# Difference between exogenous and endogenous spatial autocorrelation

I was reading a paper recently and came across the following paragraph:

Autocorrelated distribution patterns may arise in two non-mutually exclusive ways; endogenous autocorrelation is caused by contagious population processes such as local dispersal, while exogenous autocorrelation (or spatial dependence) results from independent responses to autocorrelated environmental gradients

Could anyone be able to provide a detailed and preferably simple (laymen's term) explanation to the difference between exogenous and endogenous spatial autocorrelation?

• I understand this is about spatial autocorrelation even though this was mentioned only once at the end of the original post. I tried to make it more visible. If I am wrong, please feel free to correct it. Nov 10 '15 at 14:30
• Could you please add the source of article/paper this came from. Feb 28 '17 at 10:08

The examples you gave are, in fact, examples of spatial autocorrelation.

Exogenous spatial autocorrelation comes from environmental factors showing spatial patterns. For example, if you looked at annual average primary productivity of plants on a global scale you'd find a general increase with decreasing latitude; that is, greater productivity nearer the equator. This is due to the gradient of increasing incoming solar radiation from the poles to the equator, which also leads to an increasing temperature gradient - both of which contribute to plant growth rates.

In statistical analysis, if you've specified a linear model that identifies all the environmental factors affecting what you're studying, the spatial autocorrelation will be "in" one or more of your predictor variables. The residuals should therefore not be spatially autocorrelated (as assessed from a semivariogram, or similar), and are therefore independent - so the assumption of residual independence in ordinary least squares estimation of parameters should be met.

Endogenous spatial autocorrelation most often, at least in biology, comes from genetic (or culturally inherited) factors. Using the dispersal example you suggested: imagine that a plant species develops a genetic mutation that increases growth rate and thus increases the number of seeds that the plant can produce, relative to others. Plant seeds can be dispersed by a number methods, such as wind, animal transport, and physical force (seed heads that 'pop' open). Regardless of method, seed dispersal would carry the beneficial mutation gradually further away from the original plant over successive generations. There may also be barriers to dispersal that prevent seeds with the mutation from colonising new areas - a large river or road, for example - which would contribute to the spatial pattern. As this dispersal process occurs over successive generations, you would expect to see plant populations that are nearer the original mutated plant to exhibit higher productivity than those that are further away from the original plant.

In statistical analysis - even once you include all the environmental factors that you know influence plant growth, there will still be spatial autocorrelation in the residuals. This means that the assumption of residual independence is not met, and must be accounted for via another means - for example, using generalised least squares estimation, which can explicitly account for autocorrelation.

Of course, if you included the genetic factors as a term in your model then the autocorrelation would disappear from the residuals. I don't mean to suggest that endogenous autocorrelation always remains in residuals - rather that you need to include factors arising from the object of study itself in order to account for it. To reiterate, in biological sciences, these are typically genetic or cultural factors. With exogenous spatial autocorrelation, on the other hand, you only need to include factors external to the object of study to account for the autocorrelation.

(I realise this is a very late answer. I looked up the etiquette, which seemed to suggest it was okay to give late answers - but none of the examples were quite this late. Apologies if I shouldn't have posted this.)