Application of β-function in phytoindication to account for species response curves asymmetry

Abstract

An approach for phytoindication assessment of the ecological factors based on diapasonal scales taking into account the cardinal points values and possible asymmetry of the plant species response was proposed. Ecological factors are modeled by phytoindicator scales with restricted range. In the central part of the factor range the species response curve has a shape that can be reliably approximated by the Gauss normal distribution. This allows completely grounded via cardinal points that are directly designated by diapasonal indicator values, calculate ecological optimum of the species. Average of species in community ecological optima scores weighted in accordance with their projective cover gives phytoindication estimation of an ecological factor. Species distribution asymmetry increases when approaching the marginal positions within gradient. This phenomenon is observed in the study of real gradients. These phenomena are also a result of the mathematical properties of ecological scales. To simulate the response of species distribution curves alternatively symmetric Gaussian model the β-function was used. This function can simulate both symmetric and asymmetric distributions. Since phytoindication performs the inverse problem in comparison with the modeling of the response curves, it is appropriate to β-function is also be used to solve phytoindication problems. Use of β-function is possible to estimate the species optimum zone based on its fundamental points with the probable distribution asymmetry of the response curve. Also, the simulation of distribution curve makes it possible to narrow the range of possible values of environmental factors, in terms of which species can exhibit the observed abundance in the community. Accordingly, this increases the informational value of species in the community and thus achieves greater reliability evaluations of the phytoindication.

The asymmetry of the aquatic macrophyte response to temperature increases with global warming and has to be accounted for in phytoindication

“…The weighted average of the indicator values of the species by their projected coverage was calculated for each community. The ideal indicator method was used to estimate the temperature according to Didukh's(Didukh 2011) range scales(Buzuk, 2017;Zhukov et al, 2018).…”