A Comparative Study on the Power of van Lieshout and Baddeley's J-Function

Summary functions such as the empty space function F and the nearest neighbour distance distribution function G are often used as test statistics for point patterns. Van Lieshout and Baddeley recently proposed an alternative statistic, the J-function, which is defined as J = (1 — G)/(1 — F). Theoretical advantages of the J-function over the F- and G-statistics are that it measures the type, strength and range of interaction, and that it can be evaluated explicitly for a larger class of models. In this simulation study we investigate empirically how the power of tests based on J compares to that of tests based on F and G.     

Without quality presence–absence data,discrimination metrics such as TSS can be misleading measures of model performance

The discriminating capacity (i.e. ability to correctly classify presences and absences) of species distribution models (SDMs) is commonly evaluated with metrics such as the area under the receiving operating characteristic curve (AUC), the Kappa statistic and the true skill statistic (TSS). AUC and Kappa have been repeatedly criticized, but TSS has fared relatively well since its introduction, mainly because it has been considered as independent of prevalence. In addition, discrimination metrics have been contested because they should be calculated on presence–absence data, but are often used on presence‐only or presence‐background data. Here, we investigate TSS and an alternative set of metrics—similarity indices, also known as F‐measures. We first show that even in ideal conditions (i.e. perfectly random presence–absence sampling), TSS can be misleading because of its dependence on prevalence, whereas similarity/F‐measures provide adequate estimations of model discrimination capacity. Second, we show that in real‐world situations where sample prevalence is different from true species prevalence (i.e. biased sampling or presence‐pseudoabsence), no discrimination capacity metric provides adequate estimation of model discrimination capacity, including metrics specifically designed for modelling with presence‐pseudoabsence data. Our conclusions are twofold. First, they unequivocally impel SDM users to understand the potential shortcomings of discrimination metrics when quality presence–absence data are lacking, and we recommend obtaining such data. Second, in the specific case of virtual species, which are increasingly used to develop and test SDM methodologies, we strongly recommend the use of similarity/F‐measures, which were not biased by prevalence, contrary to TSS.     

A Beta-mixture model for assessing genetic population structure

Summary An important fraction of recently generated molecular data is dominant markers. They contain substantial information about genetic variation but dominance makes it impossible to apply standard techniques to calculate measures of genetic differentiation, such as F‐statistics. In this article, we propose a new Bayesian beta‐mixture model that more accurately describes the genetic structure from dominant markers and estimates multiple F_ST s from the sample. The model also has important application for codominant markers and single‐nucleotide polymorphism (SNP) data. The number of F_ST is assumed unknown beforehand and follows a random distribution. The reversible jump algorithm is used to estimate the unknown number of multiple F_ST s. We evaluate the performance of three split proposals and the overall performance of the proposed model based on simulated dominant marker data. The model could reliably identify and estimate a spectrum of degrees of genetic differentiation present in multiple loci. The estimates of F_ST s also incorporate uncertainty about the magnitude of within‐population inbreeding coefficient. We illustrate the method with two examples, one using dominant marker data from a rare orchid and the other using codominant marker data from human populations.     

What is genetic differentiation,and how should we measure it—GST,D, neither or both?

Estimates of the fixation index, F_ST, have been used as measures of population differentiation for many decades. However, there have been persistent voices in the literature suggesting that these statistics do not measure true differentiation. In particular, the statistics Nei's G_ST and Wier and Cockerham's θ have been criticized for being ‘constrained’ to not equal one in some situations that seem to represent maximal differentiation. Here, we address the issue of how to evaluate exactly how much information a particular statistic contains about the process of differentiation. This criterion can be used to counter most concerns about the performance of G_ST (and related statistics), while also being reconciled with the insights of those who have proposed alternative measures of differentiation. In particular, the likelihood‐based framework that we put forward can justify the use of G_ST as an effective measure of differentiation, but also shows that in some situations G_ST is insufficient on its own and needs supplementing by another measure such as Jost's D or Hedrick's G′_ST. This approach will become increasingly important in the future, as greater emphasis is placed on analysing large data sets.     

The selection of parents for synthetic varieties of outbreeding diploid crops

Summary As a criterion for the selection from a population of individuals with a high potential as parents of synthetic varieties, the general varietal ability of an individual is defined as the mean expression of all possible synthetics of a given size(s) having this plant as a common parent. Using known expressions for the prediction of the performance of advanced generations of diploid synthetic varieties, general varietal ability is expressed in terms of the F ₁ and I ₁ progenies of the plants under test, and is found to be a simple function of the polycross (g.c.a.) and inbred progeny means, where the contribution of the inbred progeny varies according to n and s. The implications and use of such a progeny test in the breeding of out-pollinating crops is discussed.     

Autofertility and rate of cross-fertilization: crucial characters for breeding synthetic varieties in faba beans (Vicia faba L.)

Summary To increase the level and stability of yield in faba beans (Vicia faba L.), heterosis must be exploited. Hybrids are not available because of the instability of male sterility. Synthetic varieties can and should be bred. Thus, we studied the reproductive behavior of this partially allogamous, insect-pollinated crop. Autofertility (AF) and the rate of cross-fertilization (C) were measured in 36 inbred lines and 28 crosses in F₁, F₂, and F₃ generations for 3 years at Hohenheim, Stuttgart, FRG. Heterozygosity strongly increased AF and decreased C. AF was negatively correlated with C. AF varied from 1% to 98%, and C varied from 7% to 82%. Heritability for both characters was high. For an optimum exploitation of heterosis, breeders should utilize lines with high C as variety components. It is often labor-intensive to multiply such lines, due to low AF. Hence, breeders tend to use autofertile lines with rather limited C. We showed that even in this case about 50% of the total heterosis, which equals a yield increase of at least 25% over the inbred line level, is realized. An increase in yield stability due to heterogeneity will occur simultaneously.     

An assessment of the production and performance of F1 hybrid wheats based on Triticum timopheevi cytoplasm

Summary This work reports on the production and yield assessment of F₁ wheat hybrids from crosses between cytoplasmic male sterile lines, with Triticum timopheevi cytoplasm, and cultivars with fertility restoring genes.In four years of trials conducted between 1974 and 1977, only three F₁ hybrids out of a total of 168 yielded significantly more than the control variety Maris Huntsman, which currently occupies a substantial proportion of the area planted with winter wheat in the UK. Because of the rapid increase in yield of conventional wheat varieties, which has already led to varieties which outyielded Maris Huntsman, the yield advantage of these F₁ hybrids is insufficient for them to be developed as commercial varieties.The efficient production of uncontaminated male sterile and F₁ seed presents problems of isolation and a difficult biological problem in increasing the cross breeding potential of maintainer and restorer lines. These together with selection for other parental characters such as restoration, short straw and resistance to sprouting make the development of F₁ hybrids more difficult and expensive than that of conventional varieties.     

A clever solution to a vexing problem

F_ST (as well as related measures such as G_ST) has long been used both as a measure of the relative amount of genetic variation between populations and as an indicator of the amount of gene flow among populations. Unfortunately, F_ST and its clones are also sensitive to mutation, particularly when the mutation rate per locus is greater than the migration rate among populations. Relatively high mutation rates cause estimates of F_ST and G_ST to be much lower than researchers sometimes expect, when migration rates are low in the studied species. Several recent suggestions for dealing with this problem have been unsatisfactory for one reason or another, and no general solution exists (if we are not to abandon these otherwise useful measures of differentiation). In an important article in this issue, Jinliang Wang (2015) shows that it is possible to identify whether the genetic markers in a given study are likely to give estimates of F_ST that are strongly affected by mutation. The proposed test is simple and elegant, and with it, molecular ecologists can determine whether the F_ST from their makers can be depended on for further inference about their species’ genome and the demographic forces which shaped its patterns.     

Divergence before the host shift? Prezygotic reproductive isolation among three varieties of a specialist fly on a single host plant

1. Although divergence via host‐plant shifting is a common theme in the speciation of some phytophagous insects, it is not clear whether host shifts are typically initiators of speciation or if they instead contribute to divergence events already in progress. While host shifts appear to be generally associated with speciation events for flies in the genus Strauzia, three sympatric varieties of the sunflower fly [Strauzia longipennis (Wiedemann)] co‐occur on the same host plant in the Midwestern United States and may have evolved reproductive barriers without a host shift. 2. The strength of two prezygotic reproductive barriers was compared among the three S. longipennis varieties: one barrier that is often associated with divergent ecological selection (allochronic isolation), and another that is more likely to be independent of ecological selection (pre‐copulatory sexual isolation). The presence and relative strength of each barrier between fly varieties were evaluated using microsatellites, no choice mating experiments, studies of allochronic isolation, and field collection data. 3. Evidence for both allochronic isolation and pre‐copulatory sexual isolation was detected between the three varieties of S. longipennis. The measure of isolation calculated for each barrier between the three varieties was lower than measures calculated between different species of Strauzia found on different hosts, suggesting that subsequent host shifts may increase the degree of reproductive isolation. For Strauzia and other specialist insects, some reproductive isolation may evolve prior to, and indeed may facilitate, host shifts.     

“Ecological Armageddon” – more evidence for the drastic decline in insect numbers

The efficient use of nitrogen by crops can minimise environmental risks and maximise returns to farmers. Under organic farming systems, this can be achieved by adjusting the fertilisation management and/or using genetic variability. Seven durum wheat (Triticum durum) cultivars and three emmer (Triticum dicoccum) cultivars were assessed under an organic farming system over a non‐consecutive 4‐year period (2005–11) in Foggia (southern Italy). The objectives were to investigate the agronomic and qualitative characteristics, and to evaluate the agronomic efficiency and adaptability according to three N fertilisation levels (0, 40, 80 kg N ha^?1). A split‐plot design was used, with three replications in each year. Nine traits were investigated: heading time, plant height, seed yield, number of spikes m^?2, harvest index, specific weight, 1000‐seed weight, and protein and gluten contents. Increasing N to 80 kg ha^?1 increased plant height (+7.3%), seed yield (+22.1%), spike density (+16.6%), and protein (+9.8%) and gluten (+2.1%) contents. The emmer genotypes and the oldest durum wheat ‘Cappelli’ showed the highest protein and gluten contents (mean, 13.9%, 11.2%, respectively). The maximum N agronomic efficiency [AE(N)] and N recovery efficiency [RE(N)] were seen for the modern durum wheat cultivars under 40 kg ha^?1 N treatment: ‘Duilio’, ‘Iride’ and ‘Varano’. The significant correlation between AE(N) and RE(N) and the year of release of the durum wheat cultivars (r = 0.53, P < 0.05, F = 4.7 for AE(N) and r = 0.57, P < 0.01, F = 5.7 for RE(N), respectively; n = 14) showed that the genetic breeding of this species for high grain yield is associated with an increase in the efficiency of N fertiliser use under organic farming. The highly significant effect for the Genotype × Environment interaction (F = 18.1, P < 0.001) of seed yield indicate the possibility to select for stable genotypes across environments. Based on the additive main effects and multiplicative interaction analysis, and the yield stability index, the varieties ‘Iride’ and ‘Varano’ show high‐stability responses and good seed yields under all N fertiliser treatments. Therefore, these varieties can be recommended for organic farming systems in Mediterranean areas.     

Identification of RAPD markers linked to the ps gene and their usefulness for purity determination of breeding lines and F1 tomato hybrids

The functional male sterility controlled by ps gene proved to be a useful tool in hybrid tomato varieties breeding in Poland. The climat conditions such as excessive temperature and high humidity have a bad effect on the expression and stability of functional male sterility. Using the RAPD methods we have identified two RAPD markers linked to the ps gene. The markers OPW 13₁₂₃₀ and OPAX 10₇₈₀ were generated by 5′CACAGCGACA 3′ and 5′CCAGGCTGAC 3′ decamers respectively in F₂ population of combination 24/29 × G-1.     

Diversity in commercial varieties and landraces of black eggplants and implications for broadening the breeders' gene pool

Black‐coloured eggplants (Solanum melongena) represent the commercially most important group of eggplants in Europe and North America. Most of the modern varieties of black eggplants correspond to F₁ hybrids, which at the same time constitute an elite gene pool for the development of new varieties. However, there are many black landraces and old varieties, which could be useful as sources of variation for black eggplant breeding programmes as well as for the broadening of the genetic diversity of the breeders’ gene pool. We have studied the morphological and molecular [amplified fragment length polymorphism and simple sequence repeat (SSR)] diversity in a collection of 38 black eggplant accessions, including commercial (modern F₁ hybrid and old nonhybrid) varieties and landraces as well as in six nonblack control eggplants, from different origins. The results show that black eggplants contain a considerable morphological and molecular diversity, but commercial varieties, and in particular F₁ hybrids, display a reduced morphological and molecular diversity when compared with landraces. The principal components analysis morphological and principal coordinates analysis molecular analyses show that commercial F₁ hybrids group together, indicating that they share a common and narrow gene pool. Commercial F₁ hybrids present a series of productive advantages, like early production, intense black colour (low L*, a* and b*) values and absence of fruit calyx prickles. However, several of the landraces and old nonhybrid varieties studied present a high yield as well as other traits of interest for eggplant breeding. Furthermore, given the low genetic diversity of F₁ hybrids and the moderate level of SSR heterozygosity found in these materials (0.382), introduction of black landraces and old varieties in the present breeding programmes could contribute to broadening the gene pool used by breeders and this could help increase the heterosis for yield of F₁ hybrids, which is greatly favoured by high heterozygosity levels.     

Microsatellite variation of cassava (<Emphasis Type="Italic">Manihot esculenta</Emphasis> Crantz) in home gardens of Chibchan Amerindians from Costa Rica

We used 13 microsatellite marker loci to determine the genetic diversity of cassava (Manihot esculenta Crantz) grown in home gardens in two Chibchan Amerindian reserves in Costa Rica. We compared the levels of genetic diversity in the reserves with that of commercial varieties typically cultivated in Costa Rica. We found high levels of genetic diversity among cassava plants. Overall, 12 of the 13 loci examined were polymorphic in each Amerindian reserve (P = 92.3). Moreover, we found 36 alleles in the Coto Brus Reserve and 33 in the Talamanca Reserve. In the commercial varieties only nine loci were polymorphic (P = 69.2), and we only found 23 alleles. Heterozygosity was high for all groups of cassava (Coto Brus, Talamanca, and commercial varieties), but it was higher among the commercial varieties. The levels of heterozygosity and allele diversity indicate that there is significant genetic diversity in the home gardens that we examined. Another indication of the high diversity found in these gardens is the number of distinct multilocus genotypes, 28 at Coto Brus and 19 at Talamanca. There was also more than one distinct multilocus genotype found within the commercial varieties, as three were found in Valencia and four in Manyi. Our data also revealed low levels of genetic differentiation between the three groups of cassava (F_st = 0.03), and Nei’s genetic distances ranged from 0.0167 to 0.0343. In addition, F estimates (F_is and F_it) indicate excess heterozygotes, both at the subpopulation and the population level. A hierarchical analysis of the genetic variation revealed that variation between sampling locations within each of the three groups of cassava was larger than that between groups (Theta S = 0.0775 and Theta P = 0.0204, respectively). The variety Manyi was the group genetically most distant from all others. We discuss the consequences of these findings for in situ conservation of genetic resources.     

Relative performance of Bayesian clustering software for inferring population substructure and individual assignment at low levels of population differentiation

Traditional methods for characterizing genetic differentiation among populations rely on a priori grouping of individuals. Bayesian clustering methods avoid this limitation by using linkage and Hardy–Weinberg disequilibrium to decompose a sample of individuals into genetically distinct groups. There are several software programs available for Bayesian clustering analyses, all of which describe a decrease in the ability to detect distinct clusters as levels of genetic differentiation among populations decrease. However, no study has yet compared the performance of such methods at low levels of population differentiation, which may be common in species where populations have experienced recent separation or high levels of gene flow. We used simulated data to evaluate the performance of three Bayesian clustering software programs, PARTITION, STRUCTURE, and BAPS, at levels of population differentiation below F _ST=0.1. PARTITION was unable to correctly identify the number of subpopulations until levels of F _ST reached around 0.09. Both STRUCTURE and BAPS performed very well at low levels of population differentiation, and were able to correctly identify the number of subpopulations at F _ST around 0.03. The average proportion of an individual’s genome assigned to its true population of origin increased with increasing F _ST for both programs, reaching over 92% at an F _ST of 0.05. The average number of misassignments (assignments to the incorrect subpopulation) continued to decrease as F _ST increased, and when F _ST was 0.05, fewer than 3% of individuals were misassigned using either program. Both STRUCTURE and BAPS worked extremely well for inferring the number of clusters when clusters were not well-differentiated (F _ST=0.02–0.03), but our results suggest that F _ST must be at least 0.05 to reach an assignment accuracy of greater than 97%.     

MAXIMUM-LIKELIHOOD ESTIMATION OF POPULATION DIVERGENCE TIMES AND POPULATION PHYLOGENY IN MODELS WITHOUT MUTATION

In this paper we present a method for estimating population divergence times by maximum likelihood in models without mutation. The maximum-likelihood estimator is compared to a commonly applied estimator based on Wright's F_ST statistic. Simulations suggest that the maximum-likelihood estimator is less biased and has a lower variance than the F_ST-based estimator. The maximum-likelihood estimator provides a statistical framework for the analysis of population history given genetic data. We demonstrate how maximum-likelihood estimates of the branching pattern of divergence of multiple populations may be obtained. We also describe how the method may be applied to test hypotheses such as whether populations have maintained equal population sizes. We illustrate the method by applying it to two previously published sets of human restriction fragment length polymorphism (RFLP) data.     

Population genetic studies of the crown-of-thorns starfish,Acanthaster planci (L.), in the Great Barrier Reef region

Seven populations of the crown-of-thorns starfish, Acanthaster planci, were compared genetically using starch gel electrophoresis in order to investigate the extent of genetic exchange throughout the Great Barrier Reef (GBR) region. These populations extended from Lizard Island in the north to One Tree Island in the south, a distance of approximately 1300 km. Thirteen of 36 enzymes assayed were genetically interpretable, and 10 (77%) of these were polymorphic. Mean heterozygosity over all loci was 0.225. An analysis of the gene frequency heterogeneity between the populations using Wright's F _ST statistic gave an overall F _ST of 0.019. The mean unbiased value of Nei's genetic distance between the populations was 0.009. These values indicate a homogeneous genetic composition throughout the range, and are consistent with the hypothesis that gene flow between these populations is high, and that A. planci throughout the GBR region are members of a single, effectively panmictic population. Within this group, the Green Island population was most distinct genetically because of differences in allele frequencies at the MDH-1 locus. Although there is no rigorous method for determining the selective basis for such differences, it is argued that the differences observed in the Green Island population were the result of selection. The basis for selective differences was possibly food availability since, at the time of sampling, the Green Island A. planci were the remnants of a large, high-density population that caused extensive coral mortality, and suffered severe population decline as food became scarce. These findings are consistent with observations of a relatively ordered sequence of outbreaks from north to south along the GBR, suggesting that all outbreaks but the first are secondary. Control measures, both on the GBR and elsewhere, have been unsuccessful except on a very small scale. Unless a vulnerable part of the A. planci life cycle can be identified, it would seem that the greatest chance for successful control would be to identify and control the causes of the primary population outbreak.     

Implication of correlations among some common stability statistics — a Monte Carlo simulations

Stability analysis of multilocation trials is often based on a mixed two-way model. Two stability measures in frequent use are the environmental variance (S _i ² )and the ecovalence (W _i). Under the two-way model the rank orders of the expected values of these two statistics are identical for a given set of genotypes. By contrast, empirical rank correlations among these measures are consistently low. This suggests that the two-way mixed model may not be appropriate for describing real data. To check this hypothesis, a Monte Carlo simulation was conducted. It revealed that the low empirical rank correlation amongS _i ² and W _i is most likely due to sampling errors. It is concluded that the observed low rank correlation does not invalidate the two-way model. The paper also discusses tests for homogeneity of S _i ² as well as implications of the two-way model for the classification of stability statistics.     

How to assess the prediction accuracy of species presence–absence models without absence data?

It is very common that only presence data are available in ecological niche modeling. However, most existing methods for evaluating the accuracy of presence–absence (binary) predictions of species require presence–absence data. The aim of this study is to present a new method for accuracy assessment that does not rely on absence data. Two new statistics F_pb and F_cpb were derived based on presence–background data. With generated six virtual species, we used DOMAIN, generalized linear modeling (GLM), and maximum entropy (MAXENT) to produce different species presence–absence predictions. To investigate the effectiveness of the new statistics in accuracy assessment, we used F_pb, F_cpb, the traditional F‐measure (F), kappa coefficient, true skill statistic (TSS), area under the receiver operating characteristic curve (AUC), and the contrast validation index (CVI) to evaluate the accuracy of predictions, and the behaviors of these accuracy measures were compared. The effectiveness of F_pb for threshold selection and estimation of species prevalence was also investigated. Experimental results show that F_cpb is an estimate of F. The Pearson's correlation coefficient (COR) between F_cpb and F is 0.9882, with a root‐mean‐square error (RMSE) of 0.0171. In general, F_pb, F_cpb, F, kappa coefficient, TSS, and CVI can sort models by the accuracy of binary prediction, but AUC is not appropriate to evaluate the accuracy of binary prediction. For DOMAIN, GLM, and MAXENT, finding the threshold by maximizing F_pb and by maximizing F result in similar accuracies. In addition, the estimation of species prevalence based on binary output with maximizing F_pb as the thresholding method is significantly more accurate than simply averaging the original continuous output. The best estimate of prevalence is provided by the binary output of MAXENT, with an RMSE of 0.0116. Finally, we conclude that the new method is promising in accuracy assessment, threshold selection, and estimation of species prevalence, all of which are important but challenging problems with presence‐only data. Because it does not require absence data, the new method will have important applications in ecological niche modeling.