Use of overlapping DNA pools to discern genetic differences despite pooling error

Abstract

Genotyping pools of commercial cattle and individual seedstock animals may reveal hidden relationships between sectors enabling use of commercial data for genetic evaluation. However, commercial data capture may be compromised by inexact pool formation. We aimed to estimate the concordance between distances or genomic covariance among pooling allele frequencies (PAFs) of DNA pools comprised of 100 animals with 0% or 50% overlap of animals in common between pools. Cattle lung samples were collected from a commercial beef processing plant on a single day. Six pools of 100 animals each were constructed so that overlap between pools was 0% or 50%. Two pools of all 200 animals were constructed to estimate PAFs for all 200 animals. Frozen lung tissue (0.01 g) from each animal was weighed into a tube containing a pool; there were two pools of 200 animals each and six pools of 100 animals each. Every contribution of an individual animal was an independent measurement to insure independence of pooling errors. Lung samples were kept on dried ice during the pooling process to keep them from thawing. The eight pools were then assayed for approximately 100,000 single nucleotide polymorphisms (SNP). PAF for each SNP and pool was based on the relative intensity of the two dyes used to detect the alleles rather than genotype calls which are not tractable from pooling data. Euclidean distances and genomic relationships among the PAFs for the eight pools were estimated and distances were tested for concordance with pool overlap using permutation-based analysis of distance. Distances among pools were concordant with the planned overlap of animals shared between pools (P = 0.0024); pool overlap accounted for 70% of the variation and pooling error accounted for 30%. Pools containing 100 animals with no overlap were the most distant from one another and pools with 50% overlap were the least distant. This work shows that we can discern differences in distance between pairs of overlapping DNA pools sharing 0% and 50% of the animals. Genomic correlations among nonoverlapping pools indicated that nonoverlapping pool pairs did not share many related animals because genomic correlations were near zero for these pairs. On the other hand, one pair of nonoverlapping pools likely contained related animals between pools because the correlation was 0.21. Pools sharing 50% overlap ranged in genomic relationship between 0.21 and 0.39 (N = 12).

Relevance and accuracy of genetic evaluations of bulls produced in the seedstock sector can be improved through capturing commercial data from ranches, feedlots, and processing plants. We provide evidence that overlapping DNA pools provides a cost-effective strategy to identify genetic connections between seedstock and commercial sectors of the cattle industry despite pooling error.

Introduction

Genotyping pools of commercial animals and individual seedstock animals may reveal hidden relationships between commercial and seedstock sectors enabling genomic selection at a reasonable cost. Detecting hidden relationship between sectors may be compromised by inexact pool formation (pooling error). Computer simulation has been used to show the potential effectiveness of DNA pooling to provide input to genetic evaluation with (Vargas Jurado et al., 2021) and without (Alexandre et al., 2019; Baller et al., 2020) considering pooling error. Depending on pooling error, this strategy can dramatically reduce the cost, improve feasibility, and increase the effectiveness of capturing commercial data for genetic evaluation. Pooling error can compromise the use of pools for genetic evaluation (Keele et al., 2021); hence, an approach which jointly considers pooling error in genetic evaluation is needed.

Pooling errors (SNP and animal specific error) can be estimated by genotyping pools and the individual animals comprising them. However genotyping individual animals is expensive whether the goal is to evaluate pooling error or predict breeding values. To circumvent the high cost of individual genotyping, it may be possible to identify population and family differences among pools despite pooling error using overlapping pools which share random unrelated animals in known proportion. Overlapping pools can be used to discover novel polymorphisms associated with disease, identify animals associated with genetic differences, and normalize errors associated with pooling (Prabhu and Pe’er, 2009). Our objective was to determine if it is possible to detect overlap of common animals between pools and distinguish from spurious results caused by pooling error using SNP arrays that are commonly available for genetic evaluation.

Materials and Methods

Animals and samples

Lung samples (N = 200) were collected from a local beef processing plant in 2010. Samples were subsequently stored at −20 ºC. Use of animals was not approved through an animal care and use committee as samples were obtained from a commercial harvest facility.

Our approach relied on using overlapping pools to allow simultaneous detection of error and animal differences because overlap creates expected degree of similarity among pools which mimic differences in average relationship among pools. Our design incorporated 0% or 50% for pools with 100 animals (Figure 1, Table 1). Animals were randomly allocated to eight animal sets of 25 each with no common animals between sets and no duplication of animals within set. Pools 1 and 2 contained all eight animal sets (200 animals total) and pools 3 through 8 each contained half (N = 4) of the animal sets (100 animals total in each pool). Pools 3 through 8 were created to evaluate the genomic relationships among pools of the same size (N = 100) with 0 or 50 animals in common (Table 1). Each small pool (100 animals) has mismatching counterpart small pool with no overlapping animal sets. In addition, each small pool overlaps 50 animals with four other pools.

Figure 1.

Construction of pools from animal sets of 25 animals each. Each animal set was unique in terms of membership. Pools 1 and 2 were constructed from all 200 animals. Pools 3 through 8 are represented by arrows. Each arrow in the graph represents 25 measurements of individual animals which was done to insure stochastic independence of pooling errors. Each solid and dashed arrows of the same color point to a pair of pools with 0% overlap. Pools with different arrow colors pointing to them overlapped for 50% of the animals. Pools with 50% of their animals in common should produce similar results to offspring pools compared to pools of their dams.

Table 1.

Construction of pools from animal sets¹

	Animal set
Pool	1	2	3	4	5	6	7	8
1	1	1	1	1	1	1	1	1
2	1	1	1	1	1	1	1	1
3	1	1	1	1	0	0	0	0
4	0	0	0	0	1	1	1	1
5	1	0	1	0	1	0	1	0
6	0	1	0	1	0	1	0	1
7	1	1	0	0	0	0	1	1
8	0	0	1	1	1	1	0	0

¹Each animal set represents 25 animals; and animal sets do not share animals.

Animals within animal sets were pooled according to ­Figure 1 and Table 1 by weighing 0.01 g of frozen lung tissue into the pooled sample. Dry ice was used to keep lung tissue in a frozen state during the pooling process. For DNA extraction of the tissue pools, each tissue pool was resuspended in 10 ml PBS and homogenized with a tissue homogenizer for 30 s to break down the tissue for subsequent total DNA extraction from the pooled tissue using a standard phenol chloroform method. DNA quantity and quality were determined by DNA spectrophotometer (DeNovix DS-11 FX Series; Wilmington, DE) and gel electrophoresis, respectively. The DNA pools were evaluated using the GGP Bovine 100K beadchip assay (Illumina, San Diego, CA).

Pooling allele frequency (PAF)

PAF is a proxy for allele frequency based on normalized intensities of red and green signal from the GGP Bovine 100K beadchip assay, where relative intensity of the signal is used in the analysis rather than the traditional genotype call. This concept was previously reported in McDaneld et al. (2012). Briefly, PAF was computed from the X and Y intensity data using procedures described by Illumina and used in Keele et al. (2021). We computed PAF for an SNP and a pool as $ta{n}^{-1}\left(\frac{Y}{X}\right)\frac{2}{\mathrm{\pi }}$, where $ta{n}^{-1}(.)$ is the inverse or arc tangent function and $X$ and $Y$ were red (A allele) and green (B allele) normalized fluorescent dye intensities. Collectively, the PAF for all pools and SNP will be referred to as matrix $P$ with a row for each SNP and a column for each pool.

Statistical analysis

The overlap of animal sets in pools was specified by $Z$, a matrix with eight rows and columns with values of 0 or 1 with a value of 1 indicating which animal sets are in pools (Table 1). The matrix, $Z$, did not have full column rank, rank = 4, so it was not possible to estimate effects for each of the eight animal sets. We identified a set of four estimable functions by factoring $Z=U{V}^{\prime }$, where $U$ is a matrix with eight rows (one for each pool) and four columns in Table 2 and $V$ is a matrix with eight rows (one for each animal set) and four columns in Table 3. Both $U$ and $V$ are orthogonal. Euclidean distances (d) were computed among the eight pools (Table 4). Tests for the influence of pool overlap on distance were based on permuting the distance matrix (Anderson, 2017) using adonis under the null hypothesis that pool overlap does not affect distance among pools. The resulting F-test is based on permuting the indices of the distance matrix. Adonis2 from the vegan package (Oksanen et al., 2022) of R, adonis2($d\sim U_1+U_{234}$, permutations = 40,319) for the 3 degree of freedom test, where $U_1$ refers to the first column of $U$ and U₂₃₄ refers to columns 2 through 4 (Table 2).

Table 2.

Linear contrasts among the eight pools (matrix $U$ for evaluating distance)

	Estimable functions of animal sets 1
Pool	Mean contribution	First–Last	Odd–Even	Outside–Inside
1	1.00	0.00	0.00	0.00
2	1.00	0.00	0.00	0.00
3	0.50	0.50	0.00	0.00
4	0.50	−0.50	0.00	0.00
5	0.50	0.00	0.50	0.00
6	0.50	0.00	−0.50	0.00
7	0.50	0.00	0.00	0.50
8	0.50	0.00	0.00	−0.50

¹Each animal set (1 to 8) represents 25 animals; and animal sets do not overlap or share animals in common.

²Contrasts were first–last: 1, 2, 3, 4 vs. 5, 6 7, 8; odd–even: 1, 3, 5, 7 vs. 2, 4, 6, 8; and outside–inside: 1, 2, 7, 8 vs. 3, 4, 5, 6.

Table 3.

Estimable functions of animal sets (matrix $V$)

	Estimable functions of Animal Sets1
Animal Set	Mean contribution	First–Last	Odd–Even	Outside–Inside
1	1	1	1	1
2	1	1	−1	1
3	1	1	1	−1
4	1	1	−1	−1
5	1	−1	1	−1
6	1	−1	−1	−1
7	1	−1	1	1
8	1	−1	−1	1

¹Each animal set (1 to 8) represents 25 animals; and animal sets do not overlap or share animals in common.

²Contrasts were first–last: 1, 2, 3, 4 vs. 5, 6 7, 8; odd–even: 1, 3, 5, 7 vs. 2, 4, 6, 8; and outside–inside: 1, 2, 7, 8 vs. 3, 4, 5, 6.

Table 4.

Euclidean distance among pools. Boxed cells are from pools that do not share animal sets

	Pools
Pool	1	2	3	4	5	6	7
2	8.88
3	12.47	12.30
4	11.85	11.44	16.46
5	12.28	11.91	13.89	13.71
6	13.48	13.41	13.61	14.08	17.51
7	14.85	14.37	15.36	15.30	15.03	14.70
8	14.19	14.05	15.54	15.37	14.93	15.30	17.18

In addition to the distance matrix, we also computed the genomic relationship matrix $\left(G\right)$ among pools of 100 animals because $G$ has some advantages in interpreting PAF among overlapping and nonoverlapping pools. First, if the animals in nonoverlapping pools are truly unrelated then the genomic relationship approaches zero or negative values. Second, if there are related animals between the nonoverlapping pools then the relationship matrix will be equal to the average relationship between the pools. Pooling error shrinks the value of the genomic relationship matrix towards zero. In estimating the genomic relationship matrix, pools of 200 (pools 1 and 2) were used to estimate the allele frequency and were not included in the matrix because pool size was confounded with percentage overlap of common animals. The genomic relationship matrix for pools 3 through 8 was computed as $G=\frac{1}{a}{(P-\mu )}^{\prime }(P-\mu );$ where $P$ were PAF for pools 3 through 8, $\mu$ was a vector of length $n$, which was the average of pools 1 and 2 for each SNP, ${\mu }_i=\frac{1}{2}\underset{j=1}{\sum ^2}{P}_{ij(iϵ1,2\dots n),}a=\underset{i=1}{\sum ^n}{\mu }_i(1-{\mu }_i),$ and $n$ is the number of SNP. Pools 1 and 2 included all 200 animals so the average of the two pools would estimate the overall allele frequency with some normalization of pooling error which is expected to be smaller for pools of 200 compared to pools of 100 (Keele et al., 2021). The genomic correlation matrix was computed from the genomic relationship matrix using a ­well-known formula for computing correlations from covariances and standard deviations as $R={\sigma }^{-1}G{\sigma }^{-1}$, here $\sigma$ is a diagonal matrix with values on the diagonal equal to the square root of the diagonal values of $G.$

Results and Discussion

Euclidean distance among DNA pools

Euclidean distances among pools are in Table 4. Euclidean distance is the square root of the sum of the squared differences of PAF between two pools over SNP. The distance between pools 1 and 2 was 8.88 (Table 4) which estimates the sum of the pooling error for pools of 200 because pools 1 and 2 share 100% overlap in animals represented.

Our design did not permit estimation of pooling error for pools of 100 because we did not construct pools of 100 with 100% overlap and it cannot be assumed that pooling error for pools of 100 are the same as for pools of 200, pooling error for pools of 100 would probably be larger (Keele et al., 2021). Distances among pools of 100 sharing 50% overlap were smaller than distances among pools of 100 sharing 0% overlap indicating that it is possible to determine if the members of 1 pool share at least 50% relationship to members of another pool (Table 4; Figure 2). This would be the case if 100 offspring were included in a pool and the dams of each of the offspring were included in another pool.

Figure 2.

Interpool Euclidean distance by number of animals and sharing of animals between the pair; 200|200|200—pool of 200 animals with all animals in common; 200|100|100—pools of 200 animals compared to pools of 100 with 100 animals shared; 100|50|100—pools of 100 animals compared with 50 animals in common; and 100|0|100—pools of 100 animal compared with 0 animals in common.

Relationship between distance among pools and animal overlap

We tested animal composition differences among pools by evaluating the concordance between distances among pools and planned sharing of animals among pools (Table 5). The 3 degree of freedom test for association of distance with planned animal overlap was significant (P = 0.0024) with 70% of the variation attributable to the planned animal overlap among pools and less than 30% due to pooling error.

Table 5.

Analysis of distance table¹

Source of variation2	Degrees of freedom	Sums of squares	R2	F	P
U1	1	82.49		1.35	0.0952
U234	3	436.42	0.704	2.38	0.0024
Residual	3	183.67	0.296
Total	7	702.58	1.000

¹Number of permutations used for the analysis was 40,319.

²Linear contrasts among pools were defined in U (Table 2); U₁ (mean) was the first column and U₂₃₄ were the columns 2 through 4.

The genomic correlation estimates the combined effect of overlap between pools with known overlap or relatedness among pools shrunk by pooling error. Genomic relationships and correlations indicate minimal or zero relationship between nonoverlapping pools except for between pools 7 and 8 which have a genomic correlation of 0.21 (Table 6). Genomic correlations among pools overlapping 50 % (N = 12 pool pairs) ranged from 0.21 to 0.39. This wide range in genomic correlations indicates either pooling error or relatedness among pools varies. We did not study pools of 100 with 100% overlap so we were not able to separate the effects of pooling error from relationships between pools. Pools of animals from opposite tails of the phenotypic distribution would be more distant from one another than pools comprised of animals sampled from the middle of the distribution or from only one of the tails if the phenotype is heritable (Baller et al. 2020) because animals with different phenotypes are expected to be less related and animals with similar phenotype more related. The more heritable the phenotype, the less related are the phenotypic tails and more related are animals with similar phenotype.

Table 6.

Genomic relationship matrix (diagonal and above) and genomic correlations (below the diagonal)

	Pool
Pool	3	4	5	6	7	8
3	0.0068	−0.0006	0.0018	0.0028	0.0023	0.0019
4	−0.0910	0.0059	0.0014	0.0020	0.0019	0.0015
5	0.2653	0.2275	0.0064	−0.0006	0.0024	0.0021
6	0.3698	0.2869	−0.0813	0.0082	0.0035	0.0027
7	0.2806	0.2507	0.2996	0.3907	0.0099	0.0020
8	0.2353	0.2054	0.2768	0.3147	0.2088	0.0092

A pool of offspring and a pool of the one of the parents (sire or dam) of the pooled offspring would be expected to have similar genetic relatedness as two pools of random animals with 50% of the animals overlapping. The pedigree is typically not known for commercial cattle; hence, pools of overlapping random animals are more feasible than pools of animals with known relatedness, especially if the animals are segregated to pools within management units by phenotype means.

Comparing genomic correlations among pools with different levels of phenotypic variation between and within pools to pools with different levels of overlap would enable an estimate of heritability if the breed composition of all pools is similar.

Commercial cattle populations may contain considerable breed diversity. Previous research showed that animals sampled near each other on the beef processing chain (most likely from the same lot) were more genetically similar than cattle sampled from distant positions on the chain which would be from different lots (Keele et al., 2015). Pools comprised of multiple feedlot pens or multiple packing plant lots are less likely to be different from one another in breed composition depending on how diverse the feedlot pens and packing plant lots are.

When designing pooling studies for GWAS or genomic selection, we know that it is favorable to minimize variation in the phenotype within pools and maximize variation between pools (Alexandre et al., 2019; Baller et al., 2020; Vargas Jurado et al., 2021) to detect exploitable genetic variation and make genetic progress. Capture of commercial data to aid in genetic evaluation of seedstock animals is made complex and potentially costly by all that is unknown about the animals from which the data is recorded including genetic connections to seedstock population, breed composition, and family structure. Previous simulation studies (Alexandre et al., 2019; Baller et al., 2020; Vargas Jurado et al., 2021) have shown that there is potential to capture commercial data to aid in genetic evaluation regardless of pooling error; but feasibility depends on the balance between relationships and pooling error. Pooling error has greater effect on results for pools with smaller number of animals compared to larger (Keele et al., 2021), but these differences are likely more pronounced for smaller pool sizes compared to larger.

Overlapping pools enables assessing the balance between relationships among pools and pooling error. Knowing this balance will enable the design of genetic improvement programs incorporating commercial data capture.

Abbreviations

DNA

deoxyribonucleic acid

PAF

pooling allele frequency

PBS

phosphate buffered saline

SNP

single nucleotide polymorphism

Conflict of Interest Statement

The authors declare no real or perceived conflicts of interest.

Disclosures

Mention of trade names or commercial products in this publication is solely for the purpose of providing specific information and does not imply recommendation or endorsement by the U.S. Department of Agriculture. USDA is an equal opportunity provider and employer.