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Nearest Neighbour Analysis

An example of the search for order in settlement or other patterns in the landscape is the useof a technique known as nearest neighbour analysis. This attempts to measure thedistributions according to whether they are clustered, random or regular. Nearest neighbouranalysis may be used in sand dune vegetation succession studies to test the hypothesis that'the stone pine woodland forms the climax community'. Here, tree distribution may be expectedto be random, rather than the regular pattern expected if the trees had been deliberatelyplanted as part of a sand stabilisation scheme.

The nearest neighbour formula will produce a result between 0 and 2.15, where the followingdistribution patterns form a continuum:

The formula used is as follows:

Key

nearest neighbour value

mean observed nearest neighbour distance

area under study

total number of points

Methodology

1. Select an area of woodland using random numbers, and mark out a 30m X30m (900m)quadrat.This should be sufficient to obtain a minimum number of 30 trees (see minimumsample size below).

2. Measure the distance of each tree within the quadrat to its nearest neighbour as illustratedbelow:

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3. Apply the above formula.

Example using a 20 x 20m quadrat with 18 trees:

Tree No. Distance to nearest neighbour (m)

1 4.10

2 5.75

3 3.00

4 3.80

5 3.58

6 3.12

7 2.20

8 2.20

9 3.87

10 2.40

11 2.40

12 3.75

13 4.20

14 1.83

15 3.10

16 0.98

17 0.98

18 2.51

Total 53.77

2.99

400m

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1.27

This 1.27 Rn value (which becomes 1.32 when reworked with an alternative nearest neighbourformula provided by David Waugh) shows there is a tendency towards a regular pattern of treespacing.

However, with fewer than 30 trees, it is difficult to to say with any confidence that thedistribution has this regular distribution tendency, and the pattern may have occurred bychance. The Rn value lies within the yellow shaded area on the diagram below and thereforehas a random distribution at the 95% probability level. The Rn valuemust lie outside theshaded area before a particular distribution pattern can be accepted as significant.

Interpretation of Rn statistic: significant values (after David Waugh, with thanks)

Assumptions

1. There has been no new natural pine germination since the planting (if any) of the woodland.

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