Cooperation in species: Interplay of population regulation and extinction through global population dynamics database

Abstract

Throughout the history of evolutionary process cooperation has played a significant role in species sociological development and social groups are more likely to be survived than individuals in apparently unfavorable conditions. We bring in the concept of cooperation and introduce a new parameter γ in the generalized theta-logistic equation to model non-monotonic behavior of per capita growth rate. This phenomenological modeling approach highlights the interplay of two opposing forces, namely, the positive effect of cooperation and the negative density dependence (competition). Sibly et al. (2005) found that, the density dependent population growth curve seems to be concave in most animal populations, and follows the theta-logistic equation. To explore this phenomenon further, we investigated 715 time series from global population dynamics database and identified 28 cases, where, incorporating intra-species cooperation as an allometric trait into the logistic improves the description of the population growth. Nonlinear regression and bootstrap resampling technique were used to estimate the model parameters during the fitting of real data and the mean square error was used to compare the fitting performance of theta-logistic model and the model with cooperation. This study may help to identify the presence of cooperation from species growth profile obtained from census data. The numerical estimate of cooperation parameter and its threshold value can be used as a potential tool to decide the optimal management action in species conservation. The stability and bifurcation analysis are used to choose the critical value of γ above which the risk of extinction is high. The illustration has been provided by means of simulation and real data.