We develop a mathematical model of platelet, megakaryocyte, and thrombopoietin dynamics in humans. We show that there is a single stationary solution that can undergo a Hopf bifurcation, and use this information to investigate both normal and pathological platelet production, specifically cyclic thrombocytopenia. Carefully estimating model parameters from laboratory and clinical data, we then argue that a subset of parameters are involved in the genesis of cyclic thrombocytopenia based on clinical information. We provide model fits to the existing data for both platelet counts and thrombopoietin levels by changing four parameters that have physiological correlates. Our results indicate that the primary change in cyclic thrombocytopenia is an interference with, or destruction of, the thrombopoietin receptor with secondary changes in other processes, including immune-mediated destruction of platelets and megakaryocyte deficiency and failure in platelet production. This study contributes to the understanding of the origin of cyclic thrombocytopenia as well as extending the modeling of thrombopoiesis.

Multi-species grasslands are reservoirs of biodiversity and provide multiple ecosystem services, including fodder production and carbon sequestration. The provision of these services depends on the control exerted on the biogeochemistry and plant diversity of the system by the interplay of biotic and abiotic factors, e.g., grazing or mowing intensity. Biogeochemical models incorporate a mechanistic view of the functioning of grasslands and provide a sound basis for studying the underlying processes. However, in these models, the simulation of biogeochemical cycles is generally not coupled to simulation of plant species dynamics, which leads to considerable uncertainty about the quality of predictions. Ecological models, on the other hand, do account for biodiversity with approaches adopted from plant demography, but without linking the dynamics of plant species to the biogeochemical processes occurring at the community level, and this hampers the models’ capacity to assess resilience against abiotic stresses such as drought and nutrient limitation. While setting out the state-of-the-art developments of biogeochemical and ecological modelling, we explore and highlight the role of plant diversity in the regulation of the ecosystem processes underlying the ecosystems services provided by multi-species grasslands. An extensive literature and model survey was carried out with an emphasis on technically advanced models reconciling biogeochemistry and biodiversity, which are readily applicable to managed grasslands in temperate latitudes. We propose a roadmap of promising developments in modelling.

In mathematical grassland models, plant communities may be represented by a various number of state variables, describing biomass compartments of some dominant species or plant functional types. The size of the initial species pool could have consequences on the outcome of the simulated ecosystem dynamics in terms of grassland productivity, diversity, and stability. This choice could also influence the model sensitivity to forcing parameters. To address these issues, we developed a dynamic grassland model, DYNAGRAM, designed to simulate seasonal changes in both aboveground biomass production and species composition of managed permanent grasslands under various soil, climate and management conditions. We compared simulation results from alternative instances of DYNAGRAM that only differ by the identity and number of state variables describing the green biomass, here plant species. We assessed the sensitivity of each instance of the model to key forcing parameters for climate, soil fertility, and defoliation disturbances, using univariate and multivariate regression trees and dynamic trees. Results of 10-year simulations under various climate, fertility and defoliation conditions showed that the final total biomass was tending to increase with the size of the species pool, while species evenness and the proportion of surviving species was tending to decrease. We found a positive correlation between the species survival ratio and the defoliation intensity, and this correlation increased with the initial species richness. The sensitivity to forcing parameters of community structure and species evenness differed markedly among alternative models, showing a progressive shift from high importance of soil fertility (fertilisation level, mineralization rate) to high importance of defoliation (mowing frequency, grazing intensity) as the size of the species pool increased. By contrast, the key drivers of total biomass production were independent of species richness and only linked to resource supply (nitrogen and water). These results highlight the need to take into account the role of species diversity to explain the behaviour of grassland models.