Spatial Analysis

Chapter One

Spatial Analysis

• Patterns of spatially distributed points.

• Correlation with environmental variables.

• Interpolations and predictive models.

• Spatial autocorrelation -> spatial patterns, aggregation. Based on distance to neighbors. Kaplan-Meier estimator, Moran’s I.

• Spatial Interpolation -> estimate variables in unknown locations based on known locations. Krigging.

• Spatial Regression -> regression analysis considering spatial relationships.

• Spatial Interaction -> Gravity models. Spatially explicit interactions. Movement patterns, people movement, vehicle traffic. Fish schools and bird flocks. Game theory.

• Simulations.

Why do we care about this???

• Analyzing distributions and factors shaping them.

• Predicting locations.• Relative influence of factors in distributions.• Variation in pressure to understand selection

and evolution.

Today…

• Generate random points in a plot, using Poisson Distribution.

• Analyze the aggregation pattern of points using the Kaplan-Meier Estimator.

• Use a Chagas’ Disease data set.

Poisson Distribution

• Discrete probability distribution.• Rare events.

• Use in spatial analysis is a generalization, based on λ -> “intensity” of event occurrence.

Kaplan-Meier Estimator

• Estimation of distance distribution.

• Calculation of G(r) random distribution of nearest neighbor distance in a given space.

• Compare the observed distribution with the random G(r)

The Data Set

• Chagas Disease vectors Spatial Distribution -> Maria Victoria Suarez (PUCE).

• Look for the relationship between human settlements and spatial distribution of Chagas disease vectors in the surrounding natural areas.

Chagas Disease

• Tropical Disease caused by Trypanosoma cruzi

• Vector -> Triatomine hemipterans.

• Chronic disease. Lethal causing liver and/or heart failure

Methodology

• Random sampling of nests and palm trees in a 600x600m plot, adjacent to a human settlement in natural or semi-natural habitat.

• Compare the distribution of positive points, with the random expected distribution using G(r)