Orquestación instrumental

3.5.3.1 Effect of marker genotypes on immune responses

Distributions of antibody as well as IFN-γ responses at each time-point were positively- skewed. Hence, antibody, IFN-γ (Johnin-nil) and IFN-γ (Johnin-avian) OD values were log (OD+0.00001) transformed so as to normalize the data. The effects of genotypes were tested separately for each marker locus within each property, employing the PROC MIXED

procedure in SAS® 9.1. For each marker, only genotypes occurring in at least five individuals each of vaccinated and control groups were evaluated for their effects. Animals with less frequent genotypes were excluded from the analysis. The employed model was as follows.

Yijkl = Groupi + Genotypej + Timek +(Group*Genotype)ij + (Group*Time)ik 3

+ Σαmθm(Animalijkl) + Eijkl, where, m=0

Yijkl = phenotype (antibody or IFN-γ response) in logarithmic scale Group, i = 1, 2 (1 = controls, 2 = vaccinates)

Genotype, j = 1, 2, 3, …. n (number of genotypes varied for each marker within a property) Time, k = 0, 2, …. 54 months post-vaccination (time points varied between properties)

αm = random regression coefficient

Eijkl = residual error assumed to have an auto-regression structure for animall, within a groupi

An auto-regressive model of first order (AR 1) was found to be the most appropriate error structure for repeated measures, based on AIC values. Least square means (LSM) along with standard errors (SE) were obtained for group, genotype, time, group*genotype and

group*time and were used in multiple comparisons among different treatment effects. For graphical presentations, LSM in log-scale were back-transformed to the observed scale. Generalized SAS code employed to execute the model is given below.

Proc Mixed Data=one Method=ML;

Class Animal Group Genotype Time;

Model logPhenotype=Group Genotype Time Group*Genotype Group*Time;

Random lt0 lt1 lt2 lt3 / subject=Animal Group=Group;

Repeated / type=AR(1)subject=Animal Group=Group;

Lsmeans Group Genotype Time Group*Genotype Group*Time/Pdiff;

Quit;

Time Legendres lt0, lt1, lt2 and lt3 were computed as below.

lt0=1/SQRT(2)

lt1=SQRT(3/2)*xt

lt2=(SQRT(45/8)*(xt*xt))-(SQRT(5/8))

lt3=0.5*((5*xt*xt*xt)-(3*xt)), where

xt=(2*time-(HT+LT))/(HT-LT), HT and LT being highest and lowest time-points

3.5.3.2 Effect of marker alleles on immune responses

The effects of presence versus absence of marker alleles were determined separately for each allele at each locus within each property, employing PROC MIXED procedure in SAS® 9.1. For each marker, only alleles occurring in at least six individuals each of vaccinated and control groups were evaluated for their effects. For determining the effect of a particular allele, individuals possessing at least a single copy of that allele were classified as ‘allele 1’ (allelic presence), while the individuals that lacked at least a single copy of the allele as ‘allele 2’ (allelic absence). The employed model was as follows.

Yijkl = Groupi + Allelej + Timek +(Group*Allele)ij + (Group*Time)ik 3

+ Σαmθm(Animalijkl) + Eijkl, where, m=0

Group, i = 1, 2 (1 = controls, 2 = vaccinates)

Allele, j = 1, 2 (1 = allelic presence, 2 = allelic absence)

Time, k = 0, 2, …. 54 months post-vaccination (time points varied between properties)

αm = random regression coefficient

Θm = corresponding transformed time (Legendre) for animall

Eijkl = residual error assumed to have an auto-regression structure for animall, within a groupi

An auto-regressive model of first order (AR 1) was found to be the most appropriate error structure for repeated measures, based on AIC values. Least square means (LSM) along with standard errors (SE) were obtained for group, allele, time, group*allele and group*time and were used in multiple comparisons amongst different treatment effects. For graphical

presentations, LSM in log-scale were transformed back to normal scale. The generalized SAS code employed to determine the effect of an allele at a marker locus is given below.

Proc Mixed Data=one Method=ML;

Class Animal Group Allele Time;

Model logPhenotype=Group Allele Time Group*Genotype Group*Time;

Random lt0 lt1 lt2 lt3 / subject=Animal Group=Group;

Repeated / type=AR(1)subject=Animal Group=Group;

Lsmeans Group Allele Time Group*Allele Group*Time/Pdiff;

Quit;

Time Legendres lt0, lt1, lt2 and lt3 were computed as explained in section 3.5.3.1.

3.5.3.3 Effect of chromosome-wise haplotypes on immune responses

Because of high numbers of probable MHC haplotypes on all three properties, the effects of MHC haplotypes were not tested. Effects of SLC11A1 and IFN- γ haplotypes on antibody and IFN- γ responses were tested employing the PROC MIXED procedure in SAS® 9.1. For each individual, possible haplotype pairs that could comprise the genotype, along with the probabilities that the genotype could be resolved into each of the possible haplotype pairs, were obtained from haplotype analysis detailed in section 3.5.2.4. Probabilities of haplotypes featuring in different possible haplotype pairs for each individual were pooled separately for each haplotype. For an individual having only one possible haplotype pair that included a particular haplotype in homozygous condition, the pooled probablility of that haplotype in the individual was 2. The haplotype probabilities pooled separately for each haplotype in each individual were arranged in the form of a matrix that had rows corresponding to the number

of individuals in the group (vaccinates or controls) and columns corresponding to the number of possible haplotypes. The sum of haplotype probabilities in each row (each individual) was 2. For illustration, possible IFN- γ haplotype pairs (along with their probabilities) for three individuals and their arrangement in the form of matrix are shown below.

Possible haplotype pairs and their probabilities:

Individual o(IFN)-γ

genotype

OarKP6

genotype Possible haplotype pairs Probability

1 124/124 200/204 124-200 124-204 1.00 2 --* 200/204 124-200 124-204 0.55 124-200 128-204 0.01 124-204 128-200 0.43 128-200 128-204 0.01 3 124/128 200/202 124-200 128-202 0.65 124-202 128-200 0.35 * genotype unavailable

Pooled haplotype probabilities arranged in the form of a matrix: Pooled haplotype probabilities Individual

124-200 124-202 124-204 128-200 128-202 128-204 1 1.00 0.00 1.00 0.00 0.00 0.00 2 0.56 0.00 0.98 0.44 0.00 0.02 3 0.65 0.35 0.00 0.35 0.65 0.00

Using this haplotype probability matrix, the effects of haplotypes on antibody and IFN- γ responses were analyzed separately for controls and vaccinates of each property. The employed mixed model included the fixed effects of haplotype probabilities and random effects of animals. Covariance error structure for repeated measures over time-points within animals within group was determined based on Akaikes information criterion (AIC). Auto- regressive model of first order (AR 1) was found to be the most appropriate error structure. Differences between different haplotype combinations were tested using estimate and contrast statements. Since the phenotype data (OD readings) were log-transformed to normalize data, haplotype effects were in log-scale and were back-transformed to normal scale for graphical presentations.