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An algorithm to evaluate primitive Boolean selections over single relations is presented. It will be argued that the algorithm is efficient with respect to the number of relational accesses and with respect to the merging of inverted lists. The algorithm's unique quality is its efficiency in evaluating selections over partially inverted relations. A simple cost function is used to drive the algorithm along the most efficient access paths. The cost function can also be used to predict its response time which then forms the basis of a procedure to suboptimize the selection of the domains to be inverted. The domains to be inverted are selected by analyzing, with respect to their costs, a sample of queries. Such a method does away with usual methods of updating usage counters for every domain and relation in the system. In this approach, the selection of a good set of inverted lists is based on the algorithm which uses those lists.

Selection index theory is extended to cover the case of selection in several stages. General algebra is given for adjusting in later stages for the effects of selection in earlier stages. In addition a method is developed for the incorporation of an index into an index. This simplifies the reuse of data from earlier stages of selection. A numerical example is used to illustrate the methods and to compare three single-stage and three two-stage selection procedures.

We address the problem of automatically adjusting the physical organization of a data base to optimize its performance as its access requirements change. We describe the principles of the automatic index selection facility of a prototype self-adaptive data base management system that is currently under development. The importance of accurate usage model acquisition and data characteristics estimation is stressed. The statistics gathering mechanisms that are being incorporated into our prototype system are discussed. Exponential smoothing techniques are used for averaging statistics observed over different periods of time in order to predict future characteristics. An heuristic algorithm for selecting indices to match projected access requirements is presented. The cost model on which the decision procedure is based is flexible enough to incorporate the overhead costs of index creation, index storage and application program recompilation.

In this chapter, selection index principles are illustrated through the use of some numerical examples. Initially we consider selection index as classically applied: with an assumption of balanced data with homogeneous second moments. We first examine a simple case of index selection for a single trait in an open-pollinated progeny test, and then consider selection index for a single trait applied over a number of openpollinated tests. This is followed by an application in a single cross-pollinated test. Finally, we present an application of selection index for multiple traits, and consider how to examine sensitivity to economic weights. For each case, the objectives are two fold: 1) to illustrate how to set up the vectors and matrices necessary to apply a selection index, and 2) to demonstrate a few interesting principles about how selection indices operate. We then discuss selection index in cases where the assumptions of balanced data and homogeneous second moments may be inappropriate, and conclude by presenting approximate approaches to the selection of individuals which should be nearly optimum (and may be substantially easier to apply operationally). This chapter contains fairly detailed algebraic manipulations with linear models containing several subscripts. The reader is referred to Chapter 2 and the excellent paper by Comstock and Moll (1963) for further discussion and examples of this type of algebra.

Many database applications involve queries in which records are selected on the value of one or more (non-primary key) attributes of the records. Secondary Access Methods (SAMs) refer to data structures and techniques designed to access efficiently all the target records associated with a set of stated secondary key values defined in a query. This paper first investigates basic access methods, including multilist and inverted files, and also multiattribute access methods, including multidimensional binary trees, combined indexes, doubly chained trees, quintary trees and the grid file. It then goes on to discuss the problem of the secondary index selection.

Response from index selection for egg production traits in a Leghorn strain over 7 years was partitioned into estimates of total (delta T), temporary (delta R), and net genetic (delta G) response, by producing progeny from selected (A) and unselected (D) first year breeders and from second year breeders (B) and first year full-sisters of previous years A breeders (C). In A, B, C, and D populations, average yearly number of full-sib families was 121, 47, 37, and about 50 and of birds with complete records was 824, 287, 258, and 298. Restricting A to repeated B families added positive bias in delta G for viability, age at first egg, and rate of lay. Estimates of delta G and delta R from B and C populations were similar. Yearly environmental change (delta E) was over three times the phenotypic change (delta P) for egg numbers, emphasizing necessity for intra-year estimates of delta G and delta R. Temporary response (delta R) approached or exceeded total response (delta T) for mortality and accounted for 40% of delta T for rate of lay and 60% for economic index, suggesting adverse maternal environmental effects from relaxing selection (D). Net yearly genetic change (delta G) was 1.5% for rate of lay, $.18 per bird, and in desired direction for most traits. Estimated net yearly response for rate of lay exceeded that predicted from .64 sigma male and .92 sigma female index selection differentials and sire-component genetic parameters (.6%) but agreed ($.16) for economic index. Efficiency and bias for the repeat-mating design are handicapped by mortality and health-related maternal effects.

Estimates of heritability, phenotypic and genetic correlations were obtained for body length and weight at 5 months and body length and weight at 15 months in channel catfish. The estimates were obtained from a half-sib analysis by mating 20 males to two females each, producing 20 half-sib and 40 full-sib progeny families. Mortality of fish during the study reduced the number of families to 17 half-sib and 34 full-sib. Comparisons of selection methods were made for body length at 5 months and body weight at 15 months. The results of the study show: 1) heritability estimates for body length and weight at 5 months was 0.12 and 0.61, respectively, and body length and weight at 15 months was 0.67 and 0.75, respectively; 2) from the magnitude of the estimates of heritability, it can be inferred that large amounts of additive genetic variance exist in three of the traits (length at 5 months and length and weight at 15 months) and that selection for these traits should be successful; 3) estimates of phenotypic correlation among the four traits ranged from 0.90 to 0.30, and genotypic correlation among the four traits ranged from 1.47 to 0.71; 4) the magnitude and positive nature of the genetic correlations indicated that simultaneous selection for the four traits in channel catfish would be effective; and 5) comparisons of predicted response under individual, indirect and index selection, show that selection on an index based on all four traits gives maximum response in length at 5 months and weight at 15 months.

The use of family selection indices has been proposed as a promising selection method for increasing prolificacy in pigs. Responses of up to 0-50 pigs per litter per generation are predicted from selection programmes using information from the dam and from relatives (full and half-sibs) of the dam and sire. In order to test this method in populations of finite size, the rates of selection response and the accumulation of inbreeding have been studied by simulation along 10 generations in a selected herd of 10 sires and 100 dams using five different family selection indices (Id, Ifd, Ihd, Ifs, Ihs). Two undesirable features were evident (a) the standard deviations of indices were lower than those expected; and (b) the increase of inbreeding was up to three times that expected without selection. Both effects increased with the complexity of the family index reducing the rates of selection responses per generation, when a genetic model with dominance was assumed, to values close to 0·20 piglets, similar to those obtained with the basic index (Id). Some results of inbreeding effects on reproductive traits in three strains of an old closed herd of Iberian pigs are also presented. Multiple regression analysis of data from 4657 litters indicated a decrease in the number of live born ranging from 0·14 to 0·35 piglets per 10% increase in dam or litter inbreeding coefficient. © 1988, British Society of Animal Science. All rights reserved.

INDIVIDUAL SELECTION BASED ON FEMALE PERFORMANCE ONLY WAS CONDUCTED IN FOUR LINES OF MICE: L(+) for increased litter size, W(+) for increased 6-week body weight, L(-)W(+) for a selection index aimed at decreasing litter size and increasing 6-week body weight and L(+)W(-) for a selection index aimed at increasing litter size and decreasing 6-week body weight. A fifth line (K) served as an unselected control. All litters were standardized to eight mice at one day of age. Expected heritability was based on twice the regression of offspring on dam (h(2) (d)), which contains additive genetic variance due to direct (sigma(2) (A(o) )) and maternal (sigma(2) (A(m) )) effects and their covariance (sigma(A(o)A(m) )). Responses and correlated responses were measured either deviated (method 1) or not deviated (method 2) from the control line. Realized heritabilities (h(2) (R)) for litter size were 0.19 +/- 0.04 (1) and 0.16 +/- 0.03 (2), which were similar to h( 2) (d) of 0.17 +/- 0.04. The h(2) ( R) for 6-week body weight of 0.55 +/- 0.07 (1) and 0.44 +/- 0.07 (2) agreed with h(2) (d) of 0.42 +/- 0.02. Realized genetic correlations (r*(G(R) )) between litter size and 6-week body weight calculated from the double-selection experiment were 0.52 +/- 0.10 (1) and 0.52 +/- 0.13 (2), which were not significantly different from the base population estimate of r*( G(d) ) = 0.63 +/- 0.14. Divergence (L(-)W( +) minus L(+)W(-)) in the antagonistic index selection lines was 0.21 +/- 0.01 index units (I = 0.305 P(W) - 0.436 P(L), where P( W) and P(L) are the phenotypic values for 6-week body weight and litter size, respectively.). The h(2) ( R) of index units of 0.14 +/- 0.02 calculated from divergence agreed with h(2) (d) of 0.14 +/- 0.04. Divergences in litter size (-0.19 +/- 0.07) and 6-week body weight (0.46 +/- 0.10) were in the expected direction. Antagonistic index selection yielded about one-half the expected divergence in litter size, while divergence in 6-week body weight was only slightly less than expected. Realized genetic correlations indicated that litter size, 6-week body weight and index units each showed positive pleiotropy with 3-week body weight, postweaning gain and weight at vaginal introitus and negative pleiotropy with age at vaginal introitus. Sex ratio and several components of fitness (days from joining to parturition, percent fertile matings and percent perinatal survival) did not change significantly in the selected lines.

Two lines of Tribolium castaneum were selected in each of three replicates for egg laying between 7 and 11 days after adult emergency and for adult weight at 12 days, using theoretical (IT) and empirical (IP) index selection methods. Index coefficients were given empirically in the IP line and they were adjusted in the successive generations of selection according to the results obtained in the previous ones. Highly repeatable selection responses in all replicates occurred in both lines for the aggregate genotype (egg laying plus adult weight) and for each individual trait. The IP line tended to increase slightly more than the IT line for aggregate genotype and egg laying, while the highest response in adult weight was obtained with the IT method. The two methods gave consistently different responses in each replicate. The expected results were that IT selection should not exceed IP selection for the aggregate genotype and egg laying while theoretically the IT method should have been superior for increase adult weight. Theoretical expectations for adult weight have been fulfilled in practice. The IP method would be preferred in a practical sense because of its simplicity and freedom from need of parameter estimation. © 1985 Springer-Verlag.

Genetic correlations of heifer fertility and first-parity yield usually were negative and opposite in sign from genetic correlations of first-parity fertility and yield. Most estimates of genetic correlation between heifer and first-parity fertility were not significantly different from zero. Increasing yield may improve genetic potential for fertility, but stress of increased yield may overcome genetic potential for improved fertility. Days open and 305-day yield for first parity were considered with index selection; sires were evaluated on daughter performance. Days open had a small influence on the selection index; genetic gains in days open for first parity were largely offset by correlated losses in service period for heifers. Restricted index selection, holding days open constant, required considerable economic importance of days open.

Starting with two heterogeneous F2 populations, each based on 20 cross combinations, different selection procedures were applied for four consecutive selection cycles. Three of the selection procedures involved seed yield per plant (SYP): (i) direct selection for SYP (DSY); (ii) indexselection for SYP (ISY) with plant length, the ratio of the vegetative top to plant length, end of grain filling and duration of the generative stage as auxiliary characters and finally; (iii) independent culling levels selection (ICL) for the index described above and crude protein content. For ICL-selection the attention is focussed on SYP in this paper.

The effects of varying intensities of selection at first and second stages, for a given final intensity, on the efficiency of two-stage index selection are described. Data collected on four White Leghorn strains for part and residual egg number, body weights at 20 and 40 weeks and egg weight at 39 to 40 weeks were utilised. Four of the five traits were used in the first stage and all five traits were used in the second stage for the construction of two-stage selection indexes. The index that utilised all five traits had the maximum efficiency for one-stage selection. The relative efficiency of the two-stage index increased with increase in proportion selected at the first stage. A practical breeding schedule that adds the advantage of reduced generation interval by utilising a two-stage index selection is suggested for egg type chickens.

Heritability and genetic correlations realized from both single-trait and antagonistic index selection were compared with paternal half-sib estimates. Primary attention was focused on the genetic correlation between six-week body weight and six-week tail length. Parameters realized from single-trait selection were in excellent agreement with paternal half-sib estimates. However, the realized genetic correlation between six-week body weight and six-week tail length obtained from index selection was significantly greater than the other estimates. Differential inbreeding levels and realized selection intensities were considered and rejected as being causative factors for these results. Linkage disequilibrium probably was not a factor either, as the base population had been randomly mated and randomly selected with a large effective population size for many generations. It was concluded that with antagonistic index selection, the pleiotropic effects of genes may be more powerful in retarding response in aggregate genotype than current theory would suggest. Replication of all selected and control lines allowed the use of between-line estimators of sampling variances of realized genetic parameters in the above comparisons. Generally, standard errors of realized genetic parameters were much smaller than corresponding paternal half-sib standard errors. Thus, selection was an efficient method of estimation.

Three two-trait selection methods were analyzed for their effects on genetic variance and correlation by multivariate methods, two-locus methods and computer simulation. The two-trait selection methods studied were independent culling levels (ICL), index (IND) and extreme (EXT) selection. The effects of the selection methods on genetic variance and correlation were partitioned into permanent effects due to changes in gene frequencies and temporary effects due to nonrandom association of alleles at different loci. Multivariate methods were used to predict temporary effects from a single generation of selection by each method and from several generations of index selection. Two-locus theory was used to determine the stability and rank of temporary effects on genetic correlation for all three methods. Predictions were compared to computer simulation results. When selection increased the means of both traits, EXT had the lowest (closest to,—l.O) genetic correlation and highest variances, while ICL tended to have the highest (closest to 1.0) genetic correlation. When selection increased the mean of one trait and decreased the mean cjf the other, EXT had the highest genetic variances and correlation, while ICL had the lowest genetic variances and correlation.

Traits of dairy cattle known to contribute to genetic merit are discussed briefly. Focus is on alternative measures and research to reflect more closely genetic pathways of performance because knowledge is expanding about cellular, organ, and animal function. Improved measurement of physiological traits of economic characters portends increased genetic control of animal productivity by considering more alternative traits. Research should clarify multiple trait selection programs to maximize profit. The null hypothesis to test is that selection for milk is optimal index selection for milk income and costs of production.

This paper reviews the basic theory and summarizes various modifications of the selection index. The limitations of selection index are discussed in four parts: (1) changes of parameters due to selection. (2) sampling errors of parameter estimation. (3) evaluation of relative economic weights and (4) internal deterrents to index selection.

We have used diffusion and branching process methods to investigate fixation rates, probabilities of survival per generation, and times to fixation of mutant genes under different selection methods incorporating individual and family information. Diffusion approximations fit well to simulated results even for large selection coefficients. Methods that give much weight to family information, such as BLUP evaluation which is widely used in animal breeding, reduce fixation rates of mutant genes because of the reduced effective population sizes. In general, it is observed that even mutants with relatively small heterozygous effects (say 0.1 phenotypic standard deviation) are practically ‘safe’ (i.e. their probability of loss from one generation to the next is smaller than, say, 10%) after just a few generations, typically less than 10. For methods of selection with larger effective size, such as within-family selection, the mutant is ‘safe’ in the population somewhat earlier but eventual fixation takes a longer time. Finally we evaluate the amount by which the use of marker assisted selection reduces the fixation probability of newly arisen mutants.

Summarization: In this paper, the implementation of a pilot computerized system for the classification of landscape images (SCAPEVIEWER) is presented. A total of 108 landscape photographs have been organized, according to the mean estimation of scenic beauty from seven experts, into three classes: indistinctive (C1), typical or common (C2), and distinctive (C3). For each of the landscape photographs, 10 indices are estimated. These indices are then fed to a classifier based on neural network (NN) technology. In order to examine whether NNs are suitable for this specific application, two different approaches have been tested and compared against a linear discrimination method (LDM) classifier. The first approach is a feed forward NN (Classic-NN), while the second approach (Hybrid-NN) is based on the Classic-NN modified by using genetic algorithms (GAs). The correct classification performances achieved by the Classic-NN and the Hybrid-NN were 87% and 84%, respectively, while the classification performance of the LDM classifier was only 68%. Although the Classic-NN achieved slightly better results than the Hybrid-NN, the latter is preferred due to its ability of index selection and automatical adjustment of internal NN parameters. The pilot system has shown the feasibility for classifying landscape photographs according to scenic beauty by means of a computerized system combining the knowledge of an expert with a NN classifier. Presented on: Ecological Engineering

Divergent breeding lines of Romney sheep, selected as lambs for consistently high or low faecal worm egg count (FEC) following natural multi-species challenge by nematode parasites, were established in New Zealand at Wallaceville Animal Research Centre in 1979 and at Rotomahana Station in 1985. In 1988 the Rotomahana lines, including an unselected control line maintained under the same management conditions, were transferred to Tokanui Station where they remained for 4 years. In 1993 elite high and low FEC animals from Tokanui, along with the controls, were transferred to Wallaceville, where merged lines have since been managed together. Selection responses from the lines at Rotomahana and Tokanui, and from a further 5 years of divergent selection in the merged lines, are reported here. For the two most recent lamb crops (1996 and 1997 birth years), log-transformed FECs of the high and low lines were 1·27 and -1·46 phenotypic standard deviation units from the control. After back-transformation to the original scale, where the FEC for control line lambs averaged 1255 eggs per g, the means for the high and low lines were 3Ό5 and 0·27 times the control mean. Animal-model restricted maximum likelihood estimates of her it ability and repeatability for single-record FEC (following separate infections) were 0·28 (s.e. 0·02) and 0·42 (s.e. 0Ό1), respectively. Correlated responses in production traits include significantly decreased post-weaning weight gain and increased dags (breech soiling) in lambs, and decreased fleece weight in yearlings and ewes in the low FEC line, compared with those in the high line. However the low FEC line had proportionally 0·11 more lambs weaned per ewe mated than the high FEC line (F < 0·01). It is concluded firstly that selection for high or low FEC in Romney s has achieved an 11-fold difference between the divergent lines. Secondly, it will generally be necessary in a commercial environment to apply index selection for a combination of increased productivity, decreased FEC and possibly decreased dags, when potential candidates are recorded under conditions of nematode challenge.

Genetic variation in host resistance to nematode infection was studied in two calf crops of Angus cattle under natural pasture challenge conditions in New Zealand, using faecal egg count (FEC) as a marker trait. Genetic and phenotypic correlations of FEC with anti-nematode antibody (Ab) level and live weights were also estimated. Ab to the third larval stages of Cooperia curticei (Cc), Cooperia oncophora (Co), Ostertagia ostertagi (Oo) and Trichostrongylus colubriformis (Tc) were assayed, along with Ab to the adult stages of Co and Oo. Calves were born in the late winter/early spring of 1995 and 1996 over a 7-week period each year; they were weaned at an average of 4 months of age, and faecal samples for FEC were taken at 10 months of age (1995 crop) and at 7 months of age (1996 crop). Blood samples for Ab were taken from both calf crops at intervals between 4 and 20 months of age, and later in peri-partum heifers and cows (23 to 25, and 36 to 37 months of age). For the two calf crops combined, there were 370 animals by 24 sires. Additional blood samples were taken on related animals from the 1993 and 1994 calf crops (218 extra animals, 19 different extra sires). The heritability of loge (FEC + 100) was 0•32 (s.e. 0•16), and heritabilities of loge Ab between 4 and 9 months of age averaged 0•30, between 11 and 20 months of age 0•22, and peri-partum 0•30. Between-animal repeatabilities of Ab levels from samples taken between 4 and 9 months of age averaged 0•40, between 11 and 20 months 0•48, and peri-partum 0•35. Genetic and phenotypic correlations among loge Abs for various nematode species (in hosts aged 4 to 9 months) averaged 0•82 and 0•61, respectively. The corresponding genetic and phenotypic correlations between loge Ab and loge(FEC + 100) averaged –0•48 and –0•07, respectively, whilst those between loge Ab and yearling weight averaged 0•29 and 0•13, respectively. It was concluded that direct selection to reduce FEC should be feasible if required, but index selection combining increased live weight and reduced FEC would often be preferable; anti-nematode Ab levels were repeatable, and FEC and Ab levels were negatively associated genetically.

Background Animal breeding programs have been very successful in improving the mean levels of traits through selection. However, in recent decades, reducing the variability of trait levels between individuals has become a highly desirable objective. Reaching this objective through genetic selection requires that there is genetic variation in the variability of trait levels, a phenomenon known as genetic heterogeneity of environmental (residual) variance. The aim of our study was to investigate the potential for genetic improvement of uniformity of harvest weight and body size traits (length, depth, and width) in the genetically improved farmed tilapia (GIFT) strain. In order to quantify the genetic variation in uniformity of traits and estimate the genetic correlations between level and variance of the traits, double hierarchical generalized linear models were applied to individual trait values. Results Our results showed substantial genetic variation in uniformity of all analyzed traits, with genetic coefficients of variation for residual variance ranging from 39 to 58 %. Genetic correlation between trait level and variance was strongly positive for harvest weight (0.60 ± 0.09), moderate and positive for body depth (0.37 ± 0.13), but not significantly different from 0 for body length and width. Conclusions Our results on the genetic variation in uniformity of harvest weight and body size traits show good prospects for the genetic improvement of uniformity in the GIFT strain. A high and positive genetic correlation was estimated between level and variance of harvest weight, which suggests that selection for heavier fish will also result in more variation in harvest weight. Simultaneous improvement of harvest weight and its uniformity will thus require index selection. Electronic supplementary material The online version of this article (doi:10.1186/s12711-016-0218-9) contains supplementary material, which is available to authorized users.

Analytical queries defined on data warehouses are complex and use several join operations that are very costly, especially when run on very large data volumes. To improve response times, data warehouse administrators casually use indexing techniques. This task is nevertheless complex and fastidious. In this paper, we present an automatic, dynamic index selection method for data warehouses that is based on incremental frequent itemset mining from a given query workload. The main advantage of this approach is that it helps update the set of selected indexes when workload evolves instead of recreating it from scratch. Preliminary experimental results illustrate the efficiency of this approach, both in terms of performance enhancement and overhead.

Three selection indexes were constructed for bulls of beef cattle: IM for terminal crossing (in dairy herds), IZ for the selection of foundation sires for beef herd and IS for the selection of bulls for beef herd. Each index was constructed in five variants that differed in the number of used traits from the most important ones to all traits with known breeding values. The sources of information were breeding values routinely calculated in performance testing - 10 breeding values for direct and maternal effects for easy calving and growth, breeding value for daily gain of bulls at performance-testing stations and 10 breeding values for the type traits of young animals. The reliability of partial breeding values that enter into the indexes ranged from 11% to 36%. Reliability influences subsequent accuracy of index selection for total genotype that is in the range of 30% to 46%. The discounting of economic values (0% or 10%) did not influence the selection indexes significantly. Index selection was expressed almost exclusively in genetic gain of direct effects while maternal effects were of only small importance in the breeding objective. Direct effects for daily gain until weaning and after weaning are of the highest importance in the breeding objective, accounting for 90% to 96% of the total selection effect. The most important information sources in selection indexes are direct effect of weaning weight (importance of approximately 74% to 95%) and maternal effect of weaning weight (importance of approximately 5% to 7%). The inclusion of daily gain of bulls at performance-testing stations with the importance of about 16% in the index decreased the importance of wean - ing weight. Selection can be aimed at these main traits - calving ease (direct and maternal effect) and weight at 210 days (direct and maternal effect) only because the importance of the other traits in the index is very low.

The problem of making the best use of a limited number of performance-testing places in the genetic improvement of pigs is examined. A model is given which balances the duration of testing and its effect on the accuracy of breeding value determination, against throughput and its effect on selection intensity. The model is a phenotypic one with easily estimated parameters in lieu of the more exact genetic one whose parameters are difficult to estimate. It is illustrated with data taken from the Queensland performance-testing station which evaluates boars on an index combining feed conversion ratio, growth rate and back fat. Full performance records from 26 to 90 kg liveweight are subdivided into four consecutive parts of equal weight interval. A range of feasible one and two stage selection schemes based on performance in one or more of these parts are compared. Relative to the present full testing scheme, the best single stage selection, that based on performance in the last two parts (3 + 4), is 14% more efficient. The best two stage selection scheme, also a 3 + 4 part test with a 50% culling at the end of part 3, is 19 0%, more efficient. Highest efficiencies are achieved by imposing a preliminary culling on growth rate before entry to the testing facility; e.g. selection of the best 25% on part 3 growth rate followed by part 4 index selection within the test facility is 36% more efficient than the present full test. The limitations of the model and some practical problems of part testing schemes are discussed.

A breeding objective (aggregate genotype) for dairy cattle based on returns, net of feed costs, from yield of fat, protein and carrier (the non-fat, non-protein component of the milk) was developed. Returns were estimated using a forecast of the future Australian dairy market structure, and feed costs were estimated from the metabolizable energy required to produce each of three milk components.The effects of erors in forecasting future conditions on economic weights and efficiency of index selection of sires were examined.Economic weights varied widely when subject to errors in the price of milk components within markets, errors in the export price for milk and errors in feed cost.Selection based on an optimal index of sire expected breeding values for fat, protein and milk was sensitive to low export market prices, high feed costs, high protein price and high carrier price. This index was quite insensitive to variation in prices and costs opposite in sign to those above, to variation in milk prices on the domestic markets, and to variation in the size of quotas on domestic markets.

Early selection is essential after the first generation of a tree-breeding programme. Two main issues that it raises are (i) the optimal age for selection for the next generation and (ii) how best to use early assessment data for the selection. Attention is given mainly to the latter issue. Early selection is considered as a special type of indirect selection that can embrace multiple traits. Where a sequence of early measurements has been made for single traits it is possible to treat the expressions of a trait at different dates as separate traits in a selection index. Constructing a least-squares selection index with this feature involves a number of questions. Outstanding among these is whether, and in what way, early measurements should be used as covariates for adjusting later ones. Such indices depend, however, on good estimates of phenotypic and genetic variance–covariance matrices. Potential aids for deriving and refining such matrices are reviewed, including the "Lambeth relationship" for age–age correlations and partial correlation analysis. However, analysis of the sensitivity of expected gains with respect to variations in assumed genetic parameters is strongly advocated before decisions are made on age of selection.

The problem of making the best use of a limited number of performance-testing places in the genetic improvement of pigs is examined. A model is given which balances the duration of testing and its effect on the accuracy of breeding value determination, against throughput and its effect on selection intensity. The model is a phenotypic one with easily estimated parameters in lieu of the more exact genetic one whose parameters are difficult to estimate. It is illustrated with data taken from the Queensland performance-testing station which evaluates boars on an index combining feed conversion ratio, growth rate and back fat. Full performance records from 26 to 90 kg liveweight are subdivided into four consecutive parts of equal weight interval. A range of feasible one and two stage selection schemes based on performance in one or more of these parts are compared.Relative to the present full testing scheme, the best single stage selection, that based on performance in the last two parts (3 + 4), is 14% more efficient. The best two stage selection scheme, also a 3 + 4 part test with a 50% culling at the end of part 3, is 19%, more efficient. Highest efficiencies are achieved by imposing a preliminary culling on growth rate before entry to the testing facility; e.g. selection of the best 25% on part 3 growth rate followed by part 4 index selection within the test facility is 36% more efficient than the present full test. The limitations of the model and some practical problems of part testing schemes are discussed.

(…) The S 1 selection increased index values in the bulked inbred populations by 5.8% per cycle when averaged over populations. The RFS selection increased index values of inbred populations by 3.4% per cycle. Both methods were equally effective in improving index values of the random mated populations with average responses of 2.0% for S 1 and 1.8% for RFS selection per cycle. The average index response in the population crosses was 3.6 and 2.9% per cycle for RFS and S 1 selection, respectively. Genetic drift was observed to cause significant differences among the replicate populations for index and its components

(…) Selection based on the index was not expected to change oil concentration and no significant changes in oil were observed. In comparing the restricted index with the other selection criteria, direct selection for either yield or for total protein produced the greatest yield response. However, direct selection for yield or total protein is expected to result in significantly lower protein concentration in later cycles of selection. Thus, the use of restricted index selection appears to be the most promising long-term approach to increasing yield while maintaining high protein concentration

SUMMARY Tallis [1962] formulated and solved the problem of constrtucting a selectioin index whose use will produce changes in the means of the genotypic values of various traits that are proportional to ultimately desired changes. Several meaningftul variations of this problem are described, and their soluitions are presented in a common framework. A common problemn in animal and plant breeding is that of selecting animals or plants for breeding purposes from a group of candidates. The selections are based on a vector

Previous formulations of expected population size under phenotypic selection and index selection are extended to include tests containing mixtures of full-sib and half-sib families generated by regular mating plans. Projections of effective size are presented for a single cycle of selection from tests conducted with factorial and hierarchical mating designs, and with fractions of diallel plans. Consideration of variable family sizes enables similar projections for selection from polycross tests.

Mass selection for an index of increased postweaning average daily gain and decreased backfat thickness was practiced for five generations. Litter size and weight for 221 gilt litters, birth weight and nipple number for 2,242 piglets and weaning weight at 42 d of age for 2,111 pigs were recorded. Carcass measurements were taken on 331 pigs. Differences between means of the lines (select control) were regressed on cumulative selection differential of the index. These regression coefficients were negative (P greater than .10) for total number born, number born alive, number weaned per litter, nipple number and carcass backfat thickness. Coefficients were positive (P greater than .10) for individual pig and litter weights at birth and weaning and for the carcass traits of length, longissimus muscle area and percentage of ham and loin. Absolute values of realized genetic correlations of index with traits evaluated were all .35 or less except the correlation with carcass backfat, which was -.84. None of these was significant; therefore, index selection for lean growth should have little effect on litter size and weight but may have a beneficial effect on carcass backfat.

The selection index criterion for aggregate genetic value defined as H = v* g*, where g* is a vector of additive genetic values of the several economically important traits and v* is a vector of relative economic values is, as is well known, I = (P-'G*v*)'x, where P is the phenotypic covariance matrix of the data vector, x, and G* is the genetic covariance matrix of the economically importatn traits. When each trait has a direct and a maternal additive genetic component the selection index criterion becomes I = (P-'A'Gv)' x, where G is the covariance matrix of the direct and maternal genetic components of all the traits, (twice the order of G*), v is the vector of economic values of the direct and maternal components of all the traits (twice the length of v*), and A is a particular matrix consisting of zeros and additive relationships of the animal being evaluated with its relatives having records and with the dams of those relatives. The correlated response for the kth component (direct or maternal) of thejth trait is Agi = Agjk = v'G'AP-1(A'G)j/0-1 times the standardized selection differential, where (A'G)i is the ith column of A'G.

SUMMARY The nature of the index selection procedure when sample estimates are used in place of the true parameter values is considered. Approximate equations are developed for the low order moments of the joint distribution of the expected progress from selection for a particular calculated index and the predicted progress from this index. These equations involve the variances and covariances among the estimates used for index construction. Formulae are developed for these variances and covariances for paternal half-sib estimation. This joint distribution is also studied by a simulated sampling procedure. Numerical results for the two phases of the study are tabulated and studied for verification of the validity of the approximate equations and for assessment of the influence of the errors of estimation upon index selection procedures when estimates are obtained from paternal half-sib analyses of variance and covariance.

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The goal of many forest tree breeding programs is to increase the quantity and quality of wood products from plantations. Due to their outcrossing breeding systems, long generation times and relatively short history of domestication, breeding populations of most forest trees closely resemble the wild state. Consequently, vast stores of genetic variation are available for selection. Because wood traits are under polygenetic control (quantitative), genetic improvement will rely on selection of multiple alleles, each of relatively small individual effect. Marker-assisted selection may enhance tree breeding programs by enabling informed selection of parents for crossing; fixing desirable alleles in the homozygous state; increasing selection intensity through screening large numbers of individuals; enabling early selection in seedlings and by reducing phenotyping costs. The low linkage disequilibrium found in most forest trees makes them ideally suited to candidate gene-based association mapping approaches for marker discovery. This approach seeks to find alleles which affect phenotype and that remain linked to the trait across populations and over many generations. This methodology is well suited to tree breeding programs which aim to maintain a broad genetic base i.e. programs with a large number of families. We are using association studies to identify genes and allelic variation that influences wood fibre properties in Eucalyptus nitens. Candidate genes are being selected on the basis of their known involvement in cell wall synthesis pathways expected to impact wood traits. Single nucleotide polymorphisms (SNPs) are identified in candidate genes by sequencing in a number of unrelated individuals. Selected SNPs are being genotyped across large unrelated E. nitens populations that have been extensively phenotyped for wood properties including cellulose and lignin content, pulp yield, MFA, and density. Several SNPs significantly associated with wood properties have been identified and subsequently validated in other provenance or mapping populations growing in different environments. Selected SNPs are being investigated further to determine whether or not the SNP is the causative polymorphism and how the polymorphism influences the trait. DNA markers identified in this research may be used to complement existing index selection strategies in E. nitens breeding programs. Strategies for exploiting SNPs for marker-assisted selection in seedling-based breeding programs will be discussed.