A general method for modeling population dynamics and its applications.

Studying populations, be it a microbe colony or mankind, is important for understanding how complex systems evolve and exist. Such knowledge also often provides insights into evolution, history and different aspects of human life. By and large, populations' prosperity and decline is about transformation of certain resources into quantity and other characteristics of populations through growth, replication, expansion and acquisition of resources. We introduce a general model of population change, applicable to different types of populations, which interconnects numerous factors influencing population dynamics, such as nutrient influx and nutrient consumption, reproduction period, reproduction rate, etc. It is also possible to take into account specific growth features of individual organisms. We considered two recently discovered distinct growth scenarios: first, when organisms do not change their grown mass regardless of nutrients availability, and the second when organisms can reduce their grown mass by several times in a nutritionally poor environment. We found that nutrient supply and reproduction period are two major factors influencing the shape of population growth curves. There is also a difference in population dynamics between these two groups. Organisms belonging to the second group are significantly more adaptive to reduction of nutrients and far more resistant to extinction. Also, such organisms have substantially more frequent and lesser in amplitude fluctuations of population quantity for the same periodic nutrient supply (compared to the first group). Proposed model allows adequately describing virtually any possible growth scenario, including complex ones with periodic and irregular nutrient supply and other changing parameters, which present approaches cannot do.