Analyzing the spatial dynamics of a prey–predator lattice model with social behavior

Random walk models in the life sciences: including births, deaths and local interactions

Random walks and related spatial stochastic models have been used in a range of application areas, including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing and oncology. Classical random walk models assume that all individuals in a population behave independently, ignoring local physical and biological interactions. This assumption simplifies the mathematical description of the population considerably, enabling continuum-limit descriptions to be derived and used in model analysis and fitting. However, interactions between individuals can have a crucial impact on population-level behaviour. In recent decades, research has increasingly been directed towards models that include interactions, including physical crowding effects and local biological processes such as adhesion, competition, dispersal, predation and adaptive directional bias. In this article, we review the progress that has been made with models of interacting individuals. We aim to provide an overview that is accessible to researchers in application areas, as well as to specialist modellers. We focus particularly on derivation of asymptotically exact or approximate continuum-limit descriptions and simplified deterministic models of mean-field behaviour and resulting spatial patterns. We provide worked examples and illustrative results of selected models. We conclude with a discussion of current areas of focus and future challenges.

Modeling and analysis of melanoblast motion

Melanoblast migration is important for embryogenesis and is a key feature of melanoma metastasis. Many studies have characterized melanoblast movement, focusing on statistical properties and have highlighted basic mechanisms of melanoblast motility. We took a slightly different and complementary approach: we previously developed a mathematical model of melanoblast motion that enables the testing of biological assumptions about the displacement of melanoblasts and we created tests to analyze the geometric features of cell trajectories and the specific issue of trajectory interactions. Within this model, we performed simulations and compared the results with experimental data using geometric tests. In this paper, we developed the associated mathematical model and the main focus is to study the crossings between trajectories with new theoretical results about the variation of number of intersection points with respect to the crossing times. Using these results it is possible to study the random nature of displacements and the interactions between trajectories. This analysis has raised new questions, leading to the generation of strong arguments in favor of a trail left behind each moving melanoblast.

Deep-Reinforcement Learning-Based Co-Evolution in a Predator-Prey System

Understanding or estimating the co-evolution processes is critical in ecology, but very challenging. Traditional methods are difficult to deal with the complex processes of evolution and to predict their consequences on nature. In this paper, we use the deep-reinforcement learning algorithms to endow the organism with learning ability, and simulate their evolution process by using the Monte Carlo simulation algorithm in a large-scale ecosystem. The combination of the two algorithms allows organisms to use experiences to determine their behavior through interaction with that environment, and to pass on experience to their offspring. Our research showed that the predators' reinforcement learning ability contributed to the stability of the ecosystem and helped predators obtain a more reasonable behavior pattern of coexistence with its prey. The reinforcement learning effect of prey on its own population was not as good as that of predators and increased the risk of extinction of predators. The inconsistent learning periods and speed of prey and predators aggravated that risk. The co-evolution of the two species had resulted in fewer numbers of their populations due to their potentially antagonistic evolutionary networks. If the learnable predators and prey invade an ecosystem at the same time, prey had an advantage. Thus, the proposed model illustrates the influence of learning mechanism on a predator-prey ecosystem and demonstrates the feasibility of predicting the behavior evolution in a predator-prey ecosystem using AI approaches.

Simulation of melanoblast displacements reveals new features of developmental migration

To distribute and establish the melanocyte lineage throughout the skin and other developing organs, melanoblasts undergo several rounds of proliferation, accompanied by migration through complex environments and differentiation. Melanoblast migration requires interaction with extracellular matrix of the epidermal basement membrane and with surrounding keratinocytes in the developing skin. Migration has been characterized by measuring speed, trajectory and directionality of movement, but there are many unanswered questions about what motivates and defines melanoblast migration. Here, we have established a general mathematical model to simulate the movement of melanoblasts in the epidermis based on biological data, assumptions and hypotheses. Comparisons between experimental data and computer simulations reinforce some biological assumptions, and suggest new ideas for how melanoblasts and keratinocytes might influence each other during development. For example, it appears that melanoblasts instruct each other to allow a homogeneous distribution in the tissue and that keratinocytes may attract melanoblasts until one is stably attached to them. Our model reveals new features of how melanoblasts move and, in particular, suggest that melanoblasts leave a repulsive trail behind them as they move through the skin.