Bray-Curtis Index of Similary

Canberra's Metric Index of Similarity
ANSI C Function

(Extracted from an application written in 1986 to perform cluster/factor/nodal analyses on benthic infaunal invertebrate core samples)

The following function was written in the ANSI-compatible C language (and compiled without errors in Microsoft C) to compute the Canberra's Metric Similarity Index for community structure as represented by two benthic invertebrate core samples in a "site x site" comparison, or the similarity in the spatial distribution of two distinct species in a "species x species" comparison. It should be repeatedly called by the calling function within a "loop" that sequentially compares every possible pair of population arrays (e.g., sites), and it then returns the computed index between those pairs of populations, thereby "populating" a similarity matrix one cell at a time as the calling function progresses through the loop.

double canberra (species1, species2, small_value, num_species)

float *species1; /* number of individuals in sample 1 for each of n species where n = num_species. */

float *species2; /* number of individuals in sample 2 for each of n species where n = num_species. */

float small_value; /* replacement for zero-nonzero matches */

int num_species; /* total number of species in samples. */

{

int x; /* table index */

int nondoublezeros; /* number of sample pairs where at least one is a non-zero value */

double sigma_dif; /* sum of differences between sample pairs */

double sigma_sum; /* sum of sums of sample pairs */

double samp1, samp2, replacement_for_zero;

replacement_for_zero = small_value * 0.20;

non_doublezeros = 0;
sigma_dif = 0.0;
sigma_sum = 0.0;

for (x = 0; x < num_species; x++)
{

samp1 = (double) species1[x];

samp2 = (double) species2[x];

if ((samp1 != 0) && (samp2 != 0))

{

if (samp1 == 0)

samp1 = replacement_for_zero;

if (samp2 == 0)

samp2 = replacement_for_zero;

sigma_dif += fabs(samp1 - samp2);

sigma_sum += samp1 + samp2;

non_doublezeros++;

}

if (non_doublezeros == 0)

return (0.0);

return (1.0 - ((sigma_dif / sigma_sum) / (double)non_doublezeros));

}

Notes

1. For those of you that are unfamiliar with the "C" programming language, the text that falls between the "/*" and "*/" are merely comments inserted for legibility in the code and are ignored by the complier

2. The "*" in front of the variables "species1" and "species2" are pointers to the start of a one-dimensional array that contains the abundances of each species in a sample/station (discussion of pointers is a pretty complex aspect of the C language - suffice it to say, it works when complied)

3. Each of the "species1" and "species2" arrays are the same length, and at each position in the array is the number of individuals of that species observed (zero counts are not only acceptable, they are required space holders in the array)

4. the variables "sigma_dif" and "sigma_sum" are accumulators, representing the sum of the absolute differences between the number of individuals of a specific species at each site/station (sigma_dif) and the sum total of the number of individuals of a specific species at the same site/station (sigma_sum)

5. In C, the phrase "+=" means to take the current value of the variable and add the value of the other variable

6. In C, the phrase "++" means to increment the value of the variable by the integer value "1"

Other indices of similarity/dissimilarity that were coded in the original application included: Bray-Curtis, Squared Euclidean Distance, Percent Similarity, Mountford, Dice, Kendall, Morisita, Simplified Morisita, Sorensen, Product Moment Correlation Coefficient, Horns Index, and Whittaker.

For questions or comments regarding the above, please contact Michael D. Noah, President, Physalia Ocean Sciences, Inc.