The weird format of your file (if indeed it is in this way) is out of anyone's understanding. But I ll explain how awk could work here provided a nicely formatted tab separated table

Consider your file (say file.txt) this way, the <tab> and <space> symbols are for representation, your actual file will have whitepspace (tabs and spaces) and corresponding positions shown in the file

Bacteroides<space>fragilis<tab>0
Bacteroides<space>fragilis<tab>0
Salmonella<space>enterica<tab>1
Salmonella<space>enterica<tab>1
Salmonella<space>enterica<tab>1
Bacteroides<space>fragilis<tab>0

Now if you say

awk '$2==1{print}' file.txt | wc -l

It may not work, because, by default the field separator which awk consider here is the first white space it encounters which in this case would be the space Bacteroides <space> fragilis

Hence, you must add a field separator -F

awk -F "\t" '$2==1{print}' file.txt | wc -l

set the field separator 'F' to 'comma' and increase a value 'N' each time column 2 is '1'. At the end print the value of N.

awk -F, '($2==1){N++;}END{print N;}' file.txt

but I think most people would use

cut -d, -f 2 file.txt | grep -c -w 1

Though OP wants solution in awk, here is datamash solution:

Species (organism) wide 0's and 1's count:

$ datamash -s -t "," -g 1,2 count 2 < test.txt | sed 's/,/\t/g'
Bacteroides fragilis    0   3
Salmonella enterica 1   3

Only 0's and 1's count:

$ datamash -s -t "," -g 2 count 2 < test.txt | sed 's/,/\t/g'
0   3
1   3

input (from OP):

 $ cat test.txt 
Bacteroides fragilis,0
Bacteroides fragilis,0
Salmonella enterica,1
Salmonella enterica,1
Salmonella enterica,1
Bacteroides fragilis,0