טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentCohen Niv
SubjectExternally Induced Fast Oscillations Stabilizes the
Dynamics of Interacting Species
DepartmentDepartment of Physics
Supervisor Professor Roy Kishony
Full Thesis textFull thesis text - English Version


Abstract

Stability of multi species communities coexisting in natural environments have puzzled theoretical ecology, as simple ecological models typically result in one or few species taking over. According to the principle of mutual exclusion, applied to well mixed species in steady state in a single trophic level, the number of species is bounded by the number of available resources. A wide range of models have shown that relaxing the assumptions underlying the exclusion principle, can help to explain coexistence of large multi-species communities. Going beyond a single trophic level, or adding interactions among species can lead to many species coexistence, yet most often such interactions destabilize the community and models of many systems remain unstable.

Environmental fluctuations, which drive the species abundance across different ecological niches, are known to be important for community coexistence. Such fluctuations can generate multiple temporal niches, thereby relax the bound on community diversity. In addition, fluctuations in species abundance, which emerge spontaneously or result from environmental changes, can lead to stability of communities which are larger than the size expected by the exclusion principle. However, little is known about the effect of fast environmental fluctuations on the stability of communities within the same temporal niche.

Here, we analyze the effects of external fast oscillations on stability in different ecological models. We consider three models representing different kind of effects rising when species interactions are affected by environmental oscillations. First, we consider predator-prey Lotka Volterra model, where we introduce fluctuating cooperativity in predation rate. Second, we ask what happen when predation is mediated by a toxin, for example when one species produces a toxin that kills another species, and consider oscillations in the effectiveness of this mediating toxin. Third, we turn to a single trophic level model of resource competition and consider oscillations in the resource consumption rate. While these models are not stabilized by environmental oscillations in most of the system’s parameters, we identify specific control junctions where oscillations can create stabilization. By studying the existence of stability in periodic versus noisy fluctuations, and the dependence of stability on the fluctuation rate and amplitude, we identify distinct mechanisms by which environmental fluctuations generate stability in these different ecological models. Together, these results show new ways in which fast oscillations may create stability in ecological systems and highlight the qualitative importance of coherent external perturbations.