Index selection with nonlinear profit function as a tool to achieve simultaneous genetic gain

Summary Simultaneous improvement of several, and often negatively correlated, traits is frequently a desired objective in forest tree breeding. A profit function that includes a combination of both linear weights and weights for the cross-products of trait combinations facilitates the construction of a linear index, with an attractive response in all traits. A detailed algorithm for finding the index coefficients is provided, along with three examples of applications in tree breeding. The index is also a powerful tool in optimizing the selection for a ratio of two traits. It is argued that a more equal progress in several traits provides a safetey net when faced with economic uncertainties. The provided algorithm eliminates the need for direct search techniques. Existence of a dual set of linear weights means that the statistical properties of the index based on nonlinear profit functions are identical to those of the classical Smith-Hazel type of index.     

Selection strategies and artificial evolution

Summary Artificial selection results in biolgical changes, creating artificial evolution. When using selection indexes, the artificial evolution depends on the relative economic (or other) weight of traits in the breeding objective, and on the phenotypic and genetic variances and covariances among these traits and the traits recorded in the selection index. As shown here, the selection strategy (in this case, individual selection versus progeny test selection) can also have marked effects on the kind of artificial evolution produced. Thus, where economic weights are uncertain, choice between alternative selection strategies might take into account the different types of animal or plant resulting.     

Selection indices for non-linear profit functions

Summary Conventional selection index theory assumes that the total merit or profitability of animals is a linear function of measurable traits. However, in many cases merit may be a non-linear function of these traits. A linear selection index can still be used in this situation but the optimum index depends on the selection intensity to be used and on the number of generation over which the selection response is to be maximized. Nonlinear selection indices have been suggested but these result in a lower selection response than the best linear index. Linear selection indices suggested in the past are shown to correspond to the optimum linear index for either a very small selection response or, in the case of restricted indices, a very large selection response. The economic value of a trait may depend on management decisions taken by the farmer. In this situation the economic values should be calculated assuming that the management decisions taken maximize profit given the present genetic value of the animals.     

Converting multi-trait breeding objectives into operative selection indexes to ensure genetic gains in low-input sheep and goat breeding programmes

Small ruminant breeding programmes in low-input production systems are best organised at the community level. Participant farmers have to agree on goal traits and their relative importance. When BLUP breeding values of goal traits are not available in time, appropriate selection indexes can be used to aid visual selection. Taking Ethiopian Abergelle goat and Bonga sheep community-based breeding programmes (CBBPs) as an example, breeding objective functions were defined and selection indexes were constructed and evaluated. Breeding goals for Abergelle goats included early sale weight, survival and milk production. Breeding goals for Bonga included the number of offspring born, sale weight and survival. Economic weights of objective traits can be used in several ways depending on measured traits and the reliability of their genetic parameters. Selection indexes included combinations of objective traits measured on candidates and their dams and situations when Abergelle communities prefer to restrict genetic changes in number of offspring born or adult weight and when Bonga communities prefer to restrict changes in adult weight. Genetic and economic gains were evaluated as well as sensitivity to feed cost assumptions and to repeated dam records. After independent culling on preponderant traits such as coat colour and horn/tail type, sires in Abergelle goat community breeding programmes should be selected on indexes including at least own early live weight and their dams average milk production records. Sires for Bonga sheep programmes should be selected on own early live weight and desirably also on their dam’s number of offspring born. Sensitivity to feed cost assumptions was negligible but repeated measurements of dam records improved index accuracies considerably. Restricting genetic changes in number of offspring born or adult weight is not recommended.     

Effect of various parameter combinations on genetic gain in computer simulated two-character selection

Summary In a simulation study, the effect of various parameter combinations such as linkage, dominance, heritability, and economic weights on the individual trait means was investigated using additive genetic, genotypic and the phenotypic index of Elston (1963). The characters responded differently to these indices under various parameter combinations, indicating favourable and unfavourable effects of the mentioned parameters. Linkage was found to reduce the rate of progress through selection. Depression of genetic gain was greater where the genes governing a character showed dominance and/or heritability coefficients were low. It was, however, noticed that depression of genetic gain due to low heritability of a character could be avoided by assigning higher economic weight to that character. This suggests that desirable changes in the means of characters available for selection can be manipulated by choosing appropriate economic weights. The additive genetic index, where only the additive genetic variances and covariances go into its construction, does not seem to be affected by intra-allelic interactions since they add to variances and covariances due to dominance deviations and these have nothing to do with the additive genetic variances and covariances. It seems that from such studies, if conducted extensively incorporating still more parameters, conclusions may be drawn on the most suitable selection model for simultaneous selection under a given set of parameters available in real biological systems.     

New Approaches for Calculating Moran’s Index of Spatial Autocorrelation

Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran’s index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran’s index. Moran’s scatterplot will be ameliorated, and new test methods will be proposed. The relationship between the global Moran’s index and Geary’s coefficient will be discussed from two different vantage points: spatial population and spatial sample. The sphere of applications for both Moran’s index and Geary’s coefficient will be clarified and defined. One of theoretical findings is that Moran’s index is a characteristic parameter of spatial weight matrices, so the selection of weight functions is very significant for autocorrelation analysis of geographical systems. A case study of 29 Chinese cities in 2000 will be employed to validate the innovatory models and methods. This work is a methodological study, which will simplify the process of autocorrelation analysis. The results of this study will lay the foundation for the scaling analysis of spatial autocorrelation.     

Multistage Selection for Genetic Gain by Orthogonal Transformation

An exact transformed culling method for any number of traits or stages of selection with explicit solution for multistage selection is described in this paper. This procedure does not need numerical integration and is suitable for obtaining either desired genetic gains for a variable proportion selected or optimum aggregate breeding value for a fixed total proportion selected. The procedure has similar properties to multistage selection index and, as such, genetic gains from use of the procedure may exceed ordinary independent culling level selection. The relative efficiencies of transformed to conventional independent culling ranged from 87% to over 300%. These results suggest that for most situations one can chose a multistage selection scheme, either conventional or transformed culling, which will have an efficiency close to that of selection index. After considering cost savings associated with multistage selection, there are many situations in which economic returns from use of independent culling, either conventional or transformed, will exceed that of selection index.     

Index versus tandem selection after repeated generations of selection

Summary A theoretical comparison between two multiple-trait selection methods, index and tandem selection, after several generations of selection was carried out. An infinite number of loci determining the traits, directional and truncation selection, discrete generations and infinite population size were assumed. Under these assumptions, changes in genetic parameters over generations are due to linkage disequilibrium generated by selection. Changes continue for several generations until equilibrium is approached. Algebraic expressions for asymptotic responses from index selection can be derived if index weights are maintained constant across generations. Expressions at equilibrium for genetic parameters and responses are given for the index and its component traits. The loss in response by using initial index weights throughout all generations, instead of updating them to account for changes in genetic parameters, was analyzed. The benefit of using optimum weights was very small ranging from 0% to about 1.5% for all cases studied. Recurrence formulae to predict genetic parameters and responses at each generation of selection are given for both index and tandem selection. A comparison between expected response in the aggregate genotype at equilibrium from index and tandem selection is made considering two traits of economic importance. The results indicate that although index selection is more efficient for improving the aggregate breeding value, its relative efficiency with respect to tandem selection decreases after repeated cycles of selection. The reduction in relative efficiency is highest with the highest selection intensity and heritabilities and with negative correlations between the two traits. The advantage of index over tandem selection might be further reduced if changes in genetic parameters due to gene frequency changes produced by selection, random fluctuations due to the finite size of the population, and errors in estimation of parameters, were also considered.     

The effect of cost surface parameterization on landscape resistance estimates

A cost or resistance surface is a representation of a landscape's permeability to animal movement or gene flow and is a tool for measuring functional connectivity in landscape ecology and genetics studies. Parameterizing cost surfaces by assigning weights to different landscape elements has been challenging however, because true costs are rarely known; thus, expert opinion is often used to derive relative weights. Assigning weights would be made easier if the sensitivity of different landscape resistance estimates to relative costs was known. We carried out a sensitivity analysis of three methods to parameterize a cost surface and two models of landscape permeability: least cost path and effective resistance. We found two qualitatively different responses to varying cost weights: linear and asymptotic changes. The most sensitive models (i.e. those leading to linear change) were accumulated least cost and effective resistance estimates on a surface coded as resistance (i.e. where high-quality elements were held constant at a low-value, and low-quality elements were varied at higher values). All other cost surface scenarios led to asymptotic change. Developing a cost surface that produces a linear response of landscape resistance estimates to cost weight variation will improve the accuracy of functional connectivity estimates, especially when cost weights are selected through statistical model fitting procedures. On the other hand, for studies where cost weights are unknown and model selection is not being used, methods where resistance estimates vary asymptotically with cost weights may be more appropriate, because of their relative insensitivity to parameterization.     

Optimization of recurrent selection on the phenotypic value of doubled haploid lines

Summary Three methods of recurrent selection using doubled haploids (DH) are compared with the same resources: individual line selection (with one DH line per plant), selection between and within families, and selection index of family and line within family values. It seems that for low heritabilities at the individual level, the selection index method is the most efficient method, followed by the selection between and within families. Because of the difficulty in optimizing selection intensities, the selection between and within families can be less efficient than individual line selection. For very low heritabilities, it will be better to use selection index with a relatively low number of lines per haploidized plant, to minimize the rate of decrease of the effective population size. For a large range of situations, recurrent selection with only one DH line per plant seems one of the more efficient and the simpler methods.     

Artificial selection on phenotypically plastic traits

Many phenotypes respond physiologically or developmentally to continuously distributed environmental variables such as temperature and nutritional quality. Information about phenotypic plasticity can be used to improve the efficiency of artificial selection. Here we show that the quantitative genetic theory for 'infinite-dimensional' traits such as reaction norms provides a natural framework to accomplish this goal. It is expected to improve selection responses by making more efficient use of information about environmental effects than do conventional methods. The approach is illustrated by deriving an index for mass selection of a phenotypically plastic trait. We suggest that the same approach could be extended directly to more general and efficient breeding schemes, such as those based on general best linear unbiased prediction. Methods for estimating genetic covariance functions are reviewed.     

An empirical comparison of selection methods for the improvement of biomass

Summary A single generation of upward truncation selection on families with 20% selected was carried out in each of five replicates using Tribolium castaneum as the test organism. The experiment involved eight lines: N — selected for offspring number; W — selected for pupal weight; B — selected for biomass; Q — quadratic index selected; L₂₁ — linear index selected with relative economic weights of 21 offspring number to pupal weight; L₁₁ — linear index selected with relative economic weights of 11 offspring number to pupal weight; L₁₂ — linear index selected with relative economic weights of 12 offspring number to pupal weight; C — an unselected control.Biomass (weight of offspring per family), offspring number, and pupal weight were measured. No differences in response to selection were found among the linear index lines and the pupal weight line with regard to any trait analysed. Generally, response to selection in the linear index lines and pupal weight line was small for offspring number and high for pupal weight. Selection pressure on offspring number in these lines seemed to be dependent on the correlation between offspring number and pupal weight. As a result, response to selection for biomass was poor in the linear index and pupal weight selected lines. In the case of the linear indices, poor response to selection for biomass appeared to be due to the violation of the assumption of additivity of the traits included in the definition of aggregate genotype.The responses in the quadratic index, biomass, and offspring number selected lines were equal with respect to selection for biomass. The response of the quadratic index selected line was less than the responses of the biomass and offspring number selected lines for offspring number, but the response in the quadratic index line was as large as that of any other line included in the experiment and greater than the biomass and offspring number selected lines where pupal weight was the criterion.Highly significant amounts of variation were found for all traits indicating that more replicates are needed for precise evaluation of selection systems.     

Measuring social structure: a comparison of eight dominance indices

Measurement of social status is an important component of many behavioural studies. A variety of techniques have been developed and adopted, but while there have been some analyses of index properties using simulated data, the rationale for selecting a method remains poorly documented. As a first step in exploring the implications of index choice, we compared the characteristics of eight popular indices by applying each to the same data set from interactions between male fowl Gallus gallus, the system in which social hierarchies were first described. Data from eight social groups, observed over four successive breeding seasons, were analysed to determine whether different indices produced consistent dominance scores. These scores were then used in tests of the relation between social status and crowing to explore whether index choice affected the results obtained. We also examined the pattern of dominance index use over the last decade to infer whether this has likely been influenced by tradition, or by taxa of study animal. Overall agreement among methods was good when groups of birds had perfectly linear hierarchies, but results diverged when social structure was more complex, with either intransitive triads or reversals. While all regression analyses revealed a positive relationship between dominance and vocal behaviour, there were substantial differences in the amount of variance accounted for, even though the original data were identical in every case. Index selection can hence perturb estimates of the importance of dominance, relative to other factors. We also found that several methods have been adopted only by particular research teams, while the use of others has been taxonomically constrained, patterns implying that indices have not always been chosen solely upon their merits. Taken together, our results read as a cautionary tale. We suggest that selection of a dominance index requires careful consideration both of algorithm properties and of the factors affecting social status in the system of interest.     

A molecular selection index method based on eigenanalysis

The traditional molecular selection index (MSI) employed in marker-assisted selection maximizes the selection response by combining information on molecular markers linked to quantitative trait loci (QTL) and phenotypic values of the traits of the individuals of interest. This study proposes an MSI based on an eigenanalysis method (molecular eigen selection index method, MESIM), where the first eigenvector is used as a selection index criterion, and its elements determine the proportion of the trait's contribution to the selection index. This article develops the theoretical framework of MESIM. Simulation results show that the genotypic means and the expected selection response from MESIM for each trait are equal to or greater than those from the traditional MSI. When several traits are simultaneously selected, MESIM performs well for traits with relatively low heritability. The main advantages of MESIM over the traditional molecular selection index are that its statistical sampling properties are known and that it does not require economic weights and thus can be used in practical applications when all or some of the traits need to be improved simultaneously.     

Weighting fibre and morphological traits in a genetic index for an alpaca breeding programme

Nowadays, the fibre diameter (FD) is considered the main selection objective in alpaca populations all over the world. International Committee for Animal Recording recommendations define the FD and its CV as the first two traits to be considered in breeding programmes for this specie. In addition to these main criteria, other selection criteria of economic value used are comfort factor (CF) or standard deviation (s.d.); also other less important traits being used as selection objectives are these morphological traits: density (DE), crimp (CR) or lock structure (LS) for, respectively, Huacaya (HU) and Suri (SU) ecotypes, head (HE), coverage (CO) and balance (BA). The goal of this study was to establish how to implement a combined selection index starting from genetic parameters and to study the expected correlation between genetic trends by considering different alternative procedures of weighting all the involved traits, and the consequences of a wrongly proceeding way. Heritabilities and genetic and phenotypic correlations were estimated from the data set belonging to the PACOMARCA experimental farm for SU and HU. Two approaches were used to check the consequences of a set of subjective weights essayed. The coefficients of selection indexes were obtained for two sets of reference weights. In addition, equivalent weights were drawn if applied those reference values as coefficients of hypothetical selection indexes directly on phenotypes; relative expected genetic responses were computed in different cases. Results showed that almost in all cases for both ecotypes, the weight applied to CF should be surprisingly negative. Concerning genetic responses, only CO was compromised in some cases for the HU ecotype. The essayed methodology allowed explaining the differences between ecotypes in the genetic trends. The proposed methodology was shown to be effective to study the relative importance of the traits granted by the manager of a breeding scheme.     

Designing an integrated coastal orientation index: A cross-comparison of Mexican municipalities

To better understand the relation between coastal areas and their influence on social and economic conditions of municipalities, a set of indexes were developed to characterize coastal Mexico with an interdisciplinary approach. The composite of these bio-physical, social and economic indexes is referred to as an “integrated coastal orientation index”. Coastal characteristics should be taken into account in the coastal management policy formulation of a given region, and this index can be used to identify key areas for environmental protection or economic development at a national level. The results suggest that municipalities must manage their coastal jurisdictions, a large and diverse array of coastal space and ecosystems, medium to weak spatial demographics and settlement structures, infrastructure to improve quality of life, an overall low coastal population income, and various coastal activities. Spatial heterogeneity along the littoral zone in the coastal orientation led us to conduct a state analysis. We discuss these values and identify five highly coastal-orientated states in the extremes of the country. The development of this tool could help to pin-point different types of key areas within the regions studied and provide a tool to guide regional priorities. As an example, using a combination of extreme values of bio-physical, social and economic indexes was used to identify specific municipalities as candidates for environmental protection and others as areas where development can continue. Choices of indexes are discussed, and the relative importance given to each component of the coastal orientation (rather bio-physical, social and/or economic) will define the course of the coast's development and its sustainability.     

Economic weights of maternal and direct traits of pigs calculated by applying gene flow methods

Multiple trait selection indexes in pig breeding programmes should take into account the population structure and time delay between parent selection and expressions of traits in all production levels next to the trait impacts on economic efficiency of production systems. Gene flow procedures could be used for the correct evaluation of maternal and direct traits of pig breeds involved in breeding or crossbreeding systems. Therefore, the aim of this study was to expand a previously developed bioeconomic model and computer program to calculate the marginal economic values by including a gene flow procedure to calculate the economic weights for maternal and direct traits in pig breeds. The new program was then applied to the three-way crossbreeding system of the Czech National Programme for Pig Breeding. Using this program, the marginal economic values of traits for dam breeds Czech Large White in the dam position and Czech Landrace in the sire position, and for the sire breed Pietrain were weighted by the number of discounted gene expressions of selected parents of each breed summarised within all links of the crossbreeding system during the 8-year investment period. Economic weights calculated in this way were compared with the approximate economic weights calculated previously without a gene flow procedure. Taking into account the time delay between parent selection and trait expression (using discounting with half-year discount rates of 2% or 5%) and including more than one generation of parent progeny had little impact on the relative economic importance of maternal and direct traits of breeds involved in the evaluated three-way crossbreeding system. These results indicated that this gene-flow method could be foregone when estimating the relative economic weights of traits in pig crossbreeding systems applying artificial insemination at all production levels.     

Is Fisher's model necessary for the theory of population improvement?

Summary It is shown here that genetic advance in one cycle of recurrent selection can be formulated directly in terms of covariances between relatives by application of the general statistical principle of linear prediction. For practical use of such formulae it is necessary to estimate the corresponding covariance between relatives from the mating design used. With General Combining Ability selection such estimation is direct. For other types of selection, it is necessary to derive associated covariances from other types of covariances but it is not necessary to use classical results of covariances between relatives in terms of genetic effects. Indeed, covariances can be derived without factorial decomposition of the genetic effects at one locus, i.e., without the concept of additivity and dominance. This approach allows a simple derivation of the genetic advance after n cycles of selection, followed by m generations of intercrossing, with a minimum of assumptions.     

动物栖息地选择评估的常用统计方法

利用合适的统计学方法能够更准确地理解动物的栖息地选择。本文通过对2003~2012年期间,10个国际期刊所发表的177篇关于鸟类和兽类栖息地选择论文的30种统计学方法进行分析,简要概述了目前流行的栖息地选择统计学分析方法及特点,同时对同时期的中文文献也进行了简要分析。目前关于动物栖息地选择较为流行的分析方法主要有逻辑斯蒂回归、资源选择函数、成分分析、广义线性模型、多元方差分析、基于欧几里德距离的方法、广义线性混合模型、生态位因子分析、基于个体模型、典型相关分析、物种分布模型等。广义线性模型、逻辑斯蒂回归、多元方差分析和基于欧几里德距离这些方法可以很灵活地用来分析数据,但是缺乏一个有生态学意义的理论框架。资源选择函数和生态位因子分析各自为栖息地选择研究提供了一个统一的理论框架。基于个体的模型是一个自下而上的过程,很难在系统水平形成理论。232篇国内文章中使用较多的方法是主成分分析、Mann-Whitney U检验、t检验、卡方检验、判别分析、方差分析、Vanderloeg选择系数和Scavia选择指数、逻辑斯蒂回归、Kruskal-Wallis H检验和多元回归分析等。在实际研究中,应根据所要解决的研究问题,选择切实可行的分析方法。