# Population structure from mtDNA sequence data: A thought experiment

I have 5'-COI sequences for a species of interest, which were downloaded from the Barcode of Life Data (BOLD) systems.

Assuming for the moment that the said species was sampled across its entire geographic/ecologic range, I would like to gain some insight regarding potential structuring that may exist in this species.

I know that deme number ($$K$$) and per-generation migration rates ($$m$$) are difficult to estimate directly, though proxies such as the effective number of migrants ($$Nm$$), where $$N$$ is the effective population size computed via $$F_{ST}$$ and its variants, are often reported.

I am carrying out some computational simulations and would like to know the feasibility of taking a random subsample of these sequences and treating the reduced dataset as a single deme.

For example, suppose I have 5 DNA sequences with haplotype and country information:

Sequence 1: Germany (Haplotype 1)
Sequence 2: Romania (Haplotype 2)
Sequence 3: Italy   (Haplotype 2)
Sequence 4: Austria (Haplotype 3)
Sequence 5: Poland  (Haplotype 4)


These 5 sequences comprise 4 haplotypes with the following frequencies:

Haplotype 1: 1/5 = 20%
Haplotype 2: 2/5 = 40%
Haplotype 3: 1/5 = 20%
Haplotype 4: 1/5 = 20%


Now suppose I take a random subset of the data, say 60%. Thus my reduced dataset comprises 3 sequences, for example:

Sequence 2: Romania (Haplotype 2)
Sequence 3: Italy   (Haplotype 2)
Sequence 5: Poland  (Haplotype 4)


The new dataset has only 2 haplotypes with frequencies:

Haplotype 2: 2/3 = 66.7%
Haplotype 4: 1/3 = 33.3%


The above scheme avoids the issue of determining $$K$$ and $$m$$.

What I am wondering is: can a random subsample be treated a single deme?

What likely assumptions need to be made here for this to be a valid approach?