5 Principles of Population Ecology Applied to Human Populations | 应用于人类种群的人口生态学五原理

📚 5 Principles of Population Ecology Applied to Human Populations | 应用于人类种群的人口生态学五原理

Population ecology studies how populations change over time. When applied to human populations, its principles become powerful mathematical models. In Edexcel A-Level Mathematics, tools such as exponential functions, differential equations and matrices allow us to analyse population growth, carrying capacity, density dependence, age structure and demographic transition. This article presents five core principles with worked examples and exam-style tips.

人口生态学研究种群如何随时间变化。将其原理应用于人类种群，就得到了强大的数学模型。在 Edexcel A-Level 数学中，指数函数、微分方程和矩阵等工具使我们能够分析人口增长、承载力、密度制约、年龄结构和人口转变。本文介绍五个核心原理，并配有例题和考试技巧。

1. Overview of Population Mathematics | 人口数学概述

In population ecology, the size of a population N changes as births, deaths and migration occur. The instantaneous rate of change is given by dN/dt = B – D + I – E. For a closed population with no migration, this simplifies to dN/dt = (b – d)N, where b is the per capita birth rate and d is the per capita death rate. The difference b – d is called the intrinsic rate of increase, denoted by r.

在人口生态学中，种群大小 N 会随着出生、死亡和迁移而变化。瞬时变化率由 dN/dt = B – D + I – E 给出。对于无迁移的封闭种群，这可简化为 dN/dt = (b – d)N，其中 b 是人均出生率，d 是人均死亡率。差值 b – d 称为内禀增长率，记作 r。

dN/dt = (b – d)N

r = b – d

Human populations are open systems, but for many modelling purposes we begin with the closed-population assumption. This allows us to use simple differential equations before adding migration terms. In A-Level questions, you are often asked to set up such equations from given birth and death rates.

人类种群是开放系统，但在许多建模中我们先采用封闭种群假设。这样可以使用简单的微分方程，之后再加入迁移项。在 A-Level 题目中，经常要求根据给定的出生率和死亡率建立这类方程。

2. Principle 1: Exponential Growth Model | 原理一：指数增长模型

If r is constant and positive, the population grows exponentially. The differential equation dN/dt = rN has the solution N(t) = N₀ exp(rt), where N₀ is the initial population size at t = 0. The graph of N against t is an increasing exponential curve.

如果 r 恒定且为正，种群呈指数增长。微分方程 dN/dt = rN 的解为 N(t) = N₀ exp(rt)，其中 N₀ 是 t = 0 时的初始种群大小。N 对 t 的图像是一条递增的指数曲线。

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