Grouping genotypes by a cluster method directly related to genotype-environment interaction mean square

Summary To facilitate the interpretation of data from a genotype by environment (GE) experiment when the GE interaction is large, a cluster method is proposed to group genotypics according to their response to the environments. The dissimilarity index between a pair of genotypes is defined in terms of distance adjusted for the average effects of genotypes, and Sokal and Michener's (1958) unweighted pair-group method is used in the clustering algorithm. The new index, constructed in each cluster cycle for any group, is shown to be equivalent to within group GE interaction mean square under 2-way ANOVA. Thus, if the F-value is used as an empirical stopping criterion for clustering, there will be no significant GE interaction within groups and the genotypes within the groups can be compared by their average effects. The method of analysis is illustrated by an example.Contribution no. I-348 from the Engineering and Statistical Research Institute     

Similarity in ectoparasite faunas of Palaearctic rodents as a function of host phylogenetic, geographic or environmental distances: Which matters the most?

Different host species harbour parasite faunas that are anywhere from very similar to very different in species composition. A priori, the similarity in the parasite faunas of any two host species should decrease with increases in either the phylogenetic distance, the distinctness of the environments occupied or the geographical distance between these hosts. We tested these predictions using extensive data on the faunas of fleas (Insecta: Siphonaptera) and gamasid mites (Acari: Parasitiformes) parasitic on rodents across the Palaearctic. For each pair of host species, we computed the similarity in parasite faunas based on both species composition as well as the phylogenetic and/or taxonomic distinctness of parasite species. Phylogenetic distances between hosts were based on patristic distances through a rodent phylogeny, geographic distances were computed from geographic range data, and environmental dissimilarity was measured from the average climatic and vegetation scores of each host range. Using multiple regressions on distance matrices to assess the separate explanatory power of each of the three dependent variables, environmental dissimilarity between the ranges of host species emerged as the best predictor of dissimilarity between parasite faunas, especially for fleas; in the case of mites, phylogenetic distance between host species was also important. A closer look at the data indicates that the flea and mite faunas of two hosts inhabiting different environments are always different, whilst hosts living in similar environments can have either very similar or dissimilar parasite faunas. Additional tests showed that dissimilarity in flea or mite faunas between host geographic ranges was best explained by dissimilarity in vegetation, followed by dissimilarity in climatic conditions. Thus, external environmental factors may play greater roles than commonly thought in the evolution of host-parasite associations.     

An index to compare geographical distributions of species

We present an index for the dissimilarity/distance between geographical distributions based on reporting rates recorded on a regular lattice. Reporting rate data are common, for example, in bird atlas projects where observers fill in check lists of encountered species in a particular area. Our index is a variation of the Euclidean distance, with the contribution of each grid cell weighted by the number of checklists collected for the grid cell, and a scaling factor to ensure that the dissimilarity ranges between zero and one. Reporting rates were transformed to ordered percentile classes to make species with different mean reporting rates comparable. The index was developed for the comparison of distributions of The Atlas of Southern African Birds . We illustrate the dissimilarity index comparing distributions of whydahs and indigobirds (widowfinches), which are specialized brood parasites, to the distributions of their hosts: waxbills and other finches.     

Genetic diversity in wild species of passion fruit (Passiflora trintae) based on molecular markers

In spite of the importance of and the considerable variability observed in Passiflora (Passifloraceae), little is known about the genetic diversity of most of the species of this genus. We evaluated the genetic diversity by RAPD markers in 18 genotypes of Passiflora trintae. The 15 primers generated 112 markers, 84% of which were polymorphic. The genetic distance estimated by the complement of the Dice index (average dissimilarity = 0.30) and genotype grouping based on the UPGMA algorithm showed low variability among genotypes. More attention should be given to the study and conservation of the biodiversity of this economically important genus.     

Alternative partitioning of the genotype-by-environment interaction

Summary Alternative methods for partitioning the genotype-by-environment interaction, for an arbitrary number of genotypes or environments, were examined. Partitioning of the interaction is important in order to determine the nature of the interaction. Two methods of partitioning were examined; both separated the interaction into two types: (1) due to heterogeneous variances or (2) due to imperfect correlations. Method 1 was based on heterogeneity among environments in the scaling of differences among genotypes. Method 2 was based on heterogeneity among genotypes in the scaling of differences among environments. Any remaining interaction arises from deviations from the perfect positive correlation of genotypic rankings among environments (Method 1) or of environmental rankings among genotypes (Method 2). Method 1 is more appropriate for random genotypes that are to be tested in either fixed or random environments. With Method 1, the interactions that arise mainly from heterogeneity of genotypic scaling among environments are generally unimportant. However, if environments are fixed and interactions are mainly due to imperfect correlations of rankings, specialized lines may be indicated for each environment. Method 2 is more useful in evaluating fixed genotypes for sensitivity to random environments. A partitioning of the interaction into that due to the type of interaction within each genotype was shown to be useful in that situation.Journal Paper No. 123737 of the Purdue University Agricultural Experiment Station     

A Study on Genotype-by-Environment Interaction Analysis for Agronomic Traits of Maize Genotypes Across Huang-Huai-Hai Region in China

Facing the trend of increasing population, how to increase maize grain yield is a very important issue to ensure food security. In this study, 28 nationally approved maize hybrids were evaluated across 24 different climatic conditions for two consecutive years (2018–2019). The purpose of this study was to select high-yield with stable genotypes and identify important agronomic traits for maize breeding program improvement. The results of this study showed that the genotype ╳ environment interaction effects of the 12 evaluated agronomic traits was highly significant (P < 0.001). We introduced a novel multi-trait genotype-ideotype distance index (MGIDI) to select genotypes based on multiple agronomic traits. The selection process exhibited by this method is unique and easy to understand, so the MGIDI index will have more and more important applications in future multi-environment trials (METs) research. The genotypes selected by the MGIDI index were G22, G10, G12 and G1 as the high yielding and stable genotypes. The parents of these selected genotypes have the ability to play a greater role as the basic germplasm in the breeding process. A new form of genotype (G) main effects and genotype (G) -by-environment (E) interaction (GGE) technician, genotype*yield*trait (GYT) biplot, based on multiple traits for genotypes selection was also applied in this study. The GYT biplot ranked genotypes by combining grain yield with other evaluated agronomic traits, and displayed the distribution of their traits, namely strengths and weaknesses.     

The ecology and genetics of fitness in Chlamydomonas. X. The relationship between genetic correlation and genetic distance

Abstract.— A necessary condition for the maintenance of genetic variation in heterogenous environments is that the relative fitnesses of a collection of genotypes vary as conditions of growth change. This can be detected by estimating the amount of gene-by-environment interaction (G X E) when a range of types are tested across a range of conditions. However it is the sign and magnitude of the genetic correlation, which is a component of G X E, that governs the ultimate fate of variation. Whether genetic variation will be preserved, then, depends on how the genetic correlation changes as a function of the ecological differences among environments and the genetic differences among genotypes. To evaluate this, we assayed the performance of 15 chlorophyte species of known genetic relation in 20 environments. We found that the quantity of G X E increased as both the environmental variance across environments and the genetic distance increased. Moreover the genetic correlation declined as the environmental variance between pairs of environments and the genetic distance between pairs of genotypes increased. These results suggest that divergent selection will be more likely to maintain genetic variation when environments are strongly contrasted and genotypes widely divergent.     

Genotype x environment interaction of crossover type: detecting its presence and estimating the crossover point

Genotype-environment interaction (GEI) introduces inconsistency in the relative rating of genotypes across environments and plays a key role in formulating strategies for crop improvement. GEI can be either qualitative (i.e., crossover type) or only quantitative (i.e., non-crossover type). Since the presence of crossover-type interaction has a strong implication for breeding for specific adaptation, it is important to assess the frequency of crossover interactions. This paper presents a test for detecting the presence of crossover-type interaction using the response-environment relationship and enumerates the frequency of crossovers and estimation of the crossover point (CP) on the environment axis, which serves as a cut-off point for the two environments groups where different/specific selections can be made. Sixty-four barley lines with various selection histories were grown in northern Syria and Lebanon giving a total of 21 environments (location-year combinations). Linear regression of the genotypic response on the environmental index represented a satisfactory model, and heterogeneity among regressions was significant. At a 5% level of significance, 38% and 19% of the pairs showed crossover interactions when the error variances were considered heterogeneous and homogeneous, respectively, implying that an appreciable number of crossovers took place in the case of barley lines responding to their environments. The CP of 1.64 t/ha, obtained as the CP of regression lines between the genotype numbers 19 and 31, provided maximum genotype x environment-group interaction. Across all environments, genotype nos. 59 and 12 stood first and second for high yield, respectively. The changes in the ranks of genotypes under the groups of environments can be used for selecting specifically adapted genotypes. Received: 25 January 1999 / Accepted: 16 March 1999     

Deconstructing spatial patterns in species composition of ectoparasite communities: the relative contribution of host composition,environmental variables and geography

Aim We determined whether dissimilarity in species composition between parasite communities depends on geographic distance, environmental dissimilarity or host faunal dissimilarity, for different subsets of parasite species with different levels of host specificity. Location Communities of fleas parasitic on small mammals from 28 different regions of the Palaearctic. Method Dissimilarities in both parasite and host species composition were computed between each pair of regions using the Bray–Curtis index. Geographic distances between regions were also calculated, as were measures of environmental dissimilarity consisting of the pairwise Euclidean distances between regions derived from elevation, vegetation and climatic variables. The 136 flea species included in the dataset were divided into highly host‐specific species (using 1–2 host species per region, on average), moderately host‐specific species (2.2–4 hosts per region) and generalist species (>4 hosts per region). The relative influence of geographic distance, host faunal dissimilarity and environmental dissimilarity on dissimilarity of flea species composition among all regions was analysed for the entire set of flea species as well as for the three above subsets using multiple regressions on distance matrices. Results When including all flea species, dissimilarity in flea species composition was affected by all three independent variables, although the pure effect of dissimilarity in host species composition was the strongest. Results were different when the subsets of fleas differing in host specificity were treated separately. In particular, dissimilarity in species composition of highly host‐specific fleas increased solely with environmental dissimilarity, whereas dissimilarity for both moderately specific and non‐specific fleas increased with both geographic distance and dissimilarity in host species composition. Main conclusions Host specificity seems to dictate which of the three factors considered is most likely to affect the dissimilarity between flea communities. Counter‐intuitively, environmental dissimilarity played a key role in determining dissimilarity in species composition of highly host‐specific fleas, possibly because, although their presence in a region relies on the occurrence of particular host species, their abundance is itself mostly determined by climatic conditions. Our results show that deconstructing communities into subsets of species with different traits can make it easier to uncover the mechanisms shaping geographic patterns of diversity.     

Genotype — environment interaction in tissue cultures of birch

Summary In vitro culture experiments were carried out with three birch genotypes characterized by certain genealogical relationships which serve as indicators of genetic similarity or dissimilarity. Each genotype was grown in each of six different environments (medium types), and callus growth and colour were observed. The aim was to improve our understanding of the operation of genetic and environmental effects at the early stages of regeneration in vitro. For this purpose we tried to answer the question as to whether genetic differences exert effects that are consistently distinguishable under different environments or whether environmental differences exert effects that are consistently distinguishable between different genotypes. Since conventional analytical methods, such as the analysis of variance, are inappropriate for providing satisfactory answers to this question, we applied a new concept of interpretation. With the help of this concept we obtained the following results which appear to be unique among their kind. 1) For both characters, callus growth and callus colour, genetic differences are masked only slightly by the environments while environmental differences are almost completely masked by the genotypes. Thus, in the present experiment, interaction is one-sided in the sense that environmental effects interact strongly with genotypic effects but genotypic effects interact only slightly with the environmental ones. 2) Nuclear effects seem to be responsible for the differences observed in callus growth, while the differences in callus colour can be explained by the joint action of nuclear and extranuclear effects.     

Patterns of parasite community dissimilarity: the significant role of land use and lack of distance‐decay in a bat–helminth system

Increasing community dissimilarity across geographic distance has been described for a wide variety of organisms and understanding its underlying causes is key to understanding mechanisms driving patterns of biodiversity. Both niche‐based and neutral processes may produce a distance decay relationship; however, disentangling their relative influence requires simultaneous examination of multiple potential drivers. Parasites represent a unique opportunity in which to study distance decay because community dissimilarity may depend on environmental requirements and dispersal capability of parasites as well also those of their hosts. We used big brown bats Eptesicus fuscus and their intestinal helminths to investigate: 1) independent contributions of geographic and environmental distances on dissimilarity of intestinal helminth component communities between populations of big brown bats; 2) which environmental variables best explained variation in community dissimilarity; and 3) whether similar patterns of decay with geographic or environmental distance were observed for within‐host population and within‐individual host parasite communities. We used compositional measures of community dissimilarity to examine how parasite communities may change with geographic distance and varying environmental conditions. Non‐spatial variables strongly influenced compositional parasite community dissimilarity over multiple community scales, and we observed little evidence for spatial processes such as distance decay. Environment surrounding roost sites better predicted helminth community dissimilarity than any other class of variables and landcover classes representing anthropogenic modification consistently explained variation in community structure. Our results indicate that human disturbance drives significant patterns of parasite community dissimilarity, most likely by changing the presence or abundance of intermediate hosts in an area.     

On measures of dissimilarity between point patterns: Classification based on prototypes and multidimensional scaling

This paper presents a collection of dissimilarity measures to describe and then classify spatial point patterns when multiple replicates of different types are available for analysis. In particular, we consider a range of distances including the spike‐time distance and its variants, as well as cluster‐based distances and dissimilarity measures based on classical statistical summaries of point patterns. We review and explore, in the form of a tutorial, their uses, and their pros and cons. These distances are then used to summarize and describe collections of repeated realizations of point patterns via prototypes and multidimensional scaling. We also show a simulation study to evaluate the performance of multidimensional scaling with two types of selected distances. Finally, a multivariate spatial point pattern of a natural plant community is analyzed through various of these measures of dissimilarity.     

Choosing probe genotypes for the analysis of genotype-environment interaction in winter wheat trials

Genotype-environment interaction was analyzed in French multi-environment wheat (Triticum aestivum L.) trials using probe genotypes and bi-additive factorial regression. Probe genotypes are specific genotypes in which the comparisons of yield components to reference values describe the most-important environmental factors that limited grain yield. The time-period until flowering was described by the deviation of kernel number from a threshold number while the grain-filling period was described by the reduction of thousand-kernel weight from a potential value. The aim of this paper was to determine the convenient number and the characteristics of probe genotypes to include in wheat breeding trials. Two sets of genotypes were used to model genotype-environment interaction: set 1 with 12 varieties tested in 18 environments and set 2 with ten lines tested in 14 environments. Set 2 was used for validation. Seven probe genotypes described the environments by providing environmental covariates, namely differences in yield components, for further analysis of interaction in set 1 and set 2. Interaction was modelled with bi-additive factorial regressions including differences in yield components. Several rounds of models were fitted to determine the optimal number of probe genotypes (i.e. environmental covariates) to introduce. From the seven probe genotypes, all the possible combinations including one to seven genotypes were studied. Significance of the combinations was tested with critical values obtained from simulations through 1,000 random permutations. Taking into account the information available on the probe genotypes, one would think that two, three or four probe genotypes would be sufficient, otherwise the number should reach four or five genotypes. In all cases, these numbers will provide models more-parsimonious than the classical AMMI model. The important information to be known on the probe genotypes prior their first multilocation experiment is: interaction pattern, earliness, and differences in yield component. Tested for the first time, a quadruplet is better than a triplet because the probability of choosing complementary genotypes increases with their number.     

Conceptual analysis of methods applied to assessment of diversity within and distance between populations with asexual or mixed mode of reproduction

Measures of diversity within populations, and distance between populations, are compared for organisms with an asexual or mixed mode of reproduction. Examples are drawn from studies of plant pathogenic fungi based on binary traits including presence/absence of DNA bands or virulence/avirulence to differential hosts. Commonly used measures of population diversity or genetic distance consider either genotype frequencies or allele frequencies. Kosman's diversity and distance measures are the most suitable for populations with an asexual or mixed mode of reproduction, because by considering genetic patterns of all individuals they take into account not just the genotype frequencies but also the genetic similarities between genotypes in the populations. The Kosman distance and diversity measures for populations can be calculated using different measures of dissimilarity between individuals (the simple mismatch, Jaccard and Dice coefficients of dissimilarity). Kosman's distances based on the simple mismatch and Jaccard dissimilarities are metrics. Comparisons of diversity indices for hypothetical examples as well as for actual data sets are presented to demonstrate that inferences from diversity analysis of populations can be driven by techniques of diversity and distance assessments and not only data driven.     

Vertebrate Dissimilarity Due to Turnover and Richness Differences in a Highly Beta-Diverse Region: The Role of Spatial Grain Size,Dispersal Ability and Distance

We explore the influence of spatial grain size, dispersal ability, and geographic distance on the patterns of species dissimilarity of terrestrial vertebrates, separating the dissimilarity explained by species replacement (turnover) from that resulting from richness differences. With data for 905 species of terrestrial vertebrates distributed in the Isthmus of Tehuantepec, classified into five groups according to their taxonomy and dispersal ability, we calculated total dissimilarity and its additive partitioning as two components: dissimilarity derived from turnover and dissimilarity derived from richness differences. These indices were compared using fine (10 x 10 km), intermediate (20 x 20 km) and coarse (40 x 40 km) grain grids, and were tested for any correlations with geographic distance. The results showed that total dissimilarity is high for the terrestrial vertebrates in this region. Total dissimilarity, and dissimilarity due to turnover are correlated with geographic distance, and the patterns are clearer when the grain is fine, which is consistent with the distance-decay pattern of similarity. For all terrestrial vertebrates tested on the Isthmus of Tehuantepec both the dissimilarity derived from turnover and the dissimilarity resulting from richness differences make important contributions to total dissimilarity, and dispersal ability does not seem to influence the dissimilarity patterns. These findings support the idea that conservation efforts in this region require a system of interconnected protected areas that embrace the environmental, climatic and biogeographic heterogeneity of the area.     

Restriction fragment length polymorphisms of the phytohemagglutinin genes inPhaseolus andVigna (Leguminosae)

Restriction fragment length polymorphisms at the phytohemagglutinin (PHA) locus were determined among 21 genotypes ofPhaseolus vulgaris, P. coccineus, P. acutifolius, P. lunatus, and threeVigna species, using five restriction enzymes and one double digestion, in order to provide molecular evidence for their genetic relatedness. The dissimilarity between genotypes was estimated from binary RFLP data. The dissimilarity was high among species (from 0.75 to 0.95), and of variable extent among genotypes of the same species (0.33–0.89). InP. vulgaris, two different DNA hybridization patterns were found, giving further evidence for two major gene pools in that species. The restriction patterns ofP. vulgaris var.aborigineus, the putative ancestral form ofP. vulgaris, exhibit clear homology toP. vulgaris genotypes. An undefined landrace from Taiwan could be identified as aP. vulgaris genotype. RFLP-based trees for the phytohemagglutinin genes of the species studied were computed with several distance matrix and parsimony methods.     

The area under the function: an index for selecting desirable genotypes

The linear regression approach has been widely used for selecting high-yielding and stable genotypes targeted to several environments. The genotype mean yield and the regression coefficient of a genotype's performance on an index of environmental productivity are the two main stability parameters. Using both can often complicate the breeder's decision when comparing high-yielding, less-stable genotypes with low-yielding, stable genotypes. This study proposes to combine the mean yield and regression coefficient into a unified desirability index (D _i). Thus, D _i is defined as the area under the linear regression function divided by the difference between the two extreme environmental indexes. D _i is equal to the mean of the i ^th genotype across all environments plus its slope multiplied by the mean of the environmental indexes of the two extreme environments (symmetry). Desirable genotypes are those with a large D _i. For symmetric trials the desirability index depends largely on the mean yield of the genotype and for asymmetric trials the slope has an important influence on the desirability index. The use of D _i was illustrated by a 20-environments maize yield trial and a 25-environments wheat yield trial. Three maize genotypes out of nine showed values of D _i 's that were significantly larger than a hypothetical, stable genotype. These were considered desirable, even though two of them had slopes significantly greater than 1.0. The results obtained from ranking wheat genotypes on mean yield differ from a ranking based on D _i .     

Similarity coefficients for molecular markers in studies of genetic relationships between individuals for haploid, diploid, and polyploid species

Determining true genetic dissimilarity between individuals is an important and decisive point for clustering and analysing diversity within and among populations, because different dissimilarity indices may yield conflicting outcomes. We show that there are no acceptable universal approaches to assessing the dissimilarity between individuals with molecular markers. Different measures are relevant to dominant and codominant DNA markers depending on the ploidy of organisms. The Dice coefficient is the suitable measure for haploids with codominant markers and it can be applied directly to (0,1)-vectors representing banding profiles of individuals. None of the common measures, Dice, Jaccard, simple mismatch coefficient (or the squared Euclidean distance), is appropriate for diploids with codominant markers. By transforming multiallelic banding patterns at each locus into the corresponding homozygous or heterozygous states, a new measure of dissimilarity within locus was developed and expanded to assess dissimilarity between multilocus states of two individuals by averaging across all codominant loci tested. There is no rigorous well-founded solution in the case of dominant markers. The simple mismatch coefficient is the most suitable measure of dissimilarity between banding patterns of closely related haploid forms. For distantly related haploid individuals, the Jaccard dissimilarity is recommended. In general, no suitable method for measuring genetic dissimilarity between diploids with dominant markers can be proposed. Banding patterns of diploids with dominant markers and polyploids with codominant markers represent individuals' phenotypes rather than genotypes. All dissimilarity measures proposed and developed herein are metrics.     

Assessing three methods for identification of desirable genotypes in white cabbage (Brassica oleracea L. var. capitata)

Summary A desirable genotype is a genotype performing well in a chosen set of environments. Three methods for identification of desirable genotypes were assessed in two cabbage data sets: regression analysis, multidimensional scaling of dissimilarity matrices, and biplot of deviation matrices. Using the regression approach is not recommended mainly for two reasons: (1) it is difficult to identify the desirable genotypes since one has to unify three parameters into one decision; (2) the regression method failed to identify the most desirable genotypes in one of the data sets. Multidimensional scaling and the biplot method were in accordance with each other and with the mean tables when different subsets where compared. Consequently, they were considered more adequate for identifying desirable genotypes. In cases where rank 2 approximation of the analysed matrix was justified, the biplot revealed more information in one display and was, therefore, considered particularly useful in plant breeding for larger target areas.     

Fitting a regression model for genotype-by-environment data on heading dates in grasses by methods for nonlinear mixed models

The analysis of agricultural crop variety trials is usually complicated by the presence of genotype-by-environment interaction. A number of methods and models have been proposed to tackle this problem. One of the most common methods is the regression approach due to Yates and Cochran (1938, Journal of Agricultural Science 28, 556-580), in which performances of genotypes in the environments are regressed onto environmental means. The underlying regression model contains a multiplicative term with two unknown parameters (one for genotypes and one for environments). In the present paper, the model is modified by exchanging the role of genotypes and environments. Various diagnostic plots show that this modified model is adequate for a data set on heading dates in the grass species Dactylis glomerata. If environments are considered as a random factor while genotypes are taken as fixed, the model falls into the class of nonlinear mixed models. Recently, a number of procedures have been suggested for this class of models, which are based on first-order Taylor series expansion. Alternatively, the model can be estimated by maximum likelihood. This paper discusses the application of these methods for estimating parameters of the model.