Piecewise Exponential Survivor Function, Intrinsic Rate of Growth and Stable Population for Blue Whales (Balaenoptera Musculus): A Case Study
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Date
2022-04
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Abstract
This study delves into blue whale population dynamics and demographic modeling, emphasizing the repercussions of historical industrial hunting and the subsequent population decline. Employing continuous demographic models, we calculate intrinsic growth rates, construct life tables, and formulate stable population models. The research underscores the immense significance of blue whales, Earth's largest inhabitants, and emphasizes the drastic reduction in their population due to extensive commercial whaling during the 20th century. Using the piecewise exponential survivor function, a fitting tool for demographic modeling, we derive crucial demographic parameters and compare various models. Our findings underscore the precision and appropriateness of the piecewise exponential model, particularly in predicting demographic parameters for blue whale populations. Projections based on this model illuminate the slow recovery of the blue whale population, emphasizing the enduring impact of past exploitation.
Furthermore, we elaborate on our research approach, employing specific biological models as condensed case studies to captivate students and elucidate continuous demographic models during lectures on demography and life table analysis at the Department of Statistics, Technical University of Dortmund. It is essential to clarify that while our specialization lies in statistics and demography, our expertise is primarily centered within these domains rather than biology.
The analysis is founded on the piecewise exponential survivor function, proving to be a fitting choice for demographic modeling of blue whale populations, especially when data on mortality is limited and the primary objective does not involve analyzing the distribution of old age or estimating the maximum age. An advantageous feature of this simple function is its ability to yield fundamental formulas for key demographic parameters. Additionally, we illustrate our approach using the logistic function as a specific example, providing a tangible and insightful demonstration for our students.
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Keywords
blue whale population dynamics, population biology, life table, piecewise exponential model, demographic modeling
Subjects based on RSWK
Populationsdynamik, Blauwal, Demographie, Ãœberlebungsfunktion, Sterbetafel, Populationsbiologie