turkmath.org

Developing mechanistic models and employing statistical methods to unravel biological and ecological complexities have emerged as rapidly advancing research areas. In this presentation, it will be delved into our developed mathematical models and statistical methods designed to comprehend collective behaviors of animals and microorganisms, as well as the influence of environmental changes on their behavior. Firstly, it will be emphasized two key studies. The first involves the development of mechanistic stochastic models to understand the mechanisms underlying the patchiness of motile phytoplankton. Secondly, it will be discussed our work on the development of Markov Chain Monte Carlo (MCMC) algorithms for mapping molecular diffusion, offering insights into molecular dynamics at a microscopic level, such as the crowding within the cellular environment through the analysis of nanoparticle diffusion patterns. Moving on to ecological applications, it will be introduced a machine learning framework aimed to study the impact of global change on biodiversity dynamics. This approach enables us to predict how environmental change may alter species distributions and community compositions. Finally, it will be explored our efforts in employing statistical inference of ecological complex networks, utilizing interactions with indicator species to reconstruct biodiversity. Through these studies, it is aimed to deepen our understanding of biological and ecological systems, ultimately contributing to more effective conservation and management strategies in the face of environmental change.