In this study, the authors investigate the evolutionary history of four populations of two fungal sister species. They present a new population genomic dataset and apply tools to unravel the underlying history, focusing on population admixture. The analyses follow a clear synopsis, starting with descriptive methods and culminating with explicitly testing distinct possible demographic scenarios. With this, the authors report evidence of introgression between two populations and show that a scenario with a ghost population best describes the data. The authors also try to assess whether particular gene functions were enriched in the introgressed regions as a signature of adaptive introgression—however, the lack of functional annotations in this non-model organism impeded the statistical power of this analysis. I enjoyed reading this manuscript. I have several minor comments related to technical aspects and one suggestion for a possible complementary analysis (which I do not deem necessary for the publication of this manuscript).

Minor:
The description of the analyses lacks detail in several places:

1) phylogeny: spell out GTR (even though it is a standard model). The ASC option should be explained: ascertainment bias correction because only variable sites were used. Did the authors also include a rate across site variation model?

2) HMM: it is unclear what this analysis is doing and how. A few lines of description are needed.

3) TreeMix l300: "to avoid identical likelihoods". Some explanations are needed to understand the underlying issue.

4) Demographic modelling: an explanation of the options used is needed. For non-expect readers, one or two sentences summarizing the principle of the approach used would be helpful (basically, using fast coalescent simulations to generate an expected joint SFS, which is compared to the observed one to estimate parameters).

5) Results, PCA, l361-364: while PCA allows distinguishing groups of individuals, the distance between them and their positioning on the PC graph is not directly interpretable, notably when sample sizes differ between populations. The authors should either remove these sentences or conduct PCA analyses on random (equal) samples of individuals in each population to assess the robustness of the inter-group distances and positioning.

6) Figure 5: Could the scaling of the population sizes be increased? Most populations appear as thin lines, making the comparison of their size difficult. Legend: given the values, these must be Log likelihoods?

7) l135 typo 2x "the present study"

Possible complementary analysis:
Given the large divergence between the populations/species, I am curious about the coalescence times in the various populations. Given the estimates from figure 5, it seems possible that some regions could have a TMRCA older than the split between the two species. The authors could consider running approaches like MSMC2 to gain a finer view of how the relative cross-coalescence rate varies in time, allowing to estimate migration rates in different epochs (see https://doi.org/10.1371/journal.pgen.1008552).

The authors have addressed my comments. A remaining minor point:
Regarding TreeMIX identical likelihoods: for readers who are not experts in using TreeMIX, can the authors describe what is precisely the "identical likelihoods" issue and how it arises? In their revision, the authors explain why it has to be addressed, but it is still unclear what the problem exactly is.