PCoA plots in R on presence/absence community data: rows filled with zeros give an error

Question

I am currently making PCoA plots on Presence/Absence community data. My rows are populated with samples and my column headings are different taxa that were detected. However, since the experiment is a degradation experiment, some of the samples have rows filled with zeros (absences). The only way the distance matrix calculation will work is if I remove these zero-filled rows. However, since these rows are biologically meaningful (it means nothing was present after decay) and not just missing data, I was wondering if there was a way to keep them and avoid the "NaN" error I would get otherwise.

I am using the package 'vegan' and the function 'vegdist' to calculate my distance matrix.

Here is an example of the code:

distance_matrix <- vegdist(data, method = "jaccard", binary=TRUE)
pco <- pco(distance_matrix, negvals = "zero")

Answer 1

Computing the Jaccard distance between two sets requires that the union be non-empty.

$$d_{\operatorname{Jaccard}}(A,B) = 1 - \frac{|A \cup B| - |A \cap B|}{|A \cup B|}$$

If the union $A \cup B = \emptyset$, then $|A \cup B| = 0$. In that case you will have an undefined value. If $A = B = \emptyset$ then the numerator will also be zero, giving an indeterminate form.

R is likely assigning divide-by-zero cases to NaN.

If the Jaccard distance must be used, then any cases that result in an empty union have to be filtered out. Another approach is to use a different metric that can handle both inputs being zero/empty.