## Population dynamics models that capture interactions among living organisms

There are currently about 1.75 million known species of living organisms on Earth. Including unknown species, the data suggests that there are nearly 9 million different organisms; the magnitude of this number is difficult to comprehend. However, the population of living organisms has decreased by approximately 70% in the last 50 years owing to climate change, environmental pollution, overexploitation of plants and animals, deforestation, and invasions of alien species. It is estimated that as many as 40,000 species face extinction annually.

Biodiversity conservation is crucial for achieving a sustainable society and is a global priority. Researchers in the field of mathematics can contribute to this effort by using population dynamics models, which employ mathematical equations to describe changes in population size (e.g., number of individuals, biomass, density) over time and space. The models can be used to predict the behavior of species, which can help develop effective strategies to conserve biodiversity.

Species interact in various ways. They may compete for food or cooperate for common or mutual benefits. There are also predator/prey relationships between two species, where one species eats the other.

The Lotka-Volterra system is a mathematical model describing the population dynamics of interacting species. It was proposed about 100 years ago and is now the leading model presented in ecological textbooks. Originally designed to capture population fluctuations of species in a predator-prey relationship, another model for competing species was later derived, known as the Lotka-Volterra competition system.

Since then, numerous models have derived from the Lotka-Volterra system to describe how species interact and have produced valuable knowledge that has contributed to biodiversity conservation, including the coexistence of multiple species.

## Existing mathematical models may not work under complex situations

While population dynamics models are useful, it does not mean existing models work well in every case.

The focus should be on “niche” (ecological status), the position in an ecosystem occupied by a species. Every living organism requires an environment that is essential to its survival, such as food and habitat for animals, sunlight and soil for plants, and so on. When the niches of different species overlap, it becomes difficult for them to coexist for long periods owing to competition and predator-prey interactions for the survival of each species.

Controlling factors such as the rate of growth and spatial migration of biological species is possible through human intervention. However, manipulating the niche itself is not as straightforward. Especially when highly competitive species occupy the same niche, the difference in species competitiveness may determine their future regardless of other factors. These findings were obtained by fitting various parameters (variables) to a population dynamics model and analyzing the resulting data.

The Cabinet of Japan approved the ‘The National Biodiversity Strategy of Japan 2023-2030’ in March 2023. One of the measures to protect diverse biological niches is the management of ‘green corridors.’ This aims to conserve biodiversity by connecting habitats fragmented by human social activities and enabling the movement of animals.

We require new population dynamics models to explore how species migrate in complex networks of habitats connected by the corridor. Mathematical ecology is making rapid progress while keeping abreast of these social changes.

## Aiming for highly accurate analysis through collaboration with other fields and utilization of AI

There are two main categories of mathematics: pure mathematics and applied mathematics. Pure mathematics is the study of abstract concepts in mathematical fields, such as algebra, geometry, and analysis. Applied mathematics is the discipline that applies mathematical theory to natural sciences, social sciences, and industry. In Japan, pure mathematics had been regarded as superior to applied mathematics, although they were treated equally in other countries.

However, in recent years, there has been a growing movement in Japan to apply mathematical findings to various fields. In May 2006, the Ministry of Education, Culture, Sports, Science and Technology (MEXT) issued a report titled Forgotten Science – Mathematics. The report highlighted the difficult situation of mathematics research in Japan and expressed enthusiastic expectations for interdisciplinary efforts between mathematics and other fields. Developing mathematical theories is crucial, but the key to mathematical research will be how to return findings to society.

In addition to preserving biodiversity, there are many other ways to utilize mathematics. Let us look at a specific example in the medical field.

The human body maintains a constant internal environment through a function called homeostasis. After eating, blood glucose levels rise, but in a healthy person, they eventually fall and remain stable. However, when the pancreas does not produce enough insulin and blood glucose levels become abnormally high, it leads to a diagnosis of diabetes. Thus, disruption of homeostasis makes people susceptible to disease, but the detailed mechanism has yet to be fully understood. Mathematical models are expected to provide clues for understanding the mechanism. Collecting data from patients is a time-consuming process. However, mathematical models can perform a vast amount of analysis in a short period without burdening patients. As mathematical models are applied, they should help prevent various diseases in the future.

Furthermore, I want to highlight the potential of AI in the future. For instance, though measuring population growth or decline in a habitat can be challenging, AI can estimate various parameters and incorporate them into population dynamics models. With advances in AI technology, open problems in mathematics may eventually become solvable.

Although mathematical models can now be used to simulate various phenomena, mathematics is still not powerful enough to analyze complex phenomena and must continue to develop. I hope that groundbreaking breakthroughs will be produced, whether by humans or AI.

* The information contained herein is current as of December 2023.

* The contents of articles on Meiji.net are based on the personal ideas and opinions of the author and do not indicate the official opinion of Meiji University.

* I work to achieve SDGs related to the educational and research themes that I am currently engaged in.

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