# Sampling principles for biodiversity study

## TL;DR

This paper introduces five key principles for biodiversity sampling to improve ecological studies and biodiversity measurement.

## Contribution

The paper proposes five novel sampling principles for biodiversity study that address overlooked foundational concepts.

## Key findings

- The number of species and individuals increases with the sampled area.
- The sum of species in two areas is no less than the total species in the combined area.
- Mathematical expectations of species and individuals in sub-areas align with totals in the full area.

## Abstract

Sampling is a fundamental tool in ecology and critical for biodiversity measurement. However, basic principles of biodiversity sampling have been overlooked for many years. In this paper, I proposed and explored five principles of sampling for a specific area and biodiversity study. The first principle of sampling, species increasing with area, is that the number of species increases with the area. The second principle of sampling, individuals increasing with area, is that the number of individuals increases with the area. The third principle of sampling, sum of species number, is that the sum of species number in one area and species number in another area is no less than the total species number in the two areas. The fourth principle of sampling, individual complement, is that the sum of the mathematical expectation of individual number of one or several species in the area a and that of the same one or several species in the area A-a is the total individual number N of the same one or several species in the total area A. The fifth principle of sampling, species-area theory, is that the sum of the mathematical expectation of number of species in the area a and that of number of species lost if area A-a is cleared is the total species number M in the total area A.