Abstract:The validity of the competitive exclusion principle (the Gause's principle) at one metabolic regulation factor is demonstrated for a general model of two-species community. The competitive exclusion principle postulates that a long-term coexistence of species is impossible if their number exceeds the number of density-dependent growth-regulating factors. Previously, this principle was proved for the stationary states in a general model of a community with any number of factors. In the dynamic modes, the number… Show more
“…The result of coexistence obtained here is similar to the results obtained by other authors addressing regulation via DDGCFs, but the present rule of coexistence includes not only limitation by substrate, but also a large number of other interspecific relationships. The broader condition of species coexistence obviously leads to an extended interpretation of Gause's principle [27]: not only the single limiting resource-substrate but also any other RF prevents the two species from living together.…”
Section: The Rule Of Coexistence Of Microbial Populations In Continuo...mentioning
The present paper is a summary of the authors’ theoretical and experimental research dealing with the patterns of stable equilibrium coexistence of microbial populations in flow systems interacting through specific density-dependent growth regulators (RFs). The discovered “paradoxical” lack of dependence of the background steady-state levels (concentrations) of RFs on their input values is confirmed experimentally and theoretically through the introduced sensitivity coefficients. This effect has been termed “autostabilization” of RFs. An important theorem (formula) of “quantization” suggesting the integer value of the sum of all sensitivity coefficients, which is equal to the difference between the number of RFs and the number of populations of one trophic level, has been proven. A modification of the “quantization” formula for an arbitrary trophic web is shown. A new criterion for intra- and inter-population microbial interactions for RFs is proposed—the response of growth acceleration to a perturbation in population size. This criterion makes it possible to quantify interspecific complex relationships, which has been previously impossible. The relationship between the new coefficients of inter-population interactions and the accuracy of model verification has been shown theoretically. Based on this criterion and the autostabilization effect, a method for experimental search for unknown RFs is proposed.
“…The result of coexistence obtained here is similar to the results obtained by other authors addressing regulation via DDGCFs, but the present rule of coexistence includes not only limitation by substrate, but also a large number of other interspecific relationships. The broader condition of species coexistence obviously leads to an extended interpretation of Gause's principle [27]: not only the single limiting resource-substrate but also any other RF prevents the two species from living together.…”
Section: The Rule Of Coexistence Of Microbial Populations In Continuo...mentioning
The present paper is a summary of the authors’ theoretical and experimental research dealing with the patterns of stable equilibrium coexistence of microbial populations in flow systems interacting through specific density-dependent growth regulators (RFs). The discovered “paradoxical” lack of dependence of the background steady-state levels (concentrations) of RFs on their input values is confirmed experimentally and theoretically through the introduced sensitivity coefficients. This effect has been termed “autostabilization” of RFs. An important theorem (formula) of “quantization” suggesting the integer value of the sum of all sensitivity coefficients, which is equal to the difference between the number of RFs and the number of populations of one trophic level, has been proven. A modification of the “quantization” formula for an arbitrary trophic web is shown. A new criterion for intra- and inter-population microbial interactions for RFs is proposed—the response of growth acceleration to a perturbation in population size. This criterion makes it possible to quantify interspecific complex relationships, which has been previously impossible. The relationship between the new coefficients of inter-population interactions and the accuracy of model verification has been shown theoretically. Based on this criterion and the autostabilization effect, a method for experimental search for unknown RFs is proposed.
“…Таким образом, выявлено большое разнообразие динамических режимов фитопланктона, возникающих в результате влияния зоопланктона. В лабораторных экспериментах качественное разнообразие динамики фитопланктона действительно наблюдается [Degermendzhi, Abakumov, 2018], в природных фитосообществах известны явления «цветения» -качественного изменения типа динамики биомасс, причины которого не вполне изучены [Spilling, Markager, 2008].…”
Section: исследование модели (2) описывающей динамику планктонного сunclassified
Ключевые слова: динамика сообщества, бифуркация, модель Рикера, фитопланктон, зоопланктон, взаимодействие по принципу «хищник-жертва», каннибализм Работа выполнена при частичной поддержке РФФИ (проект № 18-01-00213).
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