Introduction

A student in the lab murmured, "Wow! There are four of them...". It is said that Rathkea octopunctatathe, which was collected yesterday and separated into containers one by one and started rearing experiments, split into two individuals on the same day, and further increased to four individuals today. I calculated 2³⁰ to see how many individuals there would be after 30 days if the number of individuals were to double every day at this rate, and the result was 1,073,741,824, or about 1 billion individuals. (Even the implicitly rounded figure of over 70 million is surprising enough.) Organisms have potentially high reproductive power. However, the earth is not yet filled with living things. What are the factors that keep them from growing?

population
　A spatial group of organisms of the same species is called a population.「The unit "species" can be said to be a breeding population divided by reproductive isolation (although the actual definition varies and the reality seems to be even darker).

And there is no spatial division between species. A population refers to a breeding population that is not only of the same species, but also of geographical unity. Populations are generally larger than families or herds. And many species are made up of multiple populations. Immigration and emigration can also occur by moving individuals from one population to another.

Population dynamics: Time variation of population size
　Now, among the various characteristics that a population has, the most basic characteristic is the number of individuals. The number of individuals in a population as a whole is called the population size. . The number of individuals per unit of something like given space (e.g. area or volume) or given resource (e.g. one seaweed, one shell) is called density. Population dynamics refers to changes in population size and density over time, that is, the increase or decrease in the number of individuals in a given population. Here, in order to consider the factors that determine population dynamics, I will introduce the most basic formulas that express population dynamics, that is, mathematical models.
　In addition, I think that the meaning of the formulas will be easier to understand if it is possible to "visually" see how the number of individuals changes over time using these formulas.In the following pages, I would like to use a diagram, but I will also briefly explain the free software R "spell" so that you can draw the diagram yourself. For explanations of the basic operations of R and statistical analysis methods in R (which is the original function), please see the following explanation site.