Using a few ENFA factors, you will now map the habitat suitability of your study area. The chosen algorithm will compute, for eaccell, a value between 0 and 100, from unsuitable to optimal habitat.

Operations

Compute a Habitat Suitability map (Habitat suitability/Habitat Suitability map)

Here you can choose the HS algorithm you want to use (for now only the “medians” algorithm is available, as described by Hirzel et al. (Ecology, in press).

Select the factor maps you want to include in the HS computation. When you click on the browse (…) button, a dialog box appears allowing you

To choose how many factors you want to include (comparing the eigenvalue distribution to Mc-Arthur’s broken-stick gives you a clue about this problem).

Then you can compute the chosen factor maps. They will be saved. As long as you do not compute again the ENFA, they will be available for HS computation, otherwise, you will have to compute them again (this is the longest part of the HS computation).

You can now modify the weight assigned to each factor. By default, the weights are computed from the eigenvalues and represent the amount of information explained by each factor. You should not modify them.

Select the HS algorithm. Four of them are available, each covering a different case (my favourite are Medians and Geometric mean): Medians: Quick, accurate in most situations, good generalisation power. The species distribution on each factor must be unimodal and more-ore-less symmetrical. Distance geometric mean: Slow, good generalisation power. No assumption is made on the species distribution. Distance harmonic mean: Slow, medium generalisation power. No assumption is made on the species distribution. It gives a high weight to each single observation and therefore could give better results when the sample size is very small and each observation might bring relevant information to the model. Minimum distance: Medium speed, low generalisation power, low predictive accuracy. No assumption is made on the species distribution. It gives a very high weight to each single observation and therefore might give better results when the sample size is very small and each observation might bring relevant information to the model. However it produces usually bad results.

Choose a name for the HS map. By double-clicking on the field, a name will be automatically filled.

Now you can compute the HS map.

You can visualise this map through the menu View/Map (or in Idrisi), or by double-clicking on its name in the output window.
You can also visualise the ecological niche in two dimensions (two factors) with the menu habitat Suitability/Niche 2D visualisation. That’s with this tool (and Idrisi’s CONTOUR operation) that I made the figures in the Environmental Management paper (2004).

Habitat Suitability algorithms

There are currently four HS algorithms available in BioMapper:

Median algorithm

Before Biomapper 3.0, it was the only algorithm available. It gives good results in most situations and is the quickest of all.
To compute the median algorithm, we divide the species range on each factor in 25 classes, in such a way that the median would exactly separate two classes. For every point in the environmental space, we count the number of observations that are either in the same class or in any class farther apart from the median. To achieve normalisation, twice this number divides the total number of observations. Thus, a point belonging to one of the two classes directly adjacent to the median will get a value of one, and a point lying outside the observation distribution will get a value of zero. Lastly, the overall suitability index for this point is computed by the weighted average of its scores on each dimension, the weights being given by the amount of information explained by each dimension.
This algorithm makes the assumption that the best habitat is at the median of the species distribution on each factor, and that these distributions are symmetric. Although this is often true, in some case it’s wrong: when the distribution is bimodal, it is even completely wrong. You can also get sub-optimal results when the study area is at the border of the species distribution.

Distance geometric-mean algorithm

The principle of this method is to draw in the factor space the influence field, or suitability field, of each species observation point in such a way that, when they are close together, their attraction powers reinforce each other. For any point P in the factor space, one computes the geometric mean HG of the distances to all observations Oi. Thus, the denser the species points in the environmental space, the higher the habitat suitability. This actually comes down to calibrating a model in the environmental space to apply it to the geographic space.

This algorithm makes no assumption about the shape of the species distribution, but the density of observations must be representative of the species niche. The geometric mean produces a smooth set of envelopes around the observations points and provides a good generalisation of the niche.

Distance harmonic-mean algorithm

This algorithm is similar to the geometric mean one but uses the harmonic mean of the distances instead:

The effect of this mean is to give a (too) high weight to all observations while keeping the information of observation density in the factor space. Therefore, it has a tendency to overfit the data, which might be good when you have a small sample size.

Minimum distance algorithm

Again this algorithm is similar to the geometric mean one but uses the minimum of the distances instead:

That means that the density of observations is not taken into account anymore. Each observation has the same weight, and the closest your are from one of them, in the factor space, the more suitable your habitat. There is no generalisation at all. Actually, on all examples I have tested this algorithm never gave good results. However, as it is described in the above paper, I decided to include it in this version of BioMapper. And perhaps someone will find a case where it proved useful.

Links

References

Hirzel A.H., Hausser J., Chessel D. & Perrin N. (2002) Ecological-niche factor analysis: How to compute habitat- suitability maps without absence data? Ecology, 83, 2027-2036.

Hirzel, A.H. & Arlettaz, R. (2003) Modelling habitat suitability for complex species distributions by the environmental-distance geometric mean. Environmental Management, 32, 614-623.

Hirzel, A.H. & Arlettaz, R. (2003) Environmental-envelope based habitat-suitability models. In 1st Conference on Resource Selection by Animals (ed B.F.J. Manly). Omnipress, Laramie, USA.

## Table of Contents

## HABITAT SUITABILITY

Using a few ENFA factors, you will now map the habitat suitability of your study area. The chosen algorithm will compute, for eaccell, a value between 0 and 100, from unsuitable to optimal habitat.## Operations

Medians: Quick, accurate in most situations, good generalisation power. The species distribution on each factor must be unimodal and more-ore-less symmetrical.Distance geometric mean: Slow, good generalisation power. No assumption is made on the species distribution.Distance harmonic mean: Slow, medium generalisation power. No assumption is made on the species distribution. It gives a high weight to each single observation and therefore could give better results when the sample size is very small and each observation might bring relevant information to the model.Minimum distance: Medium speed, low generalisation power, low predictive accuracy. No assumption is made on the species distribution. It gives a very high weight to each single observation and therefore might give better results when the sample size is very small and each observation might bring relevant information to the model. However it produces usually bad results.You can visualise this map through the menu View/Map (or in Idrisi), or by double-clicking on its name in the output window.

You can also visualise the ecological niche in two dimensions (two factors) with the menu habitat Suitability/Niche 2D visualisation. That’s with this tool (and Idrisi’s CONTOUR operation) that I made the figures in the Environmental Management paper (2004).

## Habitat Suitability algorithms

There are currently four HS algorithms available in BioMapper:## Median algorithm

Before Biomapper 3.0, it was the only algorithm available. It gives good results in most situations and is the quickest of all.To compute the median algorithm, we divide the species range on each factor in 25 classes, in such a way that the median would exactly separate two classes. For every point in the environmental space, we count the number of observations that are either in the same class or in any class farther apart from the median. To achieve normalisation, twice this number divides the total number of observations. Thus, a point belonging to one of the two classes directly adjacent to the median will get a value of one, and a point lying outside the observation distribution will get a value of zero. Lastly, the overall suitability index for this point is computed by the weighted average of its scores on each dimension, the weights being given by the amount of information explained by each dimension.

This algorithm makes the assumption that the best habitat is at the median of the species distribution on each factor, and that these distributions are symmetric. Although this is often true, in some case it’s wrong: when the distribution is bimodal, it is even completely wrong. You can also get sub-optimal results when the study area is at the border of the species distribution.

## Distance geometric-mean algorithm

The principle of this method is to draw in the factor space the influence field, or suitability field, of each species observation point in such a way that, when they are close together, their attraction powers reinforce each other. For any point P in the factor space, one computes the geometric mean HG of the distances to all observations Oi. Thus, the denser the species points in the environmental space, the higher the habitat suitability. This actually comes down to calibrating a model in the environmental space to apply it to the geographic space.This algorithm makes no assumption about the shape of the species distribution, but the density of observations must be representative of the species niche. The geometric mean produces a smooth set of envelopes around the observations points and provides a good generalisation of the niche.

## Distance harmonic-mean algorithm

This algorithm is similar to the geometric mean one but uses the harmonic mean of the distances instead:The effect of this mean is to give a (too) high weight to all observations while keeping the information of observation density in the factor space. Therefore, it has a tendency to overfit the data, which might be good when you have a small sample size.

## Minimum distance algorithm

Again this algorithm is similar to the geometric mean one but uses the minimum of the distances instead:That means that the density of observations is not taken into account anymore. Each observation has the same weight, and the closest your are from one of them, in the factor space, the more suitable your habitat. There is no generalisation at all. Actually, on all examples I have tested this algorithm never gave good results. However, as it is described in the above paper, I decided to include it in this version of BioMapper. And perhaps someone will find a case where it proved useful.

## Links

## References