Saving assets when needed: using spline interpolation functions and integral calculus to assess ecological parameters of mollusk populations and communities

Sîrbu I., Benedek A.M.

ioan.n.sirbu@ulbsibiu.ro

What can be done when there is a shortage of assets, and a population size of a bivalve species has to be assessed along an extended river's sector? The devoted method has to be replicated periodically by one or two rangers in the future. Another question: how can we explore the similarity or overlap between resource use of several mollusk species, characterizing all the pairs, while taking into consideration also the availability of resources in the environment, when all resources and gradients are varying continuously? The last question might be rephrased as: how to compute a community matrix, between n pairs of species, described by a standardized niche similarity index that considers the species demands as well as the resources' status in the environment, measured along continuous gradients? In an ideal world, we could investigate what is happening with the population or community, step by step, along the whole gradient(s). Most of the time this is not possible. We usually use a network of knots, i.e., select certain values along the gradient's range, and assess the corresponding value(s) of the parameter(s). Then we search for links between these discrete related series, by regression analysis (sensu lato) and/or canonical multivariate ordination methods. Sometimes this is not possible or recommended either. Here we propose an alternative, using cubic spline interpolation functions, which link together the discrete values (counts, densities, or resources used by species or their abundance in the environment) and then we aply integral calculus on the plotted functions. We estimate values and statistics of parameters that we use further for other purposes. For instance, the niche matrix might be used along with functional traits, environment and community data-tables in double-constrained correspondence and variation partitioning analyses. We show how this can be done and illustrated using Mathcad and other software.

Acknowledgments: contribution developed within the project financed by Lucian Blaga University of Sibiu & Hasso Plattner Foundation research grants LBUS-IRG-2019-05