The usual guidelines are that the expected counts should be greater than 5, but it can be somewhat relaxed as discussed in the following article:

Campbell , I, Chi-squared and Fisher–Irwin tests of two-by-two tables with small sample recommendations, Statistics in Medicine (2007) 26(19): 3661–3675.

See also Ian Campbell's homepage.

In you case, it appears that about 80% of the expected counts are below 5, and 40% are below 1. Would it make sense to aggregate some of the observed phenotypes?

The usual guidelines are that the expected counts should be greater than 5, but it can be somewhat relaxed as discussed in the following article:

Campbell , I, Chi-squared and Fisher–Irwin tests of two-by-two tables with small sample recommendations, Statistics in Medicine (2007) 26(19): 3661–3675.

See also Ian Campbell's homepage.

Note that in R, there's always the possibility to compute $p$-value by a Monte Carlo approach (chisq.test(..., sim=TRUE)), instead of relying on the asymptotic distribution.

In you case, it appears that about 80% of the expected counts are below 5, and 40% are below 1. Would it make sense to aggregate some of the observed phenotypes?

The usual guidelines are that the expected counts should be greater than 5, but it can be somewhat relaxed as discussed in the following article:

Campbell , I, Chi-squared and Fisher–Irwin tests of two-by-two tables with small sample recommendations, Statistics in Medicine (2007) 26(19): 3661–3675.

See also Ian Campbell's homepage.

The usual guidelines are that the expected counts should be greater than 5, but it can be somewhat relaxed as discussed in the following article:

Campbell , I, Chi-squared and Fisher–Irwin tests of two-by-two tables with small sample recommendations, Statistics in Medicine (2007) 26(19): 3661–3675.

See also Ian Campbell's homepage.

In you case, it appears that about 80% of the expected counts are below 5, and 40% are below 1. Would it make sense to aggregate some of the observed phenotypes?