The Martian interaction with the solar wind leads to the formation of a bow shock upstream of the planet. The shock dynamics appear complex, due to the combined influence of external and internal drivers. The extreme ultraviolet fluxes and magnetosonic Mach number are known major drivers of the shock location, while the influence of other possible drivers is less constrained or unknown such as crustal magnetic fields, solar wind dynamic pressure, or the Interplanetary Magnetic Field (IMF) intensity, and orientation. In this study, we compare the influence of the main drivers of the Martian shock location, based on several methods and published datasets from Mars Express (MEX) and Mars Atmosphere Volatile EvolutioN (MAVEN) missions. We include here the influence of the crustal fields, extreme ultraviolet fluxes, solar wind dynamic pressure, as well as (for MAVEN, thanks to magnetic field measurements) magnetosonic Mach number and Interplanetary Magnetic Field parameters (intensity and orientation angles). The bias due to the cross‐correlations among the possible drivers is investigated with a partial correlations analysis. Several model selection methods (Akaike Information Criterion and Least Absolute Shrinkage Selection Operator regression) are also used to rank the relative importance of the physical parameters. We conclude that the major drivers of the shock location are extreme ultraviolet fluxes and magnetosonic Mach number, while crustal fields and solar wind dynamic pressure are secondary drivers at a similar level. The IMF orientation also plays a significant role, with larger distances for perpendicular shocks rather than parallel shocks.

Let Y be a Gaussian vector of R n of mean s and diagonal covariance matrix Γ. Our aim is to estimate both s and the entries σ i = Γ i,i , for i = 1, . . . , n, on the basis of the observation of two independent copies of Y . Our approach is free of any prior assumption on s but requires that we know some upper bound γ on the ratio max i σ i / min i σ i . For example, the choice γ = 1 corresponds to the homoscedastic case where the components of Y are assumed to have common (unknown) variance. In the opposite, the choice γ > 1 corresponds to the heteroscedastic case where the variances of the components of Y are allowed to vary within some range. Our estimation strategy is based on model selection. We consider a family {Sm × Σm, m ∈ M} of parameter sets where Sm and Σm are linear spaces. To each m ∈ M, we associate a pair of estimators (ŝm,σm) of (s, σ) with values in Sm × Σm. Then we design a model selection procedure in view of selecting somem among M in such a way that the Kullback risk of (ŝm,σm) is as close as possible to the minimum of the Kullback risks among the family of estimators {(ŝm,σm), m ∈ M}. Then we derive uniform rates of convergence for the estimator (ŝm,σm) over Hölderian balls. Finally, we carry out a simulation study in order to illustrate the performances of our estimators in practice.AMS 2000 subject classifications: 62G08.

1. Calls for ecological principles in agriculture have gained momentum. Intercropping systems have long been designed by growing two, or more, annual crop species in the same field, aiming for a better resource use efficiency. However, assembly rules for their design are lacking. Notably, it is still unknown whether species performances are maximized during both the vegetative and reproductive phases given the sensitivity of reproductive allocation rules to resource limitation. Interestingly, ecological theory provides expectations regarding putative invariance of plant reproductive allometry (PRA) under non-limiting conditions for plant growth. Here we examined whether and how PRA changes in response to plant-plant interactions in intercropping systems, which can inform both ecological theory and the understanding of the functioning of intercropping systems.2. We analyzed a dataset of 28 field cereal-legume intercropping trials from various climatic and management conditions across Western Europe. PRA was quantified in both mixing and single-species situations.3. PRA was positively impacted in specific management conditions, leading to a greater increase in yield for a given increase in plant size. Variations in PRA were more beneficial for legumes grown in unfertilized mixture, which explains their use as a key component in actual intercrop systems. The response for cereals was similar but less pronounced in magnitude, and was greater under limiting resource conditions. Focusing on intercropping conditions, hierarchical competition (indicated by biomass difference between intercropped species) appears as a strong driver of the reproductive output of a given species.4. Synthesis and applications. Plant reproductive allometry behaves in crop species in the same way as it does in wild species. However, contrary to theoretical expectations about an overall invariance of PRA, we highlighted taxon-specific and context-dependent effects of plant-plant interactions on PRA. This systematic deviation to PRA expectations could be leveraged to cultivate each species up to its reproductive optimum while accounting for the performance of the other, whether farmer's objective is to favor one species or to reach an equilibrium in seed production. Sowing density and cultivar choice could regulate the biomass of each component, with specific targets derived from allometric relationships, aiming for an optimal reproductive allocation in mixtures.