 0.7 or, alternatively, 0.8, and these levels are statistically testable in a cattle breed or population.
170 Now Professor Visscher said that the 253 Application did not contain any description or support for a SNP within 500 kb of a specific SNP being in LD with the specific SNP where the extent of LD is an r2 value of equal to or greater than 0.7 or 0.8.
171 Further, he said that the 253 Application did not describe any calculation of LD between markers. There is no discussion or mention in the 253 Application of an r2 value of LD. He said that the 253 Application makes an estimate about the distance over which LD between markers is likely to extend from statistical associations between SNPs and traits based upon the pooled experiments (see Example 3, Determination of the distance of disequilibrium in cattle). But from his reading of the 253 Application, Example 3 is the only relevant discussion of LD.
172 The 253 Application states at [0199] in relation to Example 3 that:
… The degree of LD varies considerably throughout the genome and is a function of time, recombination events, mutation rate and population structure. The extent of LD can vary from a few thousand base pairs to several centimorgans.
173 It states at [0201] that:
… the study was performed to verify the assumption that markers that are in close physical proximity on the bovine genome will associate with the same trait(s) because markers in linkage disequilibrium with the associated SNP marker will also be in linkage disequilibrium with the mutation(s) influencing the trait.
174 As stated in [0208] of the 253 Application, the results of the tests in Example 3 indicate that disequilibrium in cattle exists across the region of 500,000 nucleotides from an associated SNP, in each direction. As such, the 253 Application at [0208] concludes in relation to Example 3 that:
Therefore, it is expected that when an associated SNP is identified, other markers within this 500,000 bp region will also be in disequilibrium with the associated SNP and with the trait of interest, and can be used to infer associations with the trait of interest.
175 But in Professor Visscher's opinion this is not a measurement of LD, nor does it give any assessment of LD. According to Professor Visscher, there are numerous reasons why two SNPs can be statistically significantly associated with the same trait but not be in LD. Indeed, he said that in order to overcome the fact that a value for LD was not calculated, the 253 Application estimated a distance within which non-specified SNPs are associated with the same trait variant as a specified SNP.
176 It was clear to Professor Visscher from reading Example 3 that the distance 500 kb is used as a proxy for a calculation of LD between markers (based on association with the same trait). However, Example 3 does not provide any information as to the extent of LD, nor what degree of LD is required. According to Professor Visscher, what it does tell is that a SNP within a distance of 500 kb of a specified SNP can be used in place of the specified SNP. But in order for the marker to act as a substitute for a specified SNP and provide the same information in relation to the associated trait as the specified SNP, Professor Visscher expected that the extent of LD, as a measure of r2, would need to be 0.99 or 1. This is because when a SNP is a proxy for another SNP, it will have the same statistical association (p-value) with a trait as the SNP for which it is a substitute. In that sense, they are interchangeable.
177 Now Professor Taylor agreed that the 253 Application did not in terms describe specific methods of calculating LD, including the r2 statistic. However, methods of measuring LD, including the r2 statistic, were well known before the priority date. I accept his evidence as to this.
178 Professor Taylor also disagreed with Professor Visscher that the 253 Application required that the limb (b) SNP must be in complete or virtually complete LD (r2 > 0.99) with the limb (a) SNP. I agree with Professor Taylor.
179 According to Professor Taylor, Professor Visscher's requirement for an r2 value of 0.99 or 1.0 in effect requires that the limb (b) SNP have genotypes in the population that can be coded to be identical or almost identical to the genotypes of the limb (a) SNP. He says that this misunderstands the purpose of the method described in the 253 Application which is to identify and select desirable traits in cattle through associations between SNPs and the trait. The purpose of the method is not to identify associations between candidate diagnostic SNPs. This is apparent from Example 3 where the inventors took a sample of the associated SNPs from Example 2 and tested whether additional SNPs within 500 kb were associated with the same trait. The purpose of Example 3 was to identify the usefulness of other SNPs within the region (the limb (b) SNPs) to identify and select desirable traits through association. The purpose was not to predict the genotype of the limb (a) SNP. In other words, there is no requirement that the limb (b) SNP be perfectly or nearly perfectly predictive of the limb (a) SNP. However, because the limb (a) SNP is in strong LD with a causal genetic variant that causes trait variation and because the limb (b) SNP is also in strong LD with the same causal variant, Professor Taylor said that one would expect strong, but not perfect or near perfect, LD between the limb (a) SNP and the limb (b) SNP. This is also apparent from the discussion of Example 3 in the 253 Application which indicates that the additional SNPs were identified by reason of their association with the trait and therefore their usefulness in identifying traits of interest, and not by reason of genotypic identity with the limb (a) SNP. I must say that on my own reading of the 253 Application this seems correct.
180 Furthermore, I agree with Professor Taylor that Professor Visscher's requirement for the limb (b) SNP to be in LD with the limb (a) SNP at an r2 value of 0.99 or 1 fails to recognise that there may be limb (b) SNPs which are not in perfect or near perfect LD with the limb (a) SNP but have a stronger association with the trait than the limb (a) SNP. Such limb (b) SNPs would be useful in identifying trait(s) through association even though they were not genotypically identical or nearly identical to the limb (a) SNP.
181 Now Professor Visscher did agree with Professor Taylor that a high r2 value between a marker and a trait is desirable in association studies and in selection for that trait, but the appropriate level of LD will depend on the context in which the marker is being used. But according to Professor Visscher, a statement of an r2 value of greater than 0.7 or 0.8 was arbitrary as it was not an accepted value in the field and was not described or suggested in the 253 Application.
182 Further, Professor Visscher agreed that the higher the degree of LD between a marker and a causative variant, the more information that will be captured by the marker and its usefulness therefore increases. But according to him, the reference to LD in the proposed amended claims of the 253 Application is between a specified SNP said to be associated with a trait and a non-specified SNP for which no association data is known. He said that this is not the same as the association between a marker and trait discussed in the 253 Application. Professor Visscher understood that the distance of 500 kb was included in the claims as a proxy for LD and in order to capture those SNPs that would be associated with the same trait as a specified SNP. According to his evidence, the non-specified SNP is essentially a substitute (proxy) for a specified SNP and its use is intended to provide the same information in relation to the associated trait as a specified SNP. In that context, in terms of LD, if it is necessary to ascribe an r2 value, he said that he would consider that an r2 value of greater than 0.99 or of 1 would be appropriate.
183 Now Professor Taylor had to agree that an r2 value of greater than 0.7 or 0.8 is, in one sense, arbitrary in the sense that different quantitative geneticists might define slightly different values as implying strong LD. But he said that these r2 values provide a clear threshold which he, and many other quantitative geneticists, would understand as meaning strong LD. That seems to be right in my view.
184 Further, Professor Taylor said that in relation to Professor Visscher's comment that the requirement for LD is between a trait associated SNP and a SNP for which there is no association data, the proposed amended claims require that the limb (b) SNP be significantly associated with the trait at a p-value of less than or equal to 0.05 or less than or equal to 0.01. The proposed amended claims also require that the limb (a) and limb (b) SNPs have an r2 value of greater than or equal to 0.7 or 0.8.
185 Professor Visscher said that the authors of the 253 Application made no measure of LD. And he therefore did not see how it was possible to select any value for r2 and say that value was based on or supported by what is described in the specification. And as to Professor Taylor's suggestion that the distance limitation in the claims, when considered in light of the requirement that both SNPs be associated with the same trait, suggests that two such SNPs would be in moderate or strong LD, according to Professor Visscher LD as a function of distance is likely to be 'low' over the 500 kb distance required by the claims. He pointed out that in De Roos AP et al, "Linkage Disequilibrium and Persistence of Phase in Holstein-Friesian, Jersey and Angus Cattle" (2008) 179(3) Genetics 1503-1512, on average mean values of r2 were only above 0.8 over distances less than 10 kb, and that at a distance of 500 kb the r2 values were around 0.05 to 0.1. He said that this indicates that there would be only a small degree of LD over distances of 500 kb.
186 But Professor Taylor responded that Professor Visscher's statement that "LD as a function of distance is likely to be 'low' over the 500,000 base pair distance required by [the] claims" reflects what happens 'on average' because recombination works to dissipate LD between loci that are separated by large distances on a chromosome. But in Professor Taylor's view, Professor Visscher's statement could be simply restated to say that the number of limb (b) SNPs that are in LD with a specific limb (a) SNP at r2 ≥ 0.7 (or r2 ≥ 0.8) will be fewer at a distance of 500 kb than at a distance of 10 kb. But this does not mean that limb (b) SNPs with r2 ≥ 0.7 (or r2 ≥ 0.8) at 500 kb do not exist. It simply means that limb (b) SNPs with r2 ≥ 0.7 (or r2 ≥ 0.8) with the limb (a) SNP will tend to be closer than 500 kb to the limb (a) SNP. I think what Professor Taylor says is correct.
187 Let me move to a slightly different matter. In terms of a lack of clarity, Professor Visscher gave the following evidence.
188 If one requires a marker and a trait to be associated at a specified level of statistical significance, then the level of association detected is dependent on the study design. For example, a marker that is found to be statistically significantly associated with a particular phenotype in cattle for a given population at a p-value of 0.3", which was described as a "useful" LD (Uimari P et al., "Genome-Wide Linkage Disequilibrium from 100,000 SNPs in the East Finland Founder Population" 8(3) (2005) Twin Research and Human Genetics 185).
261 Fourth, there is an explicit reference to "measures" of LD in the 253 Application. It is apparent that r2 was one such measure before December 2002. Professor Visscher so accepted this.
262 Fifth, Professor Visscher understood from reading the claim what an r2 value of greater than or equal to 0.7 was, and accepted that this was something he would have been capable of measuring as at December 2002.
263 Sixth, Professor Taylor explained how he would have gone about measuring an r2 value of LD, using standard statistical approaches. And the fact that the claim does not specify a particular sample size or details of the statistical test is not to the point. These are parameters routinely chosen by the skilled quantitative geneticist in order to derive an estimate of such a value.
264 Seventh, Professor Visscher accepted that such a statistical approach could be adopted, that an estimate of r2 with confidence intervals could be derived using such an approach, and that if a person wanted to increase the precision of the estimate a larger sample size could be used.
265 Eighth, Professor Visscher also accepted that one would not need LD of between 0.99 and 1.0 in order to identify a limb (b) SNP that was also associated with the same trait as a limb (a) SNP, and that insistence upon such a high degree of LD could result in excluding a limb (b) SNP that was more strongly associated with a relevant trait(s) than the corresponding limb (a) SNP. Moreover, Professor Visscher accepted that the specification in relevant passages did not insist upon an LD as high as between 0.99 and 1.0.
266 Generally, as is apparent, significant aspects of the evidence of Professor Visscher supported Branhaven's case. Let me now turn to address MLA's s 102 points directly.
267 MLA's first point is that there has not been in substance disclosure and, relatedly, that there is no fair basis.
268 MLA has contended that an amendment that introduces an entirely new integer or new and original material is not allowable on the basis that it is not "in substance disclosed". It contends that the 253 Application did not disclose a particular measure of LD, being r2, and at a particular value, being ≥0.7 or ≥0.8. Therefore, the introduction of such a metric and at such a value was not "in substance disclosed". Let me deal with this submission at a number of levels.
269 First, I did not find the UK cases to which my attention was drawn to be that helpful to my consideration of what was or was not "in substance disclosed" in the 253 Application. Cases such as AMP Inc v Hellerman Ltd [1962] RPC 55 at 72, Ethyl Corporation's Patent [1972] RPC 169 at 192 to 195 and Shionogi & Company Ltd's Application [1967] RPC 623 at 626 and 627 turn entirely on the particular specifications and particular amendments sought. Further, what was sought to be added in Shionogi ("new and original material so as concerns…the preparation of the starting material and…the separation technique…") is a far cry from what I am considering. In my case what is being considered, on the hypothesis that LD has been disclosed, is the measurement and narrowing degree thereof. It is hardly a new integer. Further, AMP is well away from what I am considering. That was dealing with the situation where "[t]he tool with a stop was disclosed as well as the tool without a stop. The patentee disclaims the tool without a stop and confines himself to the tool with a stop". Lord Denning saw no problem as the amendment had not sought to add "an entirely new integer". Further, Ethyl Corporation's Patent really does not assist MLA either although it is a little closer. The amendment proposed to claim 14 introduced a restriction into that claim stipulating the ratio of a hydrocarbon to tetramethyllead in an antiknock composition with the "hydrocarbon being present in amounts from 20 to 80 weight per cent of the tetramethyllead". The amendment was allowed because the original specification contained examples of compositions within the amended added range. But it is a leap to extrapolate from that case that non-reference to a metric or its degree in relation to an integer which serves a different significance in the case before me can be said to be not "in substance disclosed". MLA said that the UK cases demonstrate that "the test has been applied strictly". I am not sure where the word "strictly" comes from other than being MLA's characterisation. But what these cases demonstrate is that entirely new integers and new and original additions to the invention are not permitted. But that is not the case before me.
270 Second, the present amendments sought by Branhaven are narrowing amendments. If it is accepted that LD has been disclosed, as it must be, the amendments seek to clarify and narrow how it is to be measured and the degree thereof. Indeed I have already found in substance that there is fair basis with respect thereto.
271 Third, if it be correct to say, as I think it is, that there is a close relationship between the test for in substance disclosure and the test for fair basis, then the observations of Yates J in DSI Australia (Holdings) Pty Ltd v Garford Pty Ltd (2013) 100 IPR 19 at [240] are useful:
In the present case, Garford submitted that the notional claims propounded by the DSI parties were not fairly based on the matter described in the IRF application. I am of the view that the notional claims, if they were to be claims of the IRF application, would be fairly based on the matter described in the specification of that application for the purposes of s 40(3) of the Act. I am satisfied that there is real and reasonably clear disclosure in the body of the specification of the invention that is notionally claimed. Importantly, in this connection, the inquiry as to fair basis is directed to the question of claim width: see, for example, Olin Corporation at CLR 240; ALR 152; IPR 200. A claim may be fairly based for the purposes of s 40(3) of the Act where it adds a feature to a combination otherwise described in the specification and, by that addition, limits the described invention, as a matter of definition, to a more restrictive form than that to which the patentee might otherwise be entitled. In short, a claim may be fairly based for the purposes of s 40(3) of the Act even when all the characteristics by which the invention is defined in the claim are not described in the body of the specification itself, provided those characteristics are truly limiting ones in the sense that I have described.
272 It is apparent that there may be no need for explicit disclosure in the specification of truly limiting features; I am not here dealing with the "very general description of the invention" case of the type discussed by the Full Court in AstraZeneca, and in any event that Court expressed itself in terms of "might not contain" (my emphasis). In the present case the measure of LD and its degree which are being added are truly limiting features and matters of detail to the LD aspect already disclosed.
273 Fourth, MLA as I understood its argument said that you could not just pluck out anything from common general knowledge and add it by way of amendment, in other words r2 and its degree. Of course put so glibly that proposition is correct. But that is not what Branhaven is doing. Branhaven is narrowing its claims consistently with well understood concepts forming part of the common general knowledge as at the priority date. It is not picking an "entirely new integer" for the invention from common general knowledge.
274 Fifth, there is no dispute that it was well known at the priority date that the degree of LD varied. This understanding is consistent with the specification which, as I have said, describes at [0199]: "The degree of LD varies considerably throughout the genome and is function of time, recombination events, mutation rate and population structure."
275 Sixth, the specification indicates that the usefulness of the limb (b) SNPs in identifying traits arises from them being in LD with the limb (a) SNP (at [0035]). In particular, the specification specifies (at [0126]) that:
In another embodiment of the invention, a method is provided for identifying SNPs that are associated with a trait by using the associated SNPs disclosed herein. The method is based on the fact that other markers in close proximity to the associated SNP marker will also associate with the trait because markers in linkage disequilibrium with the associated SNP marker will also be in linkage disequilibrium with the gene(s) influencing the trait. SNPs in linkage disequilibrium can be used in lieu of determining a SNP or mutation to predict the presence or absence phenotypic trait or a contributor to a phenotypic trait. Accordingly, in certain embodiments, the present invention provides a method for identifying a SNP associated with a trait, that includes identifying a test SNP that is in linkage disequilibrium with a [limb (a)] SNP.
276 In my view in its proper context the skilled addressee would understand that the reference to LD between the limb (a) and (b) SNPs in the specification is, practically, a reference to a need for "high" or "strong" LD. An r2 value of 0.7 and above is consistent with this.
277 Seventh, MLA's principal contention is based on the fact that the specification does not explicitly identify any method for measuring LD including the r2 measure. But this ignores that the specification is not to be read in the abstract but in the light of the common general knowledge. The Court is to place itself "in the position of some person acquainted with the surrounding circumstances as to the state of [the] art and manufacture at the time" (Kimberley-Clark Australia Pty Ltd v Arico Trading International Pty Ltd (2001) 207 CLR 1 at [24]).
278 In that context, all that is being done in the proposed amendments is to use a common general knowledge measure of LD to provide an explicit definition of a feature of the invention that is already disclosed (implicitly and explicitly) in the description of the 253 Application: a requirement for LD between a limb (b) SNP and a limb (a) SNP. This involves merely clarifying or claiming a subset of what is already in substance disclosed, and does not result in any lack of fair basis.
279 Eighth, the evidence shows that stipulation of a "high" degree of LD as proposed is consistent with the disclosure in the 253 Application in that the usefulness of the limb (b) SNPs arises from them being in LD with a limb (a) SNP. A higher degree of LD directs the method to more useful limb (b) SNPs.
280 In that context, in my view the skilled addressee would understand that the reference to LD between the limb (a) and (b) SNPs in the specification to be or at least to include a reference to a need for "high" or "strong" LD. An r2 value of 0.7 and above is consistent with this.
281 Further, it is not to the point that no measurement of LD by the r2 measure is explicitly disclosed in the description. The concept of LD between a limb (b) SNP and a limb (a) SNP is clearly disclosed as a basis for the limb (b) aspect of the invention, as was the fact that LD is a relative concept that can vary. Moreover, as at the priority date, r2 was a common general knowledge measure of LD. Now other measures of LD were available in December 2002 and could have been used. But the r2 measure met that description. Further, the use by Professor Taylor and others of terms such as "high", "moderate" and "low" LD in different contexts in the literature is not really to the point. The proposed amendments specify a degree of LD in terms of a specific r2 value which is objective and clear, and would have been measurable by the skilled person in December 2002.
282 Let me now deal with MLA's second point concerning a lack of clarity and a failure to define the invention.
283 Now Professor Visscher characterised the specified r2 values of 0.7 and 0.8 as "arbitrary". But this is not a proper basis to find that the proposed claims lack clarity. The question is whether the integer in question is clear, in the sense of it being readily capable of being understood and applied by the skilled person. In my view an r2 value of equal to or greater than 0.7 or 0.8 meets that description.
284 Of course an r2 value of equal to or greater than 0.7 or 0.8 is in one sense "arbitrary", in that different quantitative geneticists might choose to define slightly different values as implying strong LD. But in that sense, any stipulation of a parameter of this kind in a patent claim could be said to be "arbitrary". On any view it is a particular but readily comprehensible limitation on the claim. Indeed, the values specified in the claims are no more "arbitrary" than the 0.99/1.0 value specified by Professor Visscher. I agree with Branhaven that the specified values in the proposed amendments provide a clear and workable standard that would be understood by the skilled addressee and readily measured.
285 Further, the proposed degree of LD is high and therefore clearly sufficient for the limb (b) SNP to be used in lieu of the specified limb (a) SNP. The proposed amendment is also generally consistent with the passages in the 253 Application at [0035] and [0126]. Further, as I have said, the amendments also require the limb (b) SNP to be associated with the trait at a high level of statistical significance.
286 Now as Professor Taylor said, which I accept, Professor Visscher's requirement for an r2 value of 0.99 or 1.0 in effect requires that the limb (b) SNPs have genotypes in the population that can be coded to be identical or almost identical to the genotypes of the limb (a) SNP. But the 253 Application does not require that the limb (b) SNP be perfectly or nearly perfectly predictive of the limb (a) SNP. The purpose of the method described in the 253 Application is to identify and select desirable traits in cattle through associations between SNPs and the trait, not to identify associations between candidate diagnostic SNPs.
287 This is apparent from the specification at [0126] and Example 3 which identifies the usefulness of other SNPs within the region (the limb (b) SNPs) to identify and select desirable traits through association, not to predict the genotype of the limb (a) SNP. This is also apparent from the discussion of Example 3 which indicates that the additional SNPs were identified by reason of their association with the trait (and therefore their usefulness in identifying traits of interest) and not by reason of genotypic identity with the limb (a) SNP. I accept Professor Taylor's evidence to this effect.
288 Moreover, because the limb (a) SNP is in strong LD with a causal genetic variant, that is, causes trait variation, and because the limb (b) SNP is also in strong LD with the same causal variant, in my view strong, but not perfect or near perfect, LD between the limb (a) and limb (b) SNPs would be expected.
289 Further, Professor Visscher's requirement for an r2 value of 0.99 or 1 also fails to recognise that there may well be limb (b) SNPs which are not in perfect or near perfect LD with the limb (a) SNP but that have a stronger association with the trait than the limb (a) SNP. As Professor Taylor said, such limb (b) SNPs would clearly be very useful in identifying trait(s) through association even though they are not genotypically identical or nearly identical to the limb (a) SNP.
290 Let me turn to another matter. I agree with Branhaven that the fact that the r2 value would depend on the sample size does not introduce a lack of clarity.
291 As with the determination of the degree of association between the SNP and a trait, the precision of estimation of r2 values will depend on sample (population) size. However, the hypothesis that r2 is greater or less than certain threshold values such as 0.7 can be statistically tested using the data that were generated to estimate the r2 value. Furthermore, it would be understood by the skilled addressee that a reasonable sample size was required in order for the null hypothesis to be rejected when it was not true.
292 Further, as Professor Taylor said, there were many association studies, albeit not genome-wide, between genetic markers and traits conducted before the priority date, both in relation to cattle and other species including humans. In all of these studies, the methodology including the sample size was designed so that meaningful and useful associations could be detected.
293 I reject MLA's s 102 arguments on lack of clarity and a failure to define the invention concerning r2 and the threshold values for measuring LD.