Imaging with spatio-temporal modelling to characterize the dynamics of plant-pathogen lesions.

Within-host spread of pathogens is an important process for the study of plant-pathogen interactions. However, the development of plant-pathogen lesions remains practically difficult to characterize beyond the common traits such as lesion area. Here, we address this question by combining image-based phenotyping with mathematical modelling. We consider the spread of Peyronellaea pinodes on pea stipules that were monitored daily with visible imaging. We assume that pathogen propagation on host-tissues can be described by the Fisher-KPP model where lesion spread depends on both a logistic growth and an homogeneous diffusion. Model parameters are estimated using a variational data assimilation approach on sets of registered images. This modelling framework is used to compare the spread of an aggressive isolate on two pea cultivars with contrasted levels of partial resistance. We show that the expected slower spread on the most resistant cultivar is actually due to a significantly lower diffusion coefficient. This study shows that combining imaging with spatial mechanistic models can offer a mean to disentangle some processes involved in host-pathogen interactions and further development may allow a better identification of quantitative traits thereafter used in genetics and ecological studies.

Optimal spatial monitoring of populations described by reaction-diffusion models.

Using spatialised population measurements and related geographic habitat data, it is feasible nowadays to derive parsimonious spatially explicit population models and to carry on their parameter estimation. To achieve such goal, reaction-diffusion models are common in conservation biology and agricultural plant health where they are used, for example, for landscape planning or epidemiological surveillance. Unfortunately, if the mathematical methods and computational power are readily available, biological measurements are not. Despite the high throughput of some habitat related remote sensors, the experimental cost of biological measurements are one of the worst bottleneck against a widespread usage of reaction-diffusion models. Hence we will recall some classical methods for optimal experimental design that we deem useful to spatial ecologist. Using two case studies, one in landscape ecology and one in conservation biology, we will show how to construct a priori experimental design minimizing variance of parameter estimates, enabling optimal experimental setup under constraints.

Relative importance of long-term changes in climate and land-use on the phenology and abundance of legume crop specialist and generalist aphids.

Insect populations are prone to respond to global changes through shifts in phenology, distribution and abundance. However, global changes cover several factors such as climate and land-use, the relative importance of these being largely unknown. Here, we aim at disentangling the effects of climate, land-use, and geographical drivers on aphid abundance and phenology in France, at a regional scale and over the last 40 years. We used aerial data obtained from suction traps between 1978 and 2015 on five aphid species varying in their degree of specialization to legumes, along with climate, legume crop area and geographical data. Effects of environmental and geographical variables on aphid annual abundance and spring migration dates were analyzed using generalized linear mixed models. We found that within the last four decades, aphids have advanced their spring migration by a month, mostly due to the increase in temperature early in the year, and their abundance decreased by half on average, presumably in response to a combination of factors. The influence of legume crop area decreased with the degree of specialization of the aphid species to such crops. The effect of geographical variation was high even when controlling for environmental variables, suggesting that many other spatially structured processes act on aphid population characteristics. Multifactorial analyses helped to partition the effects of different global change drivers. Climate and land-use changes have strong effects on aphid populations, with important implications for future agriculture. Additionally, trait-based response variation could have major consequences at the community scale.

Interpretation and approximation tools for big, dense Markov chain transition matrices in population genetics.

BACKGROUND: Markov chains are a common framework for individual-based state and time discrete models in evolution. Though they played an important role in the development of basic population genetic theory, the analysis of more complex evolutionary scenarios typically involves approximation with other types of models. As the number of states increases, the big, dense transition matrices involved become increasingly unwieldy. However, advances in computational technology continue to reduce the challenges of "big data", thus giving new potential to state-rich Markov chains in theoretical population genetics. RESULTS: Using a population genetic model based on genotype frequencies as an example, we propose a set of methods to assist in the computation and interpretation of big, dense Markov chain transition matrices. With the help of network analysis, we demonstrate how they can be transformed into clear and easily interpretable graphs, providing a new perspective even on the classic case of a randomly mating, finite population with mutation. Moreover, we describe an algorithm to save computer memory by substituting the original matrix with a sparse approximate while preserving its mathematically important properties, including a closely corresponding dominant (normalized) eigenvector. A global sensitivity analysis of the approximation results in our example shows that size reduction of more than 90 % is possible without significantly affecting the basic model results. Sample implementations of our methods are collected in the Python module mamoth. CONCLUSION: Our methods help to make stochastic population genetic models involving big, dense transition matrices computationally feasible. Our visualization techniques provide new ways to explore such models and concisely present the results. Thus, our methods will contribute to establish state-rich Markov chains as a valuable supplement to the diversity of population genetic models currently employed, providing interesting new details about evolution e.g. under non-standard reproductive systems such as partial clonality.

Response of insect relative growth rate to temperature and host-plant phenology: estimation and validation from field data.

Between 1975 to 2011, aphid Relative Growth Rates (RGR) were modelled as a function of mean outdoor temperature and host plant phenology. The model was applied to the grain aphid Sitobion avenae using data on aphid counts in winter wheat at two different climate regions in France (oceanic climate, Rennes (western France); continental climate, Paris). Mean observed aphid RGR was higher in Paris compared to the Rennes region. RGR increased with mean temperature, which is explained by aphid reproduction, growth and development being dependent on ambient temperature. From the stem extension to the heading stage in wheat, there was either a plateau in RGR values (Rennes) or an increase with a maximum at heading (Paris) due to high intrinsic rates of increase in aphids and also to aphid immigration. From the wheat flowering to the ripening stage, RGR decreased in both regions due to the low intrinsic rate of increase in aphids and high emigration rate linked to reduced nutrient quality in maturing wheat. The model validation process showed that the fitted models have more predictive power in the Paris region than in the Rennes region.

A spatiotemporal model for predicting grain aphid population dynamics and optimizing insecticide sprays at the scale of continental France.

We expose here a detailed spatially explicit model of aphid population dynamics at the scale of a whole country (Metropolitan France). It is based on convection-diffusion-reaction equations, driven by abiotic and biotic factors. The target species is the grain aphid, Sitobion avenae F., considering both its winged and apterous morphs. In this preliminary work, simulations for year 2004 (an outbreak case) produced realistic aphid densities, and showed that both spatial and temporal S. avenae population dynamics can be represented as an irregular wave of population peak densities from southwest to northeast of the country, driven by gradients or differences in temperature, wheat phenology, and wheat surfaces. This wave pattern fits well to our knowledge of S. avenae phenology. The effects of three insecticide spray regimes were simulated in five different sites and showed that insecticide sprays were ineffective in terms of yield increase after wheat flowering. After suitable validation, which will require some further years of observations, the model will be used to forecast aphid densities in real time at any date or growth stage of the crop anywhere in the country. It will be the backbone of a decision support system, forecasting yield losses at the level of a field. The model intends then to complete the punctual forecasting provided by older models by a comprehensive spatial view on a large area and leads to the diminution of insecticide sprayings in wheat crops.

The loneliness of the electrons in the bc1 complex.

A stochastic approach based on Gillespie algorithm is particularly well adapted to describe the time course of the redox reactions that occur inside the respiratory chain complexes because they involve the motion of single electrons between individual unique redox centres of a given complex and not populations of electrons and redox centres as usually considered in ordinary differential equations. In this way we approach the molecular functioning of the bc(1) complex based on its known crystallographic structure and the rate constants of electron tunnelling derived from the Moser and Dutton phenomenological equation. The main features of our simulations are the dominant and robust emergence of a Q-cycle mechanism and the near absence of short-circuits in the normal functioning of the bc(1) complex. Thus, in our paper, the Mitchell Q-cycle no longer appears as an a priori hypothesis but arises out of the bc(1) complex structure and of the kinetic laws of redox reactions.

Formal TCA cycle description based on elementary actions.

Many databases propose their own structure and format to provide data describing biological processes. This heterogeneity contributes to the difficulty of large systematic and automatic functional comparisons. To overcome these problems, we have used the BioPsi formal description scheme which allows multi-level representations of biological process information. Applied to the description of the tricarboxylic acid cycle (TCA), we show that BioPsi allows the formal integration of functional information existing in current databases and make them available for further automated analysis. In addition such a formal TCA cycle process description leads to a more accurate biological process annotation which takes in account the biological context. This enables us to perform an automated comparison of the TCA cycles for seven different species based on processes rather than protein sequences. From current databases, BioPsi is able to unravel information that are already known by the biologists but are not available for automated analysis tools and simulation software, because of the lack of formal process descriptions. This use of the BioPsi description scheme to describe the TCA cycle was a key step of the MitoScop project that aims to describe and simulate mitochondrial metabolism in silico.

The MEK-1/ERKs signalling pathway is differentially involved in the self-renewal of early and late avian erythroid progenitor cells.

Making decisions between self-renewal and differentiation is a central ability of stem cells. Elucidation of molecular networks governing this decision is therefore of prime importance. A model of choice to explore this question is represented by chicken erythroid progenitors, in which self-renewal versus differentiation as well as progenitor maturation are regulated by external factor combinations. We used this system to study whether similar or different signalling pathways were involved in the self-renewal of early, immature or more mature erythroid progenitors. We show that a transforming growth factor (TGF)-alpha-activated Ras/MEK-1/ERK1/2 pathway is strictly required for immature self-renewing cells but becomes fully dispensable when those cells are induced to differentiate. Consequently, pharmacological inhibition of this pathway led to spontaneous differentiation, only dependent on the presence of survival signals. Conversely, ectopic expression of a constitutive form of MEK-1 stimulates renewal and arrests differentiation process. Finally, we demonstrate that the ERK/MAPK signalling pathway is required in early but not in late primary erythroid progenitors, which can be turned into each other by different growth factor combinations specifically driving their renewal. To the best of our knowledge, this is the first description of a central role of ERK/MAPK signalling in regulating progenitor plasticity in the same cell type under different environmental conditions.