Inference and Validation of The Structure of Lotka-Volterra Models

For close to a century, Lotka-Volterra (LV) models have been used to investigate interactions among populations of different species. For a few species, these investigations are straightforward. However, with the arrival of large and complex microbiomes, unprecedently rich data have become available and await analysis. In particular, these data require us to ask which microbial populations of a mixed community affect other populations, whether these influences are activating or inhibiting and how the interactions change over time. Here we present two new inference strategies for interaction parameters that are based on a new algebraic LV inference (ALVI) method. One strategy uses different survivor profiles of communities grown under similar conditions, while the other pertains to time series data. In addition, we address the question of whether observation data are compliant with the LV structure or require a richer modeling format.

Inference and Validation of the Structure of Lotka-Volterra Models

For close to a century, Lotka-Volterra (LV) models have been used to investigate interactions among populations of different species. For a few species, these investigations are straightforward. However, with the arrival of large and complex microbiomes, unprecedently rich data have become available and await analysis. In particular, these data require us to ask which microbial populations of a mixed community affect other populations, whether these influences are activating or inhibiting and how the interactions change over time. Here we present two new inference strategies for interaction parameters that are based on a new algebraic LV inference (ALVI) method. One strategy uses different survivor profiles of communities grown under similar conditions, while the other pertains to time series data. In addition, we address the question of whether observation data are compliant with the LV structure or require a richer modeling format.

Early Stopping Criterion for Recursive Least Squares Training of Behavioural Models

As the physical makeup of cellular base-stations evolve into systems with multiple parallel transmission paths the effort involved in modelling these complex systems increases considerably. One task in particular which contributes to signal distortion on each signal path, is the power amplifier. In power amplifier modelling, Recursive Least Squares has been used in the past to train Volterra models with memory terms, however instability can occur when training the model weights. This manuscript provides a computationally efficient technique to detect the onset of instability and subsequently to inform the decision when to stop adaptive training of dynamic nonlinear behavioural models and avoid the onset of instability. This technique is experimentally validated using four different signal modulation schemes.

Comparative Numerical Study of SBA (Somé Blaise-Abbo) Method and Homotopy Perturbation Method (HPM) on Biomathematical Models Type Lotka-Volterra

In this work the Homotopy Perturbation Method (HPM) is used to find an exact or approximate solutions of Lotka-Volterra models. Then we compare the HPM solution with the solution given by SBA (Somé Blaise Abbo) method.

Microbial Interactions as Drivers of a Nitrification Process in a Chemostat

This article deals with the inclusion of microbial ecology measurements such as abundances of operational taxonomic units in bioprocess modelling. The first part presents the mathematical analysis of a model that may be framed within the class of Lotka–Volterra models fitted to experimental data in a chemostat setting where a nitrification process was operated for over 500 days. The limitations and the insights of such an approach are discussed. In the second part, the use of an optimal tracking technique (developed within the framework of control theory) for the integration of data from genetic sequencing in chemostat models is presented. The optimal tracking revisits the data used in the aforementioned chemostat setting. The resulting model is an explanatory model, not a predictive one, it is able to reconstruct the different forms of nitrogen in the reactor by using the abundances of the operational taxonomic units, providing some insights into the growth rate of microbes in a complex community.

Heavy-tailed abundance distributions from stochastic Lotka-Volterra models

Microbial communities found in nature are composed of many rare species and few abundant ones, as reflected by their heavy-tailed abundance distributions. How a large number of species can coexist in those complex communities and why they are dominated by rare species is still not fully understood. We show how heavy-tailed distributions arise as an emergent property from large communities with many interacting species in population-level models. To do so we rely on stochastic logistic and generalized Lotka-Volterra models for which we introduce a global maximal capacity. This maximal capacity accounts for the fact that communities are limited by available resources and space. In a parallel ‘ad-hoc’ approach, we obtain heavy-tailed abundance distributions from non-interacting models through specific distributions of the parameters. We expect both mechanisms, interactions between many species and specific parameter distributions, to be relevant to explain the observed heavy tails.

Structured environments foster competitor coexistence by manipulating interspecies interfaces

Natural environments, like soils or the mammalian gut, frequently contain microbial consortia competing within a niche, wherein many species contain genetically encoded mechanisms of interspecies competition. Recent computational work suggests that physical structures in the environment can stabilize local competition between species that would otherwise be subject to competitive exclusion under isotropic conditions. Here we employ Lotka-Volterra models to show that interfacial competition localizes to physical structures, stabilizing competitive ecological networks of many species, even with significant differences in the strength of competitive interactions between species. Within a limited range of parameter space, we show that for stable communities the length-scale of physical structure inversely correlates with the width of the distribution of competitive fitness, such that physical environments with finer structure can sustain a broader spectrum of interspecific competition. These results highlight the potentially stabilizing effects of physical structure on microbial communities and lay groundwork for engineering structures that stabilize and/or select for diverse communities of ecological, medical, or industrial utility.