Spatial Dispersion Point Pattern Analysis

Point data can be used to represent

• Locations of individuals • Nest sites • Patches of habitat

Point pattern analysis

asks about the dispersion of points, whether this varies with scale, and the causes of these patterns

Types of questions we might ask with point pattern analysis:

Simple (basic point pattern): ➢ Are trees clumped? (e.g. due to patchy resources) ➢ Do individuals show signs of “repelling" each other? (e.g. due to territoriality or competition)

Point patterns analysis Basic Steps:

1) Observe the point pattern 2) Describe/summarize the point pattern 3) Model the potential underlying point process 4) Use simulations to evaluate whether the observed point pattern is consistent with the hypothesized point pattern

point pattern

consists of the coordinates for a set of points as well as the boundary or window of analysis

First-order statistics (in step 2)

describe how the number of points vary across the region of interest without focusing on interactions among points

Intensity (in relation to first order statistics):

Expected number of points per unit area (under a point process model)

Density (in relation to first order statistics):

Observed number of points per unit area (what you get)

Quadrat counts (1st order statistics observed point patern then do this)

estimated density across space

Intensity surface (1st order statistics observed point patern then do this)

estimate of intensity i.e created using kernel density estimation / expected number of points across landscape

Second-order statistics (step 2)

describe how points relate to each other in space, often based on distances Focused on describing extent to which points are near each other • Common metrics: ➢ Ripley’s K-function (and L) ➢ Pair correlation function (g-function) ➢ Nearest-neighbour distribution function (G-function)

Ripley’s K-function (step 2)

For a given focal point, K(r) measures the expected number of points within a circle of a given radius, r, scaled to average intensity

g-function (step 2)

For a given focal point, measures the number of other points a certain distance, r, away. K(r) measures cumulative clustering whereas g(r) looks at local clustering an exact distance away

Complete spatial randomness (CSR) model (setp 3)

CSR is the null point process model for many point pattern analyses It assumes that points are distributed a) independently of one another b) uniformly across space such that each point has equal probability of being anywhere in the study area The CSR is a type of Homogenous point process, which means ➢ Intensity (expected number of points per unit area) is constant across space ➢ The probability of finding a point does not depend on location

Test statistical significance (step 4)

Returning to Ripley’s K plot, the dashed line is our expectation under CSR Our observed line (solid) is above the expected line at every r…can we conclude we have clustering of points?

Simulations under the CSR (step 4)

Simulations allow us to generate many realistic realizations of the CSR accounting for random variability due to: ➢ Sample size ➢ Shape/size of our window ➢ Edge effects. Simulated realizations are used to create a Monte Carlo confidence envelope around expectations under our null model Used to assess whether our observed value at any given radius is statistically meaningful or just random noise