An iterative selection strategy, based on estimated breeding values (EBV) and average relationship among selected individuals, is proposed to optimise the balance between genetic response and inbreeding. Stochastic simulation was used to compare rates of inbreeding and genetic gain with those of other strategies. For a range of heritabilities, population sizes and mating ratios, the iterative strategy, denoted ADJEBV, outperforms other strategies, giving the greatest genetic gain at a given rate of inbreeding and the least breeding at a given genetic gain. Where selection is currently by truncation on the EBV, with a restriction on the number of full-sibs selected, it should be possible to maintain similar levels of genetic gain and inbreeding with a reduction in population size of 10-30%, by changing to the iterative strategy. If performance is measured by the reduction in cumulative inbreeding without losing more than a given amount of genetic gain relative to results obtained under truncation selection on the EBV, then with the EBV based on a family index, the performance of ADJEBV is greater at low heritability, and is generally greater than where EBV are based on individual records. When comparisons of genetic response and inbreeding are made for alternative breeding scheme designs, schemes which give higher genetic gain within acceptable inbreeding levels would usually be favoured. If comparisons are made on this basis, then the selection method used should be ADJEBV, which maximises the genetic gain for a given level of inbreeding. The results indicated that all selection strategies used to reduce inbreeding had very small effects on the variance of gain, and so differences in this respect are unlikely to affect choices among selection strategies. Selection criteria are recommended based on maximising a selection objective which specifies the desired balance between genetic gain and inbreeding.

Effects of lactation length and weaning-to-conception interval on the subsequent litter size of purebred sows were estimated using an animal model. Data on 2,847 Landrace sows with 7,125 litters born between January 1989 and May 1997 and on 1,234 Yorkshire sows with 2,999 litters born between January 1990 and May 1997 were obtained from two Canadian selection herds. Sows having a lactation of less than 14 d (MMEW) were usually not mated until their second estrus, whereas sows weaned after at least 14 d of lactation (later weaning) were usually mated on their first estrus. Litter size included both number of pigs born alive and those stillborn. Linear, quadratic, and logarithmic effects of lactation length were tested. The effect of weaning-to-conception interval on litter size was modeled using an approach based on threshold variables and an approach using segmented polynomials. Results indicated linear and logarithmic effects of lactation length on subsequent litter size for Yorkshire and Landrace breeds, respectively. Litter size decreased as weaning-to-conception interval increased up to 7 and 10 d for Yorkshire and Landrace, respectively, then increased with further increases in weaning-to-conception interval up to 35 and 30 d for the two breeds, and then remained constant. The MMEW sows did not have lower subsequent litter sizes than later-weaned sows because the negative effect of a shorter lactation was offset by the positive effect of a longer weaning-to-conception interval. However, average time spent open per parity was longer for MMEW sows than for later-weaned sows. Both lactation length and weaning-to-conception interval should be considered in models for the genetic evaluation of litter size in purebred swine. Segmented polynomials can be used to predict litter size as a continuous function of weaning-to-conception interval or to derive weaning-to-conception interval adjustment factors for litter size.

A selection strategy is investigated which should improve upon methodology previously introduced for reducing inbreeding by including genetic relationships in selection decisions. The new strategy includes predictions of stabilised genetic contributions of parents to descendants in selection decisions. An additive infinitesimal genetic model is assumed with discrete generations of selection and random mating of selected parents. Stochastic simulation is used to compare rates of inbreeding and genetic gain from the strategy using relationships with those from the strategy using predicted genetic contributions. The latter strategy gives slightly higher genetic gain at a given level of cumulate inbreeding, but the advantage is small, and the calculations are more complex and difficult to apply in practice, and therefore the previous strategy using relationships is more useful for practical application. inbreeding / selection / genetic gain

Summary Deterministic methods were used to calculate the accuracy of evaluation, and the correlation of estimated breeding values (EBV) among sibs, when evaluation is based on phenotypic records of the individual and relatives, or on quantitative‐trait‐locus (QTL) information. An additive infinitesimal genetic model was assumed, with discrete generations of truncation selection on EBV, and random mating of selected parents in a hierarchical design. It was shown that the overlap of phenotypic data between the evaluations of relatives causes large increases in correlations of EBV with only modest increases in accuracy. This explains the disproportionate increases in inbreeding observed by other authors. By contrast, the use of major‐locus information leads to low correlations of EBV among relatives, provided that functional loci are directly identified or there is complete linkage disequilibrium. Use of information from QTL should reduce EBV correlations and, hence, inbreeding, but use of information from markers may not be so useful, since errors of estimation of association with QTL will be shared by family members, leading to increased correlations of EBV. Zusammenfassung Genauigkeit und Korrelation der geschätzten Zuchtwerte von verwandten Tieren mit Information von Verwandten oder von identifizierten Genen Zur Kalkulation der Genauigkeit und Korrelation der geschätzten Zuchtwerte von Geschwistern sind deterministische Methoden angewandt worden für die Situation, daß die geschätzten Zuchtwerte auf phänotypischen Beobachtungen von einem Individuum und dessen Verwandten oder auf der Information von Loci, die quantitative Merkmale beeinflußen (QTL), basieren. Ein additiv‐genetisches Infinitisimalmodell wurde unterstellt, nach diskreten Generationen mit Selektion nach geschätzten Zuchtwerten und Zufallspaarung der selektierten Eltern in einem hierarchischen Design. Es konnte gezeigt werden, daß die Überlappung der phänotypischen Daten bei der Zuchtwertschätzung von verwandten Tieren zu einer erheblichen Erhöhung der Korrelation wischen geschätzten Zuchtwertenführte, während die Genauigkeit der Schätzwerte nur geringfügig erhöht war. Diese Ergebnisse können die unverhältmässige Erhöhung der Inzucht, die andere Autoren beobachtet haben, erklären. Im Gegensatz dazu führte die Verwendung der Information von QTL zu einer niedrigenen Korrelation der geschätzten Zuchtwerte von verwandten Tieren, vorausgesetzt die funktionellen QTL können direkt identifiziert werden oder es besteht ein vollständiges Kopplungsungleichgewicht. Die Berücksichtigung der Information von QTL sollte die Korrelation der geschätzten Zuchtwerte reduzieren können und führt deshalb zur Verminderung der inzucht. Die Verwendung von Markerinformation könnte weriger nützlich sein, weil Fehler bei der Schätzung der Kopplung zwischen Marker und QTL für alle Mitglieder einer Familie gemeinsam sind und deshalb zu erhöhten Korrelationen zwischen geschätzten Zuchtwerten führen können. Resumen Precisión de la Evaluación y Correlación de los Valores Reproductivos...

Investigations are made of variations in an iterative methodology previously introduced for reducing inbreeding by including genetic relationships in selection decisions, using adjusted estimated breeding values (EBV). An alternative computing strategy for maximising the value of the population selection criterion is shown to involve less computation, which results in function values as great or greater than the original method. Alteration of weights for different types of relationships in the adjusted EBV has no detectable effect on genetic gain at a given level of inbreeding. Selection using the adjusted EBV method in one sex and truncation on EBV in the other sex results in less genetic gain at a given level of inbreeding than using adjusted EBV in both sexes, but results in more gain at a given level of inbreeding than three selection strategies that do not include genetic relationships in selection decisions. The advantage of the adjusted EBV method over these three methods is retained when selection is for a sexlimited trait.