Estimation of growth regulation in natural populations by extended family of growth curve models with fractional order derivative: Case studies from the global population dynamics database

• Published in: Ecological informatics Vol. 53; p. 100980
• Main Authors: Bhowmick, Amiya Ranjan, Sardar, Tridip, Bhattacharya, Sabyasachi
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-09-2019
• Subjects: Memory; Model selection; Population time series; Posterior distribution; Return rate; Return rate; Model selection; Memory; Posterior distribution; Population time series
• ISSN: 1574-9541
• DOI: 10.1016/j.ecoinf.2019.100980

Estimating the trend in population time series data using growth curve models is a central idea in population ecology. Several models, mainly governed by differential or difference equations, have been applied to real data sets to identify general growth pattern and make predictions. In this article, we analyze ecological time series data by fitting mathematical models governed by fractional differential equations (FDE). The order of the FDE (α) is used to quantify the evidence of memory in the population processes. The application of FDE is exemplified by analyzing time series data on two bird species Phalacrocorax carbo (Great cormorant) and Parus bicolor (Tufted titmouse) and two mammal species Castor canadensis (Beaver) and Ursus americanus (American black bear) extracted from the global population dynamics database. Five different population growth models were fitted to these data; density-independent exponential, negative density-dependent logistic and θ-logistic model, positive density-dependent exponential Allee and strong Allee model. Both ordinary and fractional derivative representations of these models were fitted to the time series data. Markov chain Monte Carlo (MCMC) method was used to estimate the model parameters and Akaike information criterion was used to select the best model. By estimating the return rate for each of the time series, we have shown that populations governed by FDE with a small value of α (high level of memory) return to the stable equilibrium faster. This demonstrates a synergistic interplay between memory and stability in natural populations.
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•Fractional order derivative was used to incorporate memory in population process•Time series data were analysed using fractional differential equation•Comparison with the ordinary differential equation models was carried out•Explored the interrelation between memory and growth intrinsic growth rate•The evidence of memory was exemplified by the estimating the return rate