880 WWW.CROPS.ORG CROP SCIENCE, VOL. 50, MAY– JUNE 2010 RESEARCH T he main objective of a plant breeding program is selection of breeding lines which represent the greatest improvement relative to established varieties in terms of one or more traits. Therefore the eiciency of a breeding program is measured through changes in yield performance over time (genetic gain). In statistical context it is expressed as potential genetic gain, mea- suring the average diference in per formance among the lines entering the breeding program and those inally selected. The main concern in the selection process is the efect of V×E inter- actions, and the degree of uncertainty in identi icat ion of variet- ies with broad or speci ic adaptat ion to the target environments. Eicient analysis of multi-environment trials (METs) reduces the uncertainty and helps in understanding the V×E interactions. The linear mixed model approach to the analysis of plant breeding experiments, METs in particular, has become popular and widely used. These comprise: variance component models (Patterson et al., 1977; Talbot, 1984; Patterson and Nabugoomu, 1992; Frensham et al., 1997; Cullis et al., 1998); mixed models Multiplicative Mixed Models for Genetic Gain Assessment in Lupin Breeding Katia T. Stefanova* and Bevan Buirchell ABSTRACT Genetic gain is used as a long-term measure of the eficiency of a breeding program. A spatial linear mixed model that includes a multiplicative mixed model (MMM) for the variety by environ- ment (V×E) effect has been used for the analysis of 39 trials of 25 historical lupin varieties for the period of 1997 to 2006. The 25 varieties were produced by the Australian breeding effort from 1967 to 2007 and are a result from ive cycles of breeding. Genetic gain was assessed on the basis of the overall performance of the variet- ies across all environments based on the MMM results. The genetic gain from the irst early lowering variety, Unicrop, to the highest yield- ing variety, Mandelup, represents a yield gain of 81% over 31 yr. The varieties’ yield stability across the environments and their broad or spe- ciic adaptations are discussed. Dep. of Agriculture and Food Western Australia, 3 Baron Hay Court, South Perth WA 6151, Australia. Received 23 July 2009. *Correspond- ing author (kstefanova@agric.wa.gov.au). Abbreviations: AMMI, additive main efects and multiplicative inter- action; AR1 × AR1, irst order autoregressive by irst order autoregres- sive; BLUE, best linear unbiased estimate; BLUP, best linear unbiased predictor; FA, factor analytic; GGE, genotype main efects and gen- otype × environment interaction; MET, multi-environment trials; MMM, multiplicative mixed model; PCA, principal components anal- ysis; REML, residual maximum likelihood; REMLRT, residual maxi- mum likelihood ratio test; V×E, variety by environment. Published in Crop Sci. 50:880–891 (2010). doi: 10.2135/cropsci2009.07.0402 Published online 11 Mar. 2010. © Crop Science Society of America | 5585 Guilford Rd., Madison, WI 53711 USA All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.