Quadrat Count Analysis

What is Quadrat Count Analysis?¶

Quadrat Count Analysis is a method used in spatial point pattern analysis to determine whether a pattern of points is randomly distributed, clustered, or evenly spaced. It involves dividing the study area into smaller, equal-sized areas called “quadrats” (typically square or rectangular in shape) and counting the number of points fall in each quadrat.

Calculating Quadrat Count¶

The main steps in Quadrat Count Analysis are:

1. Divide the study area into a grid of quadrats.

2. Count the number of points in each quadrat.

3. Calculate the expected number of points per quadrat under the assumption of Complete Spatial Randomness (CSR).

4. Compare the observed frequency distribution (the counts) with the expected frequency distribution (under CSR) to assess the degree of similarity or difference between them.

5. Apply statistical tests, such as the chi-squared goodness-of-fit test, to determine whether the observed frequency distribution significantly differs from the expected distribution under CSR---whether the spatial pattern exhibits randomness, clustering, or regularity.

Count the number of points in each quadrat¶

Then, how to compare?

Chi-squared test¶

Use Chi-squared test, which is suitable for comparing frequencies.

The quadrat method partitions the study region into $r$ rows and $c$ columns, which define $m=r\times c$ non-overlapping subregions or quadrats of equal area. This method relies on the fact that, under CSR, the expected number of observations within any region of equal size is the same. Let $n$ be the number of observed points, $m$ the number of quadrats of equal size, and $n_i$ the number of points in quadrat $i$. The expected number of points in each quadrat is $N/m$. The test statistic is calculated as

Why?

A CSR would have a mean at the average with a non-zero spread (non-zero deviation).

Use Chi-squared test, which is suitable for comparing the frequencies against an expected frequency or distribution.

Clustered example

• chi-squared statistic$= 354.332$, p-value$= 2.606e-66$$

• significantly different from random

Random example

• chi-squared statistic$= 19.332$, p-value$= 0.199$

• non-significant; the distribution is not different from random

Regular example

• chi-squared statistic$= 8.332$, pvalue$= 0.910$

• non-significant; the distribution is not different from random

Since the expected number of points are the average number of points---the test do not consider the spread mathematically---thus the regular example ‘is not different from random’.

Key considerations¶

Some key considerations in Quadrat Count Analysis include:

• Quadrat size: The size of the quadrats should be carefully chosen to ensure that it is appropriate for the scale of the pattern being studied.

• Quadrat shape: While square quadrats are common, other shapes (such as rectangular or circular) may be used depending on the specific study requirements.

• Edge effects: Care should be taken to account for edge effects, which occur when quadrats at the edge of the study area contain fewer points due to the smaller overlapping area.

Is the analysis result sensitive to the parameter settings?

Quadrat Count Analysis provides a simple and intuitive approach to analyzing spatial point patterns, but it has some limitations compared to more advanced methods, such as distance-based or density-based approaches. Nonetheless, it is a useful tool for exploratory analysis and can be helpful in understanding the general characteristics of a spatial point pattern.