How do I compare categorical data with multiple uneven populations?

Is there a difference in lineage occurrence/proportion between study 1 compared to the other 4 studies?

There are 5 populations. We need to compare population 1 to each of the other 4 populations (4 previous studies). 
We are comparing the occurrence of Lineages (4 Levels- A, B, C, D) in population 1 compared to their occurrence in each of the other 4 populations.

The Lineages are categorical (A,B,C, D) every sample will fit within one of these lineages. The sample sizes are uneven between the different studies, therefore I thought it best to work with proportions.

I thought that I could just use a proportion test or chi-square test but I'm a bit confused since I have the 4 lineages and the 5 studies. Do I just look at one lineage at a time and since it's a proportion, it factors in the other lineages?

i.e.: LineageB <- prop.test(x = c(198,140,31,35,205), n = c(213,140,31,39,250)); LineageB
p-value = 3.502e-08 (This isn't specific enough, tells me there is likely a different between all studies)

Since I'm only concerned with population 1 compared to each of the others should I only include my study and one other at a time?

Lineages Pop 1 Pop 2 Pop 3 Pop 4 Pop 5
A 4 0 0 0 0
B 198 140 31 35 205
C 6 0 0 4 18
D 5 0 0 0 27
Total 213 140 31 39 250
Count of Lineage by Study.

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