Thesis Format
Monograph
Degree
Master of Science
Program
Applied Mathematics
Supervisor
Zou, Xingfu
Abstract
The age and weight at maturation are crucial traits in an organism’s life cycle, influencing its growth, survival, and reproduction. We propose a biphasic energy allocation model, distinguishing pre-maturity and post-maturity, to study the mechanisms of maturation and estimate the age and weight at maturation. This model is parameterized for female lake whitefish (Coregonus clupeaformis). We compare different functions involved in the model, estimate parameters, and do sensitivity analysis. Our results indicate that (i) weight at maturation is positively related to the fraction of energy allocated to growth which, by data fitting, is almost a constant; (ii) age at maturation is highly sensitive to the coefficient and exponent in the energy assimilation rate; (iii) higher energy conversion efficiency to weight can lead to earlier maturation with larger weight. Additionally, the results offer new insights into the ratio between asymptotic weight and mature weight across populations.
Summary for Lay Audience
Fish maturation is a fundamental topic in ecology and fisheries management. Fish maturation is influenced by how they allocate their energy between various life processes, particularly growth, storage, and reproduction. Understanding these energy allocation strategies is crucial for predicting fish age and weight at maturation, which has significant implications for managing fish populations and ensuring sustainable fishing practices.
Researchers have found that energy allocation shifts from growth to reproduction as organisms mature. Initially, surplus energy supports growth, but as fish approach maturity, energy is increasingly redirected toward developing reproductive organs and supporting reproductive behaviours. For example, early maturation often means that an organism allocates more energy to reproduction at a younger age, leaving less energy available for growth. As a result, early-maturing fish may be smaller in size compared to those that mature later. However, early-maturing fish can start reproducing sooner, potentially producing more offspring over their lifetime. This can be advantageous for reproduction, although the survival probability of the offspring may be lower due to their smaller size.
While verbal descriptions suggest that energy allocation shifts from growth to reproduction as fish mature, these ideas have not been rigorously analyzed and may be inaccurate. To provide a more thorough analysis of the mechanisms behind fish maturation, this study uses a mathematical model to explore how fish allocate their energy between growth storage and reproduction, and how this affects their age and weight at maturity. Focusing on lake whitefish as a case study, the study highlights the complex and dynamic interplay between energy allocation, energy conversion, and maturation thresholds in different populations. These factors collectively determine the age and weight at which fish mature, offering new insights that can help in the effective management and conservation of fish populations.
Recommended Citation
Zhang, Siyi, "Impact of Energy Allocation on Fish's Age and Weight at Maturation by Mathematical Models" (2024). Electronic Thesis and Dissertation Repository. 10361.
https://ir.lib.uwo.ca/etd/10361
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.