A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Environmental dimensionality
Tekijät: Parvinen Kalle, Dieckmann Ulf
Kustantaja: Elsevier
Julkaisuvuosi: 2018
Journal: Journal of Theoretical Biology
Tietokannassa oleva lehden nimi: Journal of theoretical biology
Lehden akronyymi: J Theor Biol
ISSN: 0022-5193
eISSN: 1095-8541
DOI: https://doi.org/10.1016/j.jtbi.2018.03.008
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/39297661
Tiivistelmä
The number of regulating variables n in a given system is an upper bound to the number of coexisting species at equilibrium according to the competitive exclusion principle. However, it may be possible to formulate the model with a lower number of regulating variables, the smallest number of which is the dimension of the environmental feedback. Here we investigate how that dimension can be determined by analysing the two parts of environmental feedback: The impact map describes how the extant species affect the regulating variables, and the sensitivity map describes how population growth depends on the regulating variables. For the equilibrium condition it is enough to know the sign of each population growth rate, and therefore as the sensitivity map, different measures of population growth can be chosen, such as the basic reproduction number. The dimension of the environmental feedback must not depend on that choice. Different sensitivity maps can have different global dimensions, on which the definition thus cannot be based. Here we show that the local sensitivity dimension is independent of the choice, so that the concept is well-defined. The impact dimension is lower than n when the feasible set of environments is of lower dimension than n, and sensitivity dimension is lower than n when not all environmental variables affect the sign of population growth independently. Their combined effect can result in even lower environmental dimension. We illustrate such situations with examples. In conclusion, the dimension of environmental feedback gives valuable information about the potential coexistence of species.
The number of regulating variables n in a given system is an upper bound to the number of coexisting species at equilibrium according to the competitive exclusion principle. However, it may be possible to formulate the model with a lower number of regulating variables, the smallest number of which is the dimension of the environmental feedback. Here we investigate how that dimension can be determined by analysing the two parts of environmental feedback: The impact map describes how the extant species affect the regulating variables, and the sensitivity map describes how population growth depends on the regulating variables. For the equilibrium condition it is enough to know the sign of each population growth rate, and therefore as the sensitivity map, different measures of population growth can be chosen, such as the basic reproduction number. The dimension of the environmental feedback must not depend on that choice. Different sensitivity maps can have different global dimensions, on which the definition thus cannot be based. Here we show that the local sensitivity dimension is independent of the choice, so that the concept is well-defined. The impact dimension is lower than n when the feasible set of environments is of lower dimension than n, and sensitivity dimension is lower than n when not all environmental variables affect the sign of population growth independently. Their combined effect can result in even lower environmental dimension. We illustrate such situations with examples. In conclusion, the dimension of environmental feedback gives valuable information about the potential coexistence of species.
Ladattava julkaisu This is an electronic reprint of the original article. |  |
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