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How biologists use mathematics to unravel the mysteries of population dynamics.
As the global population continues to grow, ecologists are paying more and more attention to the study of population dynamics. Mathematical models are one of the tools that allow biologists to gain a clearer understanding of how biological populations change over time and how various factors interact to affect biological populations. These models are not only useful for understanding biodiversity, but can also play an important role in protecting endangered species and managing resources.
Models can provide a way for people to understand complex interactions and processes.
In the late 18th century, biologists began to develop population models in order to understand the dynamics of how various populations of organisms grow or shrink. Early biologists, notably Thomas Malthus, observed that population growth followed a geometric pattern and were thinking beyond the future of humanity. He speculates that many biological populations in nature face similar pressures and challenges.
The most basic and landmark population growth model is the logistic growth model proposed by Pierre-François Verhuister in 1838.
Wehrhuis's model, characterized by an S-shaped curve, describes three main stages of population growth: initial exponential growth, followed by a slowdown in growth, and eventually approaching the carrying capacity of the environment. The proposal of this theory laid the foundation for subsequent ecological research.
In the early 20th century, the development of various population models further prompted biologists to pay attention to interactions in nature and how humans affect ecosystems. As populations in parts of Europe grew rapidly due to limited food resources, biologist Raymond Pearl began to study the issue. In 1921, he invited physicist Alfred J. Lotta to collaborate, and Lotta developed a pair of differential equations to model the interaction between parasites and their prey.
The Lotaka-Volterra model, developed together with Vito Volterra, explores the relationships between species such as competition, predation and parasitism.
In 1939, biomathematician Patrick Leslie's contributions advanced the precision and scope of population modeling. He stressed the importance of life tables, a tool for summarizing the dynamic characteristics of biological populations at different stages of life. By combining matrix algebra with life tables, Zhang Hua further expanded Lotaka's work, allowing population models to more accurately calculate the growth of biological populations.
Over time, biologists have adapted and refined these models so that they can account for unique ecological situations that arise in the real world. The study of island biogeography was led by Robert MacArthur and E. O. Wilson, who developed equilibrium models that explained how species on isolated islands reach a balance with immigration and extinction.
Today, the logistic growth model, the Lotaka-Volterra model, the life table matrix model, etc. have become the basis of current ecological population models.
The use of these models not only enables us to better understand the laws governing the operation of nature, but can also play an important role in many practical situations. For example, in agriculture, producers can use models to calculate optimal harvest amounts; in environmental protection, conservation organizations can track changes in endangered species through population models to develop conservation measures. In addition, the model also provides key data for analyzing the spread of diseases, which is particularly important in preventing epidemics.
Through these mathematical models, biologists have unravelled many of the mysteries of population dynamics in nature. But at the same time, we should also reflect on whether these models can really help us find a more sustainable way of survival in the face of increasingly severe environmental challenges?
