Research Interest

My primary research arena can be classified into two broad domains, viz. (1) Statistical/ Mathematical Ecology and (2) Experimental Biology. By training, I am a Mathematician, but during my master's degree, I got in touch with some of the fundamental aspects associated with ecology, where mathematical modeling and the statistical inferential procedure is highly demanding with challenging datasets involving facet of experimental and field oriented studies. 

Statistical / Mathematical Ecology

The growth curve can be broadly classified into two categories: density independent and dependent. The simplest law of population growth is characterized by the constant per-capita growth rate (henceforth, PGR), leading to an exponential function, popularly known as Malthusian law (Malthus, 1798). This is the first member of the density-independent family. The density-dependent models refer to the population dynamics with growth rate depending on population size or density functions. Hence, the relationship between per capita growth rate and abundance of a population has fundamental implications in population dynamics and different areas of ecology. Sibly (Science, 2005) undertook an ambitious analysis of this problem by examining growth rates of 1780 time series of 674 species of four taxonomic groups, namely, birds, mammals, bony fishes, and insects from the Global Population Dynamics Database (NERC Centre for Population Biology, Imperial College, 2010).  

Species growth models account for two opposite factors that govern population dynamics: (1) the natural proclivity of the species population for exponential (Malthusian) growth and (2) a negative density-dependence feedback governed by the environmental carrying capacity (K), which restrains population growth. However, Sibly's proposition on the density-PGR relationship of species & their cooperative behaviors is well explained through two density-regulated models the theta logistic growth equation & an extended theta logistic model (Bhowmick et al., 2015) respectively. An extended density regulated Allee equation is equally essential for modeling species growth. Nevertheless, the models discussed so far are all deterministic and ignore the environmental fluctuations. When the typical size of the population is large, fluctuations in the observed number of individuals are typically small in the absence of external or environmental noise. Many factors influence the sources of these fluctuations, viz., intrinsic noise, the discreteness of individuals, and the stochastic nature of the species interactions (Golec, 2003; Chakraborty et al., 2017), etc.

In the case of the logistic equation, the population evolves from an initial condition to a stable stationary state, where the population size equals the carrying capacity and will persist forever. Nevertheless, due to the small population size, internal fluctuation plays the role of a positive catalyst for the extinction of the species. The effects of internal fluctuations have been studied in predator-prey models, epidemic models, cell biology, and ecological systems. Moreover, the extinction of a stochastic population plays a vital role in population biology and epidemiology, which has also attracted scrutiny in cell biochemistry and in physics (Gardiner, 1990). So the research area on the stochastic growth curves has been rising over time.

Moreover, Genetic variation, individual stress, and adaptability of the species etc., are also affected by demographic & environmental fluctuations, which are well explained in Bhowmick et al. (2014), and Chakraborty et al. (2017). So, stochasticity can be introduced in the growth curve models through these parameters, and the modified model can then be interpreted as a non-autonomous stochastic differential equation. Hence, it will be better to develop some environmental bound so that the model is stochastically asymptotically stable and synergistic with the Lyapunov stability concept in the deterministic case. So, the motto of our present research on the Statistical/Mathematical Ecology is to represent the extended deterministic through Ito-type differential equation by introducing the standard Brownian process.  

Recently, we have been dealing with the stochastic analog of the theta-logistic growth dynamics. Since Sibly et al. (2005) described that most species have a fundamental characteristic of following the theta-logistic growth trait with the convex downward trend. The fundamental yardstick of this research work builds under the deterministic setup, whereas the involvement of the external noise in any growth system is inevitable. However, the involvement of external affairs in any species growth can't be well judged only through its density dependence; it requires a further assessment. So, we frame the theta-logistic model with the stochastic analog in two directions, i.e., the discrete and continuous setup. The analysis of the discrete stochastic model is manifested by the bifurcation analysis, which shows that the attainment of the chaotic regime enhances with the increase in noise intensity. Although the role of chaos in species extinction is debatable, a literature survey suggests that chaos with stochasticity accelerates the extinction of species.

Similarly, in the case of the continuous version, we performed a theoretical study on the stochastic theta-logistic model to provide a critical value of the noise intensity parameter. This threshold magnitude act as the sustainability criteria of any species environmental tolerability. In this connection, we use the data of four major taxonomic groups, i.e., Bird, Insect, Mammal, and Fish, from the GPDD database and classify the species based on environmental sensitivity. The high sensitive species have a low tolerance level, associated with the small magnitude of environmental noise intensity parameter. Moreover, the simulation prediction model for these four taxonomic classes also shows that the overall extinction probability of the considered birds in our research is almost negligible for the current time window (2021). However, we are also involved in producing a new growth metric apart from the per-capita growth rate to capture the species precise growth status. It is worth mentioning that PGR is treated as the proxy of species fitness. So, the precise growth information can't be captured through the PGR metric when any species undergoes any adaptation. In this connection, we will try to develop such a growth measure that can build a connection to the species precise growth status with its fitness structure. Apart from the single species dynamics, our present research also includes the prey-predator interactions. We are mostly interested in bringing sustainable criteria under the light of a stochastic environment so that the species can be recovered from its extinction threat.

Experimental Biology

Satisfying the consumers' load for foods cost-effectively is a tremendous challenge for the hatchery industries. Since hatchery industries always search for new ideas or techniques to achieve their desired goals. Extensive uses of different phytoplankton and zooplankton as live foods for the shrimp and fish hatcheries enlighten the importance of the regular maintenance and monitoring of the plankton's live cultures. Artemia sp. is prominent zooplankton used widely in hatchery industries and aquaculture research for the high dietary values of its cysts, nauplii, and adults. The market demands for Artemia sp. are rising equivalently with the increasing popularity of aquaculture.

Theoretical explorations on the growth process of species to identify the inherent growth mechanics and minute differences among the growth profiles. Consequently, the species' growth process needs extensive laboratory iterations and optimizations to get the maximum yields. Hence, analysis of the growth trajectories through theoretical approaches makes the processes easy to optimize the high yielding and economic growth conditions for the hatcheries with minimum laboratory iterations. However, the iteration process imparts enormous costs to the entire culture protocol, and the hatchery people need to fulfill the market demands cost-effectively. So, we will try to figure out the optimal conditions for Artemia sp. culture based on experimental and modeling knowledge.