Aggregation index (Aggregation metric)

lsm_l_ai(landscape)

## Arguments

landscape Raster* Layer, Stack, Brick, SpatRaster (terra), stars, or a list of rasterLayers

tibble

## Details

$$AI = \Bigg[\sum\limits_{i=1}^m \Big( \frac{g_{ii}}{max-g_{ii}} \Big) P_{i} \Bigg](100)$$

where $$g_{ii}$$ is the number of like adjacencies based on the single-count method and $$max-g_{ii}$$ is the classwise maximum number of like adjacencies of class i and $$P_{i}$$ the proportion of landscape compromised of class i.

AI is an 'Aggregation metric'. It equals the number of like adjacencies divided by the theoretical maximum possible number of like adjacencies for that class summed over each class for the entire landscape. The metric is based on he adjacency matrix and the single-count method.

Percent

0 <= AI <= 100

### Behaviour

Equals 0 for maximally disaggregated and 100 for maximally aggregated classes.

## References

McGarigal, K., SA Cushman, and E Ene. 2012. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical and Continuous Maps. Computer software program produced by the authors at the University of Massachusetts, Amherst. Available at the following web site: http://www.umass.edu/landeco/research/fragstats/fragstats.html

He, H. S., DeZonia, B. E., & Mladenoff, D. J. 2000. An aggregation index (AI) to quantify spatial patterns of landscapes. Landscape ecology, 15(7), 591-601.

lsm_c_ai
lsm_l_ai(landscape)