Livestock Production Science 67 2000 143–153 www.elsevier.com locate livprodsci
Comparison of two computing algorithms for solving mixed model equations for multiple trait random regression test day
models
J. Jamrozik, L.R. Schaeffer
Centre for Genetic Improvement of Livestock , Department of Animal and Poultry Science, University of Guelph, Guelph, ON,
Canada N 1G 2 W1
Received 29 July 1999; received in revised form 24 January 2000; accepted 9 February 2000
Abstract
Two computing algorithms for solving mixed model equations for a multiple lactation, multiple trait random regression test day model were compared. The model for each trait yields of milk, fat, and protein, and somatic cell scores in the first
three lactations included fixed contemporary groups, fixed regressions within levels of time–region–age–season parity subclasses at calving and two sets of random regressions: animal genetic and permanent environmental effects, giving a total
of twelve traits and 36 equations for each animal genetic effect and each animal permanent environmental effect. Algorithm A utilized the iteration on data with blocking strategy with contemporary group and animal blocks in a Gauss–Seidel
iteration scheme. Block sizes for animal genetic and permanent environmental effects were of order 36. Algorithm B utilized an alternative blocking strategy for animal effects with separate blocks for each lactation of order 12. This allowed for
significant reduction in memory requirements, less time per iteration, but slightly slower convergence compared to Algorithm A. The algorithms were compared in an application of the test day model to the national Canadian Jersey test day
data set. Memory and disk space requirements for the two algorithms as well as extensions of the model were discussed.
2000 Elsevier Science B.V. All rights reserved.
Keywords : Test day models; Genetic evaluation; Computing
1. Introduction the
complexity of
the model,
the size
and idiosyncrasies of the data, the computing environ-
The implementation of computing algorithms to ment, and possible future enhancements to the
solve BLUP mixed model equations MME for model, data, or computing environment. Data sets
genetic evaluation requires careful consideration of tend to grow in numbers of animals and records over
time; models tend to become more complex; and computing tends to become faster and to have more
Corresponding author. Tel.: 11-519-8244-120; fax: 11-519-
available memory, disk space, and multiple pro-
7670-573. E-mail address
: lrssherlock.aps.uoguelph.ca L.R. Schaeffer.
cessors. Generalized computing software is often
0301-6226 00 – see front matter
2000 Elsevier Science B.V. All rights reserved. P I I : S 0 3 0 1 - 6 2 2 6 0 0 0 0 1 8 6 - X
144 J
. Jamrozik, L.R. Schaeffer Livestock Production Science 67 2000 143 –153
sufficient for many research tasks and saves the user mink’s function Wilmink, 1987 with three parame-
from software development time and from possible ters per trait giving 72 equations per cow with TD
programming errors. However, efficient, routine records and 36 equations per animal without data.
genetic evaluations from specially developed soft- For the Holstein breed, CTDM required processing
ware can save time for delivery of results and may over 21 million TD records on 1.3 million cows in 2
be necessary when general software can not accom- million contemporary groups and 2.2 million animals
modate the model or data size. in total. The total number of equations was more
Iteration on data Schaeffer and Kennedy, 1986 than 135 million.
has been used widely as a method of solving MME. Several requests were received from Europe by
The MME are not constructed explicitly, but data Canadian Dairy Network CDN to acquire the
files are read each round of iteration or stored in computer programs used in the CTDM, but the cost
memory, and diagonal elements, right hand sides, of the programs was a major obstacle. The decision
and solutions need to be stored in memory. Iteration was made, therefore, to publish the gory computa-
on data allows for a variety of techniques to be tional details in this journal so that others may write
applied, such as Gauss–Seidel, Jacobi, or combina- their own programs if they want. Also, the details
tions of both, sparse matrix techniques Misztal, given here can serve as the beginning of the history
1999, transformations to simplify multiple trait on computing algorithms for random regression
problems Ducrocq and Besbes, 1993, or parallel models. First attempts, such as given here, are
processor algorithms for solving large sparse equa- usually replaced with better algorithms over time.
tion systems Madsen and Larsen, 1998. Thus, the objectives of this paper were to present the
The scale of the equations to be solved has computing details used in the CTDM, to present an
dramatically increased with the introduction of test outline for an alternative computing procedure that
day TD models Ptak and Schaeffer, 1993 for uses less memory and disk space, and to compare the
genetic evaluation of dairy cattle. Reents et al. computing requirements of the two algorithms when
1995 presented an efficient iteration on data algo- applied to data of the Canadian Jersey dairy breed.
rithm for a multiple lactation TD model that has been applied in Canada and Germany. Random regression
RR TD models Jamrozik et al., 1997 added
2. Material and methods
