Mixed models in phenotype modeling of population F2 developed for qtl mapping in chickens
Published: October 20, 2011
By: MF Rosário1*, FEJ Silva1, R Gazaffi2, ASAMT Moura3, MC Ledur4, AAF Garcia2, LL Coutinho1 - 1Department of Animal Husbandry, ESALQ/USP; 2Department of Genetics , ESALQ/USP; 3Department of Animal Production, FMVZ/UNESP; 4Embrapa Swine and Poultry. Braz
Summary
Modeling phenotypic data from populations developed for QTL mapping is an essential step, because there are several effects considered as either fixed or random that need to be modeled properly. This paper reports the use of mixed models and the selection of a co(variance) structure to model phenotypic data from an F2 experimental population designed to map QTLs for performance and carcass traits. Approximately 2,000 F2 chickens were obtained by crossing males of a broiler line with females of a layer line, and their phenotypes measured for 24 carcass and performance traits. We modeled the effects of sex and family (both fixed), hatch (random) and double interactions, plus the selection of co(variance) structure using seven structures based on the lowest Akaike’s Information Criterion. The final model selected was the one containing only the effects of sex, family and incubation, without interactions, because it contained the highest level of information with the fewest parameters. The random effect of hatch was modeled with the first order autoregressive structure (AR1), and the error with the variance components (VC) structure. Using these approaches, it is possible that both positions and effects of QTLs mapped in this population might be more consistent with the experimental design.
Key Words: Akaike, Genomics, Poultry, PROC MIXED.
Introduction
Mapping of QTLs (locus controlling quantitative characteristics) by relationship analysis consists of several stages, namely: 1) the design of an experimental population (F2 or backcrossing), by crossing of genetically divergent lines or races, 2) genotyping, 3) phenotyping of the animals and, finally, 4) the implementation of genetic-statistical analysis.
Different approaches have been used to increase the power of detection and facilitate the identification of QTLs in domestic chicken, such as, for example, the selection of families and the most informative DNA markers (Zhu et al., 2001). However, the modeling of phenotype data based on mixed models has not been used routinely in mapping QTLs in chicken. This is due to the fact that the QTL Express program (Seaton et al., 2002), so widely used in mapping QTLs in this species, only considers fixed effects.
Macgregor et al. (2005) suggested phenotype modelling for mapping QTLs with simulated data, while Rodriguez-Zas et al. (2002) did so with milk-producing bovines staring from longitudinal phenotypes. These studies demonstrated the importance of modeling the phenotype data properly through the selection of covariance structures that could explain most of the phenotypic variation.
This paper reports the use of mixed models and the selection of a covariance structure to model phenotype data of an F2 experimental population designed to map QTLs for performance and carcass traits.
Materials & Methods
Experimental populations
Experimental populations
A population named TCTC was designed through crosses between a breed of meat-producing chicken (TT) and a line of layers (CC) at Embrapa Swine and Poultry (Suínos e Aves), Concordia, Santa Catarina, Brazil. Seven males TT were crossed with seven females CC for the generation of F1 TC birds. A total of seven males and 21 females were selected, to obtain a ratio of one male by three females of each family of the generation F1, to form the parents of the generation F2, for which each male F1 was housed with three females F1 no-related. Each female F1 produced approximately 100 animals F2 per family of F1 in 17 incubations, totaling about 2,000 birds F2. The details can be found in Rosário et al. (2009).
The generation F2 was identified using rings to control the pedigree and to evaluate various performance and carcass traits. The birds received rations made from corn and soybean cake (pasta), to cover the nutritional requirements of each parenting period. Management suitable for broiler chickens was used, with food and water supply ad libitum.
Birds were kept in rearing galleys (ships, barns or sheds) up to 35 days of age, when birds were weighed and housed in individual cages for testing feed conversion at 35 and 41 days. At 42 days of age, the birds were slaughtered to assess the carcass traits.
Phenotype data
In the birds F2 the following phenotype features were asessed: live weight (g) at 35, 41 and 42 days of age; weight gain (g), food consumption (g), food efficiency and feed conversion (g.g-1; absolute value) from day 35 to 41. At 42 days of age, the birds were slaughtered at the Suruvi experimental slaughterhouse, belonging to Embrapa Suínos e Aves, Concordia/SC, Brazil, in compliance with sanitary and animal welfare standards, to obtain the weights of parts (g) and organs (g): head, feet, wings, legs (legs and thighs), chest (with skin and bone), back, abdominal fat, liver, heart, gizzard, lung and intestines (small and large). The weight of the eviscerated carcass (g) (without feet, head, neck and abdominal fat) was obtained by the sum of the parts. Blood parameters were also assessed: Hematocrit (%), cholesterol (mg/dl- 1) and triglycerides (mg/dl-1).
Phenotype data modeling
With the purpose of selecting the linear model which better conformed to the phenotype data, in a first phase, the following mixed model PROC MIXED of the SAS® program (2007 SAS) was considered for the analysis:
random error.
Interactions involving the effect of hatchability were considered as mixed, and the others as fixed.
Interactions involving the effect of hatchability were considered as mixed, and the others as fixed.
The effect of incubation was considered random, not because of the process itself, as this is a controlled process (temperature, humidity and time of egg rotation), but Yes by considering the effect of the age of the mother among egg-laying times. During development, the females had an egg-laying curve in which the chicks born at the beginning of such a curve were more lightweight than those born at the end of the curve. This fact depends on the size of the egg at the beginning of egg-laying, which is less than that observed at the peak of the curve (McLoughlin and Gous, 2000). Furthermore, given that the animals F2 were generated over 17 fortnightly incubations (approximately eight months), and that measurement of phenotypes was done in adjacent times, there is a greater correlation between the animals obtained at the beginning, at the peak, and at the end of the egg-laying curve. This scenario fits within the concept of measurements repeated over time. The possibility of minimizing the effect of this intrinsic correlation is modeling the structure of the covariance matrix for the random effect of incubation and error.
For Ik and eijkm we considered the covariance matrices 
and 
, respectively, which were modelled according to seven structures: First-order autoregressive (AR1), first-order autoregressive heterogeneous (ARH1), composed symmetry (CS), composed symmetry heterogenia (CSH), variance components (CV), Toeplitz (TOEP) and Toeplitz heterogenia (TOEPH). The best structure was selected, based on the Akaike Information Criterion (AIC) (Akaike, 1974). The lower the value for this criterion, the more appropriate the model. The live weight at 35 days was used as a covariate of weight gain and food consumption, food conversion and food efficiency from day 35 to day 41. For all of the carcass traits, including the organs, live weight at 42 days was used as a covariate.
and , respectively, which were modelled according to seven structures: First-order autoregressive (AR1), first-order autoregressive heterogeneous (ARH1), composed symmetry (CS), composed symmetry heterogenia (CSH), variance components (CV), Toeplitz (TOEP) and Toeplitz heterogenia (TOEPH). The best structure was selected, based on the Akaike Information Criterion (AIC) (Akaike, 1974). The lower the value for this criterion, the more appropriate the model. The live weight at 35 days was used as a covariate of weight gain and food consumption, food conversion and food efficiency from day 35 to day 41. For all of the carcass traits, including the organs, live weight at 42 days was used as a covariate.Results and Discussion
To make a decision on the most appropriate model, we took, as a reference, the live weight at 42 days, because this feature introduced high correlation with the other characteristics (data not shown).
After evaluating the models with the combinations among the structures of the proven covariance matrix, the model which contained only the effects of family, sex and incubation, as well as average and error was selected. For the matrix G, associated with incubation, the selected covariance structure was AR1 and for matrix R, associated with error, we selected the variance components (CV), since this is the combination that presented lower value for AIC (Table 1). The structure AR1 is interesting, as it is considered that the correlation between each adjacent incubation is reduced to the course of time (r1, r2, r3, r17), i.e., it considerss the greatest correlation between any two adjacent incubations and the lowest correlation between any two distant incubations.
Table 1. Akaike Information Criteria (AIC)†, for the random effects of incubation (
) and residue (
) for the live weight of 42 day old animals.
) and residue () for the live weight of 42 day old animals.Residue | ||||||||
AR(1) | ARH(1) | CS | CSH | VC | TOEP | TOEPH | ||
Incubation | AR(1) | 7166.2 | 7166.2 | 7166.5 | 7166.2 | 7164.2 | 7164.8 | 7164.8 |
ARH(1) | 7281.3 | 7204.4 | 7182.5 | 7204.4 | 7201.5 | 7279.1 | 7202.3 | |
CS | 7167.2 | 7167.2 | 7167.2 | 7167.2 | 7165.2 | 7165.2 | 7165.2 | |
CSH | 7283.1 | 7201.3 | 7185.3 | 7201.3 | 7199.0 | 7281.1 | 7199.8 | |
VC | 7165.2 | 7165.2 | 7165.2 | 7165.2 | 7166.2 | 7166.2 | 7166.2 | |
TOEP | 7215.6 | 7207.3 | 7201.5 | 7207.3 | 7204.1 | 7207.5 | 7204.1 | |
TOEPH | 7308.2 | * | * | * | * | 7309.9 | * |
AR1: First-order autoregressive, ARH1: First-order autoregressive heterogeneous, CS: Compound symmetry, CSH: Compound heterogeneous symmetry, VC: Variance components, TOEP: Toeplitz and TOEPH: Heterogeneous Toeplitz.
† the lower the value, the better.
* Non -positive, defined Hessian matrix.
† the lower the value, the better.
* Non -positive, defined Hessian matrix.
Because incubations were held every fortnight and traits were measured at adjacent times, there is a greater correlation between these traits and those taken at more distant times. In this way, errors are not independently distributed with a mean zero and variance 
, violating one of the proposals of variance analysis. For this reason, the concept of measurements repeated in time and modeling of the covariance structure were used, according to Littell et al. (1996), in order to properly model the phenotype data of the studied population.
, violating one of the proposals of variance analysis. For this reason, the concept of measurements repeated in time and modeling of the covariance structure were used, according to Littell et al. (1996), in order to properly model the phenotype data of the studied population.In the analysis of the QTLs we do not know any studies that model the covariance structure of the phenotype data for the mapping of QTLs, specifically in hens. Mapping of QTLs that involves longitudinal data was already done by Macgregor et al. (2005) with simulated data and real data in bovine dairy by Rodriguez-Zas et al. (2002). However, the covariance structure AR1 was not evaluated in any of these two studies; therefore, for our study we chose this structure, since it showed the lowest AIC value, in other words, the final model presented the highest level of information with the smallest number of parameters.
By using the phenotype modeling presented in this paper, it is possible that both egg-laying as the effects of the QTLs that are mapped in the population under study can be estimated more consistently with the experimental design used. The next step will be to investigate the extent of possible differences in QTL mapping using incubation as fixed and random effect.
Conclusions
The use of mixed models and the selection of the covariance structure to model phenotype data for the population F2 developed for mapping of QTLs proved to be appropriate. Thus, it was possible to the model that presents a higher level of information with the fewest parameters.
Acknowledgements
Our gratitude to FAPESP for the scholarships granted (process number 10/50019-1) and to CNPq and PRODETAB/EMBRAPA for their financial aid.
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