Relationships among analytical methods used to study genotypic variation and genotype-by-environment interaction in plant breeding multi-environment experiments

Following the recognition of the importance of dealing with the effects of genotype-by-environment (G ×E) interaction in multi-environment testing of genotypes in plant breeding programs, there has been substantial development in the area of analytical methodology to quantify and describe these interactions. Three major areas where there have been developments are the analysis of variance, indirect selection, and pattern analysis methodologies. This has resulted in a wide range of analytical methods each with their own advocates. There is little doubt that the development of these methodologies has greatly contributed to an enhanced understanding of the magnitude and form ofG ×E interactions and our ability to quantify their presence in a multi-environment experiment. However, our understanding of the environmental and physiological bases of the nature ofG ×E interactions in plant breeding has not improved commensurably with the availability of these methodologies. This may in part be due to concentration on the statistical aspects of the analytical methodologies rather than on the complementary resolution of the biological basis of the differences in genotypic adaptation observed in plant breeding experiments. There are clear relationships between many of the analytical methodologies used for studying genotypic variation andG ×E interaction in plant breeding experiments. However, from the numerous discussions on the relative merits of alternative ways of analysingG ×E interactions which can be found in the literature, these relationships do not appear to be widely appreciated. This paper outlines the relevant theoretical relationships between the analysis of variance, indirect selection and pattern analysis methodologies, and their practical implications for the plant breeder interested in assessing the effects ofG ×E interaction on the response to selection. The variance components estimated from the combined analysis of variance can be used to judge the relative magnitude of genotypic andG ×E interaction variance. Where concern is on the effect of lack of correlation among environments, theG ×E interaction component can be partitioned into a component due to heterogeneity of genotypic variance among environments and another due to the lack of correlation among environments. In addition, the pooled genetic correlation among all environments can be estimated as the intraclass correlation from the variance components of the combined analysis of variance. WhereG ×E interaction accounts for a large proportion of the variation among genotypes, the individual genetic correlations between environments could be investigated rather than the pooled genetic correlation. Indirect selection theory can be applied to the case where the same character is measured on the same genotypes in different environments. Where there are no correlations of error effects among environments, the phenotypic correlation between environments may be used to investigate indirect response to selection. Pattern analysis (classification and ordination) methods based on standardised data can be used to summarise the relationships among environments in terms of the scope to exploit indirect selection. With the availability of this range of analytical methodology, it is now possible to investigate the results of more comprehensive experiments which attempt to understand the nature of differences in genotypic adaptation. Hence a greater focus of interest on understanding the causes of the interaction can be achieved.     

Environmental and nutritional responses of a Pinus radiata plantation to biosolids application

Since the mid-1990s, a Pinus radiata (D. Don) plantation growing on a sandy, low fertility soil at Rabbit Island near Nelson, New Zealand received aerobically digested liquid biosolids. An experimental research trial was established on the site to investigate the effects of biosolids applications on tree growth, nutrition, soil and ground water quality. Biosolids were applied to the trial site in 1997 and 2000, at three application rates: 0 (control), 300 (standard) and 600 kg N ha⁻¹ (high). Biosolids application significantly increased tree growth. This was mainly attributed to improved N supply, demonstrated by the enhanced N concentration in the tree foliage. Soil analysis indicated that biosolids application have not caused significant changes in concentrations of most nutrients. However, biosolids treatments significantly increased the available P (Olsen P). Of the heavy metals only total Cu concentrations in the soil increased after biosolids application. Groundwater quality, which was monitored quarterly, has not been affected by biosolids application. The concentrations of nitrate and heavy metals in groundwater were well below the maximum acceptable values in drinking water standards. Biological treatment of sewage and digestion of sewage sludge resulted in the enrichment of ¹⁵N in the biosolids (δ¹⁵N values between 5.0 and 8.7‰). Such enrichment was used as a tracer to study the fate of biosolids derived N. The elevated δ¹⁵N in biosolids treated pine foliage indicated that a considerable amount N was sourced from biosolids. Analysis of δ¹⁵N in understorey plants showed that both non-legume and legume understorey plants took up N from the biosolids, and acted as a N sink, reducing N availability for leaching. Our study showed that application of biosolids to a plantation forest can significantly improve tree nutrition and site productivity without resulting in any measurable adverse effect on the receiving environment.     

Aggregation of Leslie matrix models with application to ten diverse animal species

Some grouping is necessary when constructing a Leslie matrix model because it involves discretizing a continuous process of births and deaths. The level of grouping is determined by the number of age classes and frequency of sampling. It is largely unknown what is lost or gained by using fewer age classes, and I address this question using aggregation theory. I derive an aggregator for a Leslie matrix model using weighted least squares, determine what properties an aggregated matrix inherits from the original matrix, evaluate aggregation error, and measure the influence of aggregation on asymptotic and transient behaviors. To gauge transient dynamics, I employ reactivity of the standardized Leslie matrix. I apply the aggregator to 10 Leslie models developed for animal populations drawn from a diverse set of species. Several properties are inherited by the aggregated matrix: (a) it is a Leslie matrix; (b) it is irreducible whenever the original matrix is irreducible; (c) it is primitive whenever the original matrix is primitive; and (d) its stable population growth rate and stable age distribution are consistent with those of the original matrix if the least squares weights are equal to the original stable age distribution. In the application, depending on the population modeled, when the least squares weights do not follow the stable age distribution, the stable population growth rate of the aggregated matrix may or may not be approximately consistent with that of the original matrix. Transient behavior is lost with high aggregation.     

A set of microsatellite markers for fingerprinting and breeding applications in Pinus radiata.

Fifty microsatellite markers were developed and characterized in Pinus radiata, and from among these, a subset of 10 easily scored and highly polymorphic markers was selected for use in fingerprinting, quality control, and breeding applications. The markers were characterized based on reliable and reproducible amplification, observed and expected heterozygosities, number of alleles, a low frequency of null alleles, and a lack of close linkage with other selected markers. Allele numbers and frequencies were estimated using 24 first-generation breeding clones from Australia and New Zealand. Observed heterozygosities for the selected markers were all greater than 0.67, and there was an average of 10.5 alleles/locus. The occurrence of null alleles was checked with megagametophytes from mother trees for loci that appeared to be homozygous. The 10 markers are not closely linked (r < 0.20 and LOD > 3) to each other. The selected microsatellites fall into three discrete size classes, and with appropriate selection of fluorescent dyes for 5' end labeling, can be multiplexed with up to 6 markers/sample on an ABI PRISM 310 or similar instrument.     

Evidence that creation of a Pinus radiata plantation in south-eastern Australia has reduced habitat for frogs

Loss and fragmentation of habitat resulting from the clearing of forests for agriculture and urban development threaten the persistence of thousands of species worldwide. The clearing of native forest to plant a monoculture of exotic trees may also reduce and fragment the habitat available for indigenous plants and animals. Metacommunity theory suggests that the species richness of a community in a patch of habitat will increase with patch size but decrease with patch isolation. We investigated whether replacement of native Eucalyptus forest with a plantation of Pinus radiata has reduced and fragmented habitat for frogs, leading to a lower species richness of frog communities in the pine plantation and in small and/or isolated remnant patches of native forest. We surveyed frogs at 60 sites at streams and wetlands in the pine plantation, remnant patches of native forest surrounded by pines, and adjacent areas of contiguous native forest near Tumut in New South Wales, Australia. Only two of eight species of frogs were recorded in the pine plantation, and regression modelling indicated that streams and wetlands in the pines supported fewer frog species than those in remnant patches or the intact native forest. In addition, species richness tended to be higher at wide, shallow swamps and marshes near the headwaters of streams, with herbs, grasses, shrubs, reeds, sedges and rushes in the emergent and fringing vegetation. There was little evidence to suggest that larger eucalypt remnants supported more species of frogs, or that remnants isolated by greater expanses of pines supported fewer species, but we had low power to detect these effects with our data set. Our results support the preservation of all remnants of native forest along drainage lines and around swamps, soaks and bogs, regardless of size. Where new pine plantations are established, for example, on cleared agricultural land, care should be taken to maintain the structural and vegetative characteristics of water bodies to ensure that they continue to provide suitable breeding habitat for frogs.     

Identifying environmental variables explaining genotype-by-environment interaction for body weight of rainbow trout (Onchorynchus mykiss): reaction norm and factor analytic models

Background

Identifying the relevant environmental variables that cause GxE interaction is often difficult when they cannot be experimentally manipulated. Two statistical approaches can be applied to address this question. When data on candidate environmental variables are available, GxE interaction can be quantified as a function of specific environmental variables using a reaction norm model. Alternatively, a factor analytic model can be used to identify the latent common factor that explains GxE interaction. This factor can be correlated with known environmental variables to identify those that are relevant. Previously, we reported a significant GxE interaction for body weight at harvest in rainbow trout reared on three continents. Here we explore their possible causes.

Methods

Reaction norm and factor analytic models were used to identify which environmental variables (age at harvest, water temperature, oxygen, and photoperiod) may have caused the observed GxE interaction. Data on body weight at harvest was recorded on 8976 offspring reared in various locations: (1) a breeding environment in the USA (nucleus), (2) a recirculating aquaculture system in the Freshwater Institute in West Virginia, USA, (3) a high-altitude farm in Peru, and (4) a low-water temperature farm in Germany. Akaike and Bayesian information criteria were used to compare models.

Results

The combination of days to harvest multiplied with daily temperature (Day*Degree) and photoperiod were identified by the reaction norm model as the environmental variables responsible for the GxE interaction. The latent common factor that was identified by the factor analytic model showed the highest correlation with Day*Degree. Day*Degree and photoperiod were the environmental variables that differed most between Peru and other environments. Akaike and Bayesian information criteria indicated that the factor analytical model was more parsimonious than the reaction norm model.

Conclusions

Day*Degree and photoperiod were identified as environmental variables responsible for the strong GxE interaction for body weight at harvest in rainbow trout across four environments. Both the reaction norm and the factor analytic models can help identify the environmental variables responsible for GxE interaction. A factor analytic model is preferred over a reaction norm model when limited information on differences in environmental variables between farms is available.     

Estimation of genealogical coancestry in plant species using a pedigree reconstruction algorithm and application to an oil palm breeding population

Key message

Explicit pedigree reconstruction by simulated annealing gave reliable estimates of genealogical coancestry in plant species, especially when selfing rate was lower than 0.6, using a realistic number of markers. Genealogical coancestry information is crucial in plant breeding to estimate genetic parameters and breeding values. The approach of Fernández and Toro (Mol Ecol 15:1657–1667, 2006) to estimate genealogical coancestries from molecular data through pedigree reconstruction was limited to species with separate sexes. In this study it was extended to plants, allowing hermaphroditism and monoecy, with possible selfing. Moreover, some improvements were made to take previous knowledge on the population demographic history into account. The new method was validated using simulated and real datasets. Simulations showed that accuracy of estimates was high with 30 microsatellites, with the best results obtained for selfing rates below 0.6. In these conditions, the root mean square error (RMSE) between the true and estimated genealogical coancestry was small (<0.07), although the number of ancestors was overestimated and the selfing rate could be biased. Simulations also showed that linkage disequilibrium between markers and departure from the Hardy–Weinberg equilibrium in the founder population did not affect the efficiency of the method. Real oil palm data confirmed the simulation results, with a high correlation between the true and estimated genealogical coancestry (>0.9) and a low RMSE (<0.08) using 38 markers. The method was applied to the Deli oil palm population for which pedigree data were scarce. The estimated genealogical coancestries were highly correlated (>0.9) with the molecular coancestries using 100 markers. Reconstructed pedigrees were used to estimate effective population sizes. In conclusion, this method gave reliable genealogical coancestry estimates. The strategy was implemented in the software MOLCOANC 3.0.     

Reassociation of a modified mycorrhiza with the host plant roots (Pinus radiata) and the transfer of acetylene reduction activity

Summary Experiments were carried out to assess the potential for reassociation of modified strains of the mycorrhizal fungus Rhizopogon sp., capable of acetylene reduction activity in vitro, with the roots of its host plant (Pinus radiata). Reassociation was effected and acetylene reduction assays indicated that nitrogenase activity was present in the reassociated whole plants. Those host plants symbiotic with the modified strains had higher levels of nitrogen than those associated with the wild type fungus under nitrogen deprived conditions. Uptake of phosphate was unimpaired in the modified mycorrhiza. Electron microscopy showed that hyphae of the modified strains as well as lying in the intercellular spaces were often found within the cells of the root cortex. This was in contrast with the wild type strains where no such intracellular growth was found. One strain was sound to be pathogenic to seedlings of Pinus radiata. re]19760603     

Survival of Escherichia coli and Salmonella spp. after application of sewage sludge to a Pinus radiata forest

AIMS: This study investigated the survival of Escherichia coli and Salmonella spp. in sewage sludge applied to young and old Pinus radiata forest in Spring and Autumn/Winter. METHODS AND RESULTS: Large numbers of E. coli were present in sludge applied to the forest blocks but Salmonella spp. numbers were low or nondetectable. In the mature stand in Spring, numbers of E. coli returned to back-ground after 3 weeks and die-off was significantly correlated with per cent solids of sludge. E. coli survived longer in mature and young stands in Autumn/Winter where numbers did not significantly decrease until weeks 5 and 13, respectively. Salmonella spp. was detectable in the mature stand until week 4 and in the young stand until week 11 in Autumn/Winter. CONCLUSIONS: Microbial die-off was related to desiccation of the sewage sludge, and was faster in warmer, drier conditions. SIGNIFICANCE AND IMPACT OF THE STUDY: In many countries, environmental and health risks associated with the application of sewage sludge to land are minimized by 'best management practice' guidelines, where risks are managed by restriction of public access to these sites. This study provides supporting evidence that withholding periods of greater than 6 months are sufficient to reduce microbial contaminants to background levels.     

Bayesian QTL analyses using pedigreed families of an outcrossing species,with application to fruit firmness in apple

Key message

Proof of concept of Bayesian integrated QTL analyses across pedigree-related families from breeding programs of an outbreeding species. Results include QTL confidence intervals, individuals’ genotype probabilities and genomic breeding values.

Abstract

Bayesian QTL linkage mapping approaches offer the flexibility to study multiple full sib families with known pedigrees simultaneously. Such a joint analysis increases the probability of detecting these quantitative trait loci (QTL) and provide insight of the magnitude of QTL across different genetic backgrounds. Here, we present an improved Bayesian multi-QTL pedigree-based approach on an outcrossing species using progenies with different (complex) genetic relationships. Different modeling assumptions were studied in the QTL analyses, i.e., the a priori expected number of QTL varied and polygenic effects were considered. The inferences include number of QTL, additive QTL effect sizes and supporting credible intervals, posterior probabilities of QTL genotypes for all individuals in the dataset, and QTL-based as well as genome-wide breeding values. All these features have been implemented in the FlexQTL^? software. We analyzed fruit firmness in a large apple dataset that comprised 1,347 individuals forming 27 full sib families and their known ancestral pedigrees, with genotypes for 87 SSR markers on 17 chromosomes. We report strong or positive evidence for 14 QTL for fruit firmness on eight chromosomes, validating our approach as several of these QTL were reported previously, though dispersed over a series of studies based on single mapping populations. Interpretation of linked QTL was possible via individuals’ QTL genotypes. The correlation between the genomic breeding values and phenotypes was on average 90 %, but varied with the number of detected QTL in a family. The detailed posterior knowledge on QTL of potential parents is critical for the efficiency of marker-assisted breeding.     

Single-parent segregant pools for allocation of markers to a specified chromosomal region in outcrossing species

Bulked co-segregant analysis is a method of rapidly allocating unmapped genetic markers to a specific chromosomal region. Although originally developed for utilization in populations derived from crosses between fully inbred lines, it has been proposed that co-segregant pools could also serve the same purpose in outbreeding populations, if individuals from only a single large family are pooled. Large, fully mapped, single-sire backcross and half-sib families are presently available as part of the international chicken and bovine reference family panels respectively. In this study, power and tests of significance for single-parent co-segregant analysis are derived for full-sib, single-parent back-cross and single-parent half-sib families, as a function of proportion of recombination between index marker and linked marker, proportion of single-parent alleles among the mates, number of individuals in each segregant pool and technical error variance. Power was found to be greater than 0–80 for many reasonable parameter combinations. The method is illustrated using microsatellite markers and a large single-sire bovine family, part of the international bovine reference family panel.     

Estimation of outcrossing rate in a breeding population of Eucalyptus urophylla with dominant RAPD and AFLP markers

 Eucalyptus breeding is typically conducted by selection in open-pollinated progenies. As mating is controlled only on the female side of the cross, knowledge of outcrossing versus selfing rates is essential for maintaining adequate levels of genetic variability for continuous gains. Outcrossing rate in an open-pollinated breeding population of Eucalyptus urophylla was estimated by two PCR-based dominant marker technologies, RAPD and AFLP, using 11 open-pollinated progeny arrays of 24 individuals. Estimated outcrossing rates indicate predominant outcrossing and suggest maintenance of adequate genetic variability within families. The multilcous outcrossing rate (t_m) estimated from RAPD markers (0.93±0.027), although in the same range, was higher (α>0.01) than the estimate based on AFLP (0.89±0.033). Both estimates were of similar magnitude to those estimated for natural populations using isozymes. The estimated Wright’s fixation index was lower than expected based on t_m possibly resulting from selection against selfed seedlings when sampling plants for the study. An empirical analysis suggests that 18 is the minimum number of dominant marker loci necessary to achieve robust estimates of t_m. This study demonstrates the usefulness of dominant markers, both RAPD and AFLP, for estimating the outcrossing rate in breeding and natural populations of forest trees. We anticipate an increasing use of such PCR-based technologies in mating-system studies, in view of their high throughput and universality of the reagents, particularly for species where isozyme systems have not yet been optimized. Received: 25 March 1997 / Accepted: 13 May 1997     

Enhancing a regional vegetation map with predictive models of dominant plant species in chaparral

Abstract. Data from more than 900 vegetation plots surveyed in the evergreen shrublands of southern California were used to develop predictions of the distributions of eight dominant shrub species for a 3880 km² region. The predictions, based on classification tree (CT) models, were validated using independent field data collected during a vegetation survey conducted in the 1930s. Presence and absence were correctly predicted an average of 75% of the time for the eight species. At the same time, these models minimized false positives, so that presence was predicted in the correct proportion of the cases for most species. The areal proportion of the landscape on which the species were predicted to occur was in the same rank order, and of the same magnitude, as their frequency (proportion of plots in which they occurred) within the field data sets. Predictive maps of species presence were overlaid and combined with an existing regional vegetation map. The shrub species ‘assemblages’ that resulted from this procedure had analogs with vegetation series defined using field data in previous studies. The resulting multiple species map will be used in a landscape simulation model of fire disturbance and succession.     

Marked reduction in demographic rates and reduced fitness advantage for early breeding is not linked to reduced thermal matching of breeding time

Warmer springs may cause animals to become mistimed if advances of spring timing, including available resources and of timing of breeding occur at different speed. We used thermal sums (cumulative sum of degree days) during spring to describe the thermal progression (timing) of spring and investigate its relationship to breeding phenology and demography of a long‐distant migrant bird, the northern wheatear (Oenanthe oenanthe L.). We first compare 20‐year trends in spring timing, breeding time, selection for breeding time, and annual demographic rates. We then explicitly test whether annual variation in selection for breeding time and demographic rates associates with the degree of phenological matching between breeding time and thermal progression of spring. Both thermal progression of spring and breeding time of wheatears advanced in time during the study period. But despite breeding on average 7 days earlier with respect to date, wheatears bred about 4 days later with respect to thermal spring progression. Over the same time period, selection for breeding time changed from distinct within‐season advantage of breeding early to no or very weak advantage. Furthermore, demographic rates (nest success, fledgling production, recruitment, adult survival) and nestling weight declined markedly by 16%–79%. Those temporal trends suggest that a reduced degree of phenological matching may affect within‐season fitness advantage of early breeding and population demographic rates. In contrast, when we investigate links based on annual variation, we find no significant relationship between either demographic rates or fitness advantage of early breeding with annual variation in the degree of phenological matching. Our results show that corresponding temporal trends in phenological matching, selection for breeding time and demographic rates are inconclusive evidence for demographic effects of changed phenological matching. Instead, we suggest that the trends in selection for breeding time and demographic rates are due to a general deterioration of the breeding environment.     

Experimental evaluation of realized niche models for predicting responses of plant species to a change in environmental conditions

Abstract. We estimated, using logistic regression techniques, the realized niches of the four dominant species in an experimental marsh complex located in the Delta Marsh, Manitoba, Canada. These models were then used to predict the probability of occurrence of these species in selected elevation ranges when water levels were raised in 1985 either 0, 30 or 60 cm above the long-term normal water level. These realized-niche models were calculated using elevation and species data collected in 1980. After having been eliminated by two years of deep flooding, the emergent vegetation in this complex had been re-established during a drawdown beginning in either 1983 or 1984. Our hypothesis was that from 1985 to 1989 the frequencies of occurrence of species in selected elevation ranges would converge to their probabilities predicted from the 1980 logistic models. This was not borne out by our results. Actual frequencies and predicted probabilities of occurrence of a species were similar at best less than 40% and then mostly in the control (0 cm) treatment. The realized-niche models were not adequate to predict the distribution of emergents after an increase in water level in the short term because the emergent species did not migrate upslope. Emergent species in the medium and high treatments either (1) died out - Scolochloa festucacea and Scirpus lacustris - after 3 yr because they could not survive permanent flooding, (2) stayed where they were - Phragmites australis - because they were unable to move upslope through clonal growth, or (3) became more widespread - Typha glauca only because of the expansion of small local populations already established in 1985 in areas dominated formerly by other species.     

Selection for yield and yield components in the early generations of a potato breeding programme

Summary A number of unselected potato (Solanum tuberosum L.) clones were grown at two locations (a seed site and a ware site) in three consecutive years. The repeatability of total yield and yield components in the first two clonal years was compared with the same characters recorded in the third clonal year. Selection for yield in the first clonal year was only marginally more effective than a random reduction in number of genotypes, while selection in the second clonal year appeared to be somewhat more effective as judged by performance in the third clonal year. The inefficiency of selection in the first clonal year was ascribed, at least in part, to the inaccuracy of yield assessment as well as the carry-over effect of the mother tubers. Correlations of total yield were higher between different years in the same location than between different locations. Selection under growing conditions suitable for production of seed tubers tended to result in selection of early maturing clones which would not necessarily be optimal for ware growing conditions.     

Response of transpiration and photosynthesis to a transient change in illuminated foliage area for a Pinus radiata D. Don tree

Sudden but transient changes in the fraction or illuminated foliage area in a well-watered 7-year-old Pinus radiata D. Don tree were imposed by completely covering either the upper 22% or the lower 78% of the foliage for periods of up to 36 h. Measurements of transpiration flux density (E), tree conductance (g_t), stomatal conductance (g_s) and net photosynthesis (A) were made to test the hypothesis that compensatory responses would occur in the remaining illuminated foliage when the cover was installed. When the lower foliage was covered there was an immediate decrease in g_t. However, when tree conductance was normalized with respect to the illuminated leaf area (g_t'), it increased between 50 and 75%, depending on the value of air saturation deficit (D). The effect was also apparent from concurrent measurements of increases in g_s and A up to 59 and 24%, respectively, for needles in the top third of (he crown. When the cover was removed these effects were reversed. The changes in the lower foliage when the upper foliage was covered were much smaller. Changes in bulk needle water potential were small. It is suggested that the observed responses occurred because of a perturbation to the hydraulic pathway in the xylem that could have triggered the action of a chemical signal to regulate stomatal conductance and photosynthesis.