Minimax Estimation of Nonregular Parameters and Discontinuity in Minimax Risk

When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic minimax estimation theory for a parameter that is a nondifferentiable transform of a regular parameter, where the nondifferentiable transform is a composite map of a continuous piecewise linear map with a single kink point and a translation-scale equivariant map. The contribution of this paper is two fold. First, this paper extends the local asymptotic minimax theory to nondifferentiable transforms that are a composite map of a Lipschitz continuous map having a finite set of nondifferentiability points and a translation-scale equivariant map. Second, this paper investigates the discontinuity of the local asymptotic minimax risk in the true probability and shows that the proposed estimator remains to be optimal even when the risk is locally robustified not only over the scores at the true probability, but also over the true probability itself. However, the local robustification does not resolve the issue of discontinuity in the local asymptotic minimax risk

When virulence originates from non-agricultural hosts: New insights into plant breeding

Monogenic plant resistance breakdown is a model for testing evolution in action in pathogens. As a rule, plant pathologists argue that virulence – the allele that allows pathogens to overcome resistance – is due to a new mutation at the avirulence locus within the native/endemic population that infects susceptible crops. In this article, we develop an alternative and neglected scenario where a given virulence pre-exists in a non-agricultural host and might be accidentally released or introduced on the matching resistant cultivar in the field. The main difference between the two scenarios is the divergence time expected between the avirulent and the virulent populations. As a consequence, population genetic approaches such as genome scans and Approximate Bayesian Computation methods allow explicit testing of the two scenarios by timing the divergence. This review then explores the fundamental implications of this alternative scenario for plant breeding, including the invasion of virulence or the evolution of more aggressive hybrids, and proposes concrete solutions to achieve a sustainable resistance

Magic traits drive the emergence of pathogens

An important branch of evolutionary biology strives to understand how divergent selection for an ecologically important trait can foster the emergence of new species specialized on different niches. Such ecological speciation is usually difficult to achieve because recombination between different subsets of a population that are adapting to different environments counteracts selection for locally adapted gene combinations. Traits pleiotropically controlling adaptation to different environments and reproductive isolation are therefore the most favourable for ecological speciation, and are thus called “magic traits”. We used genetic markers and cross-inoculations to show that pathogenicity-related loci are responsible for both host adaptation and reproductive isolation in emerging populations of Venturia inaequalis, the fungus causing apple scab disease. Because the fungus mates within its host and because the pathogenicity-related loci prevent infection of the non-host trees, host adaptation pleiotropically maintains genetic differentiation and adaptive allelic combinations between sympatric populations specific to different apple varieties. Such “magic traits” are likely frequent in fungal pathogens, and likely drive the emergence of new diseases.

The genetic structure of a Venturia inaequalis population in a heterogeneous host population composed of different Malus species

Adaptation, which induces differentiation between populations in relation to environmental conditions, can initiate divergence. The balance between gene flow and selection determines the maintenance of such a structure in sympatry. Studying these two antagonistic forces in plant pathogens is made possible because of the high ability of pathogens to disperse and of the strong selective pressures exerted by their hosts. In this article, we analysed the genetic structure of the population of the apple scab fungus, Venturia inaequalis, in a heterogeneous environment composed of various Malus species. Inferences were drawn from microsatellite and AFLP data obtained from 114 strains sampled in a single orchard on nine different Malus species to determine the forces that shape the genetic structure of the pathogen

Host-specific differentiation among populations of Venturia inaequalis causing scab on apple, pyracantha and loquat

Patterns of multilocus DNA sequence variation within and between closely related taxa can provide insights into the history of divergence. Here, we report on DNA polymorphism and divergence at six nuclear loci in globally distributed samples of the ascomycete Venturia inaequalis, responsible for scab on apple, loquat, and pyracantha. Isolates from different hosts were differentiated but did not form diagnosable distinct phylogenetic species. Parameters of an Isolation-with-Migration model estimated from the data suggested that the large amount of variation shared among groups more likely resulted from recent splitting than from extensive genetic exchanges. Inferred levels of gene flow among groups were low and more concentrated toward recent times, and we identified two potentially recent one-off shifters from apple and pyracantha to loquat. These findings support a scenario of recent divergence in allopatry followed by introgression through secondary contact, with groups from loquat and pyracantha being the most recently differentiated

Differential selection pressures exerted by host resistance quantitative trait loci on a pathogen population: a case study in an apple × Venturia inaequalis pathosystem

Understanding how pathogens evolve according to pressures exerted by their plant hosts is essential for the derivation of strategies aimed at the durable management of resistant cultivars. The spectrum of action of the resistance factors in the partially resistant cultivars is thought to be an important determinant of resistance durability. However, it has not yet been demonstrated whether the pressures exerted by quantitative resistance are different according to their spectrum of action.To investigate selection pressures exerted by apple genotypes harbouring various resistance quantitative trait loci (QTLs) on a mixed inoculum of the scab disease agent, Venturia inaequalis, we monitored V. inaequalis isolate proportions on diseased apple leaves of an F1 progeny using quantitative pyrosequencing technology and QTL mapping. Broad-spectrum resistances did not exert any differential selection pressures on the mixed inoculum, whereas narrow-spectrum resistances decreased the frequencies of some isolates in the mixture relative to the susceptible host genotypes. Our results suggest that the management of resistant cultivars should be different according to the spectrum of action of their resistance factors. The pyramiding of broad-spectrum factors or the use of a mixture of apple genotypes that carry narrow-spectrum resistance factors are two possible strategies for the minimization of resistance erosion