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 and quantify beyond the common traits such as lesion area. We tackle the spatio-temporal dynamics of interactions 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 local 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 decrease of diffusion and, to a lesser extent, local growth. These results demonstrate that spatial models with imaging allows one to disentangle the processes involved in host-pathogen interactions. Hence, promoting model-based phenotyping of interactions would allow a better identification of quantitative traits thereafter used in genetics and ecological studies.

Optimal location of resources and Steiner symmetry in a population dynamics model in heterogeneous environments

The subject of this paper is inspired by Cantrell and Cosner (1989) and Cosner, Cuccu and Porru (2013). Cantrell and Cosner (1989) investigate the dynamics of a population in heterogeneous environments by means of diffusive logistic equations. An important part of their study consists in finding sufficient conditions which guarantee the survival of the species. Mathematically, this task leads to the weighted eigenvalue problem \(-\Delta u =\lambda m u \) in a bounded smooth domain \(\Omega\subset \mathbb{R}^N\), \(N\geq 1\), under homogeneous Dirichlet boundary conditions, where \(\lambda \in \mathbb{R}\) and \(m\in L^\infty(\Omega)\). The domain \(\Omega\) represents the environment and \(m(x)\), called the local growth rate, says where the favourable and unfavourable habitats are located. Then, Cantrell and Cosner (1989) consider a class of weights \(m(x)\) corresponding to environments where the total sizes of favourable and unfavourable habitats are fixed, but their spatial arrangement is allowed to change; they determine the best choice among them for the population to survive. In our work we consider a sort of refinement of the result above. We write the weight \(m(x)\) as sum of two (or more) terms, i.e. \(m(x)=f_1(x)+f_2(x)\), where \(f_1(x)\) and \(f_2(x)\) represent the spatial densities of the two resources which contribute to form the local growth rate \(m(x)\). Then, we fix the total size of each resource allowing its spatial location to vary. As our first main result, we show that there exists an optimal choice of \(f_1(x)\) and \(f_2(x)\) and find the form of the optimizers. Our proof relies on some results in Cosner, Cuccu and Porru (2013) and on a new property (to our knowledge) about the classes of rearrangements of functions. Moreover, we show that if \(\Omega\) is Steiner symmetric, then the best arrangement of the resources inherits the same kind of symmetry. (Actually, this is proved in the more general context of the classes of rearrangements of measurable functions.

Decision Support Tool for Tree Species Selection in Forest Regeneration Based on Harvester Data

Precision forestry—i.e., the division of a stand to smaller units and managing of the stand at a micro-stand level—provides new possibilities to increase forest growth, arrange forest stand structure and enhance forest health. In the regeneration phase by adjusting the tree species selection, soil preparation, intensity of regeneration measures (method, planting density, and material), and young stand management procedures according to precise information on soil properties (e.g., site fertility, wetness, and soil type) and microtopography will inevitably lead to an increase in growth of the whole stand. A new approach to utilizing harvester data to delineate micro-stands inside a large forest stand and to deciding the tree species to plant for each micro-stand was piloted in central Finland. The case stands were situated on Finsilva Oyj forest property. The calculation of the local growth (m3/ha/year) for each 16 × 16-m grid cell was based on the height of the dominant trees and the stand age of the previous tree generation. Tree heights and geoinformation were collected during cutting operation as the harvester data, and the dominant height was calculated as the mean of the three largest stems in each grid cell. The stand age was obtained from the forest management plan. The estimated local growth (average of nine neighboring grid cells) varied from 3 to 14 m3/ha/year in the case stands. When creating micro-stands, neighboring grid cells with approximately the same local growth were merged. The minimum size for an acceptable micro-stand was set to 0.23 ha. In this case study, tree species selection (Scots pine or Norway spruce) was based on the mean growth of each micro-stand. Different threshold values, varying from 6 to 8 m3/ha/year, were tested for tree species change, and they led to different solutions in the delineation of micro-stands. Further stand development was simulated with the Motti software and the net present values (NPVs (3%)) for the next rotation were estimated for different micro-stand solutions. The mixed Norway spruce–Scots pine stand structure never produced a clearly economically inferior solution compared to the single species stand, and in one case out of six, it provided a distinctly better solution in terms of NPV (3%) than the single species option did. Our case study showed that this kind of method could be used as a decision support tool at the regeneration phase.

Growth Coordination Between Butyrate-Oxidizing Syntrophs and Hydrogenotrophic Methanogens

Syntrophy is a thermodynamically required mutualistic cooperation between fatty acid-oxidizing bacteria and methanogens that plays the important role in organic decomposition and methanogenesis in anoxic environments. In this study, three experiments were conducted to evaluate the cell-to-cell interaction in a thermophilic coculture consisting of Syntrophothermus lipocalidus and Methanocella conradii and a mesophilic coculture consisting of Syntrophomonas wolfei and Methanococcus maripaludis. First, syntrophs and methanogens were inoculated at different initial cell ratios to evaluate the growth synchronization. The quantitative PCR analysis revealed that the organism with a lower relative abundance at the beginning always grew faster, and the cell ratio converged over time to relative constant values in both the thermophilic and mesophilic cocultures. Next, intermittent ultrasound and constant shaking treatments were used to evaluate the influence of physical disturbance on microbial aggregation in the mesophilic coculture. The fluorescence in situ hybridization and scanning electron microscopy revealed that the tendency of syntrophic aggregation was not affected by the physical disturbances, although the activity was slightly depressed. Syntrophomonas dominated in the initial microbial aggregates, which, however, did not grow until Methanococcus was attached and increased to a significant extent, indicating the local growth synchronization during the formation and maturation of syntrophic aggregates. Last, microfluidic experiments revealed that whether or not Syntrophomonas or Methanococcus was loaded first, the second organism preferred moving to the place where the first organism was located, suggesting the cell-to-cell attraction between Syntrophomonas and Methanococcus. Collectively, our study demonstrated the growth synchronization and cell-to-cell attraction between the butyrate-oxidizing bacteria and methanogens for optimizing the syntrophic cooperation.

STUDY OF FRACTIONAL ORDER DELAY CAUCHY NON-AUTONOMOUS EVOLUTION PROBLEMS VIA DEGREE THEORY

This work is devoted to derive some existence and uniqueness (EU) conditions for the solution to a class of nonlinear delay non-autonomous integro-differential Cauchy evolution problems (CEPs) under Caputo derivative of fractional order. The required results are derived via topological degree method (TDM). TDM is a powerful tool which relaxes strong compact conditions by some weaker ones. Hence, we establish the EU under the situation that the nonlinear function satisfies some appropriate local growth condition as well as of non-compactness measure condition. Furthermore, some results are established for Hyers–Ulam (HU) and generalized HU (GHU) stability. Our results generalize some previous results. At the end, by a pertinent example, the results are verified.

A competitive advantage through fast dead matter elimination in confined cellular aggregates

Competition of different species or cell types for limited space is relevant in a variety of biological processes such as biofilm development, tissue morphogenesis and tumor growth. Predicting the outcome for non-adversarial competition of such growing active matter is non-trivial, as it depends on how processes like growth, proliferation and the degradation of cellular matter are regulated in confinement; regulation that happens even in the absence of competition to achieve the dynamic steady state known as homeostasis. Here, we show that passive by-products of the processes maintaining homeostasis can significantly alter fitness. Even for purely pressure-regulated growth and exclusively mechanical interactions, this enables cell types with lower homeostatic pressure to outcompete those with higher homeostatic pressure. We reveal that interfaces play a critical role in the competition: There, growing matter with a higher proportion of active cells can better exploit local growth opportunities that continuously arise as the active processes keep the system out of mechanical equilibrium. We elucidate this effect in a theoretical toy model and test it in an agent-based computational model that includes finite-time mechanical persistence of dead cells and thereby decouples the density of growing cells from the homeostatic pressure. Our results suggest that self-organization of cellular aggregates into active and passive matter can be decisive for competition outcomes and that optimizing the proportion of growing (active) cells can be as important to survival as sensitivity to mechanical cues.

CITIZEN-GENERATED GEODATA FOR NATURAL PARKS USE ANALYSIS: INSIGHTS FROM FACEBOOK IN THE INSUBRIA REGION

Green areas such as natural parks provide citizens with a number of health and leisure benefits, often accessible with a few minutes of travel from urban centres. Moreover, the natural heritage enclosed in most green areas plays a pivotal role also in the economic integrity of these territories by driving local growth thanks to the establishment of tourism activities. In this context, the monitoring of both visitors and dwellers fluxes, as well as destination preferences, is key to provide land managers with critical information to shape local management and promotion strategies. This paper presents a preliminary investigation on the use of citizen-generated geodata -provided by Facebook- to empower the generation of space- and time-resolved insights into people fluxes in natural parks through a comparison with neighbouring urbanized areas. The Insubria region, a historical-geographical area between Northern Italy and Southern Switzerland, is considered a case study. Facebook users’ population and movements data are analysed to identify trends and metrics on fluxes and support the estimation of the recreational and tourism value of natural parks. Results are presented as graphs and summary statistics and discussed according to their possible integration into territorial management and promotional practices.

Leaf Shape Diversity: From Genetic Modules to Computational Models

Plant leaves display considerable variation in shape. Here, we introduce key aspects of leaf development, focusing on the morphogenetic basis of leaf shape diversity. We discuss the importance of the genetic control of the amount, duration, and direction of cellular growth for the emergence of leaf form. We highlight how the combined use of live imaging and computational frameworks can help conceptualize how regulated cellular growth is translated into different leaf shapes. In particular, we focus on the morphogenetic differences between simple and complex leaves and how carnivorous plants form three-dimensional insect traps. We discuss how evolution has shaped leaf diversity in the case of complex leaves, by tinkering with organ-wide growth and local growth repression, and in carnivorous plants, by modifying the relative growth of the lower and upper sides of the leaf primordium to create insect-digesting traps.