Comments to the authors:
The presented research article “Linear polyacrylamide is highly efficient in precipitating and purifying environmental and ancient DNA” by Maixner et al. offers very interesting insights into environmental and ancient DNA extraction of samples including inhibitory substances. This article is potentially very exciting for the field of ancient DNA research, however in its current state it requires additional modifications prior to publication. I acknowledge that the authors addressed many of the previously pointed out issues with the way they reported the methodology. Unfortunately, some parts still need more details and clarification.
Below you will find general comments, followed by more specific comments, which hopefully the authors will find helpful.

General comments:
Generally, the sample/material description should be included at the very beginning of the Material and Methods section. Please describe the three different types of environmental samples and the two? different types of fossil samples. How many samples were processed for each type? The number of samples mentioned throughout the manuscript varies. This needs clarification. Additionally, the processed number of replicates per samples is unclear.
An explanation for the rational behind the sample selection would be necessary as well.

The authors are using a confusing mix of names for the tested extraction protocols. For example, Griffith protocol or (P/C/I). I suggest including a table with the published protocols, the precipitation reagents and the code/ID referred to throughout the manuscript. This will help the reader distinguish between the different methods much more easily.

The discussion is missing why LPA could be an advantage over established ancient and environmental DNA extraction methods.

Table S1: It is unclear with what the DNA comp. of samples 2634, 2653, 889 and 2053 were compared, as the table does not indicate them as being gone through the LPA purification-precipitation test!

Figure 3: It would be much more informative to have the sample types rather than the sample numbers in the figure. The current display with the legend and sample information at the very end, makes it very difficult for the reader to compare the different sample types.
Furthermore, the last plot in the figure is labelled as FS, but in the legend below I assume it corresponds to 3039.

Please proof-read all in-text citations, as sometimes the formatting includes a “,” after et al. and sometimes it doesn’t.

Specific comments:
l77-l87: Could go into the supplement
l87-l88: Unclear sentence and unclear connection to the following paragraph. It sounds like you are referring to a specific type of precipitation. Please clarify.
l94: Better start with an introduction to ancient material and then mention their drawbacks, such as inhibitory substances. You want to sell your method to the ancient DNA community, so make sure that you don’t lose focus of the sample material. It’s important.
l103-l108: stress that this presented approach is highly applicable to a variety of ancient samples, as demonstrated through the here presented sample selection. Also please be more specific about the exact number of tested samples and the different sample types.
l110: why all of a sudden just one environmental sample? Above you mention three different types of environmental samples.
l109-l113: Either be less or more specific, but like this the question of why just one environmental sample comes to mind. Also, which one? Soil, animal faeces or activated sludge?
l129: The residual ethanol is removed …
l143: The residual ethanol is further …
l152-l153: Please add the elution volume.
l162: These classic nucleic …
l166: Which commonly used extraction methods are the authors referring to here? Please include the citations.
l182-l186: Based on what do you decide which lysis buffer to use? A short explanation at the beginning of this section would be extremely useful.
l197-l200: What is the difference between points iii) and iv)?
l201-l203: Improve readability! E.g. end the sentence after the citation: (Green & Sambrook 2016). Subsequently
l203-l205: Does this only apply to iv) or to all precipitation methods used?
l210: which samples do you mean by “three samples” and why did you select those three? Please be much more specific when talking about the samples. This is absolutely essential information, especially for ancient DNA researchers who might be considering to apply your proposed method to their own samples.
l218: existing nucleic acid extracts: needs more details
l224: what selection are you referring to? What is the reasoning behind the selection?
l237: What was the environmental sample selection based on? How did you get from three different sample types to just one sample?
l261: Is the centrifugation speed of 500g correct? This sounds extremely slow.
l266: double-stranded DNA libraries – of what? All samples or just a selection?
l267: citation should be changed to Meyer & Kircher (2010).
l268: sample replicates: details needed. How many replicates?
l269-l271: What was the reasoning behind the DNA fragmentation of the environmental soil sample?
l273: Was the library control sequenced as well?
l286-l288: Why was the data randomly subsampled?
l292-l294: In the following, we removed all reads < 35 bp from the … to the whole human genome (build Hg19, Rosenbloom et al., 2015)  Citation not listed in the references!
l307: Did you use HaploGrep or HaploGrep2.0?
l310: selected samples  unclear which ones you are referring to
l315: Which version of DIAMOND did you use? And please add the reference.
l316: Please add version and reference for MEGAN
l343: minor change: Please highlight the change you observed in the description of the results.
l383: What are the “various other mummified human remains”? Please add more details!
l389-l393: A table with details of samples and purification types would be extremely useful to add.
l399: What material are you referring to here?
l421: Generally, both methods revealed highly reproducible results in our replicated approach.
l423: Please include a data table with the DNA yield measurements.
l446-l447: Why were the two soft tissue samples treated with different lysis buffers?
l464: What about contamination occurring during the original sampling, storage and/or handling?
l485-l486: In contrast to the bone tissues, the soft tissue of the Bolivian mummy (2653) displays …
l533: specify the type of material
l562: Explanation/discussion of the statement “have no effect on the library preparation” is missing.
l564: If both the classic and the LPA approach show similar fragment lengths and library complexities, what is the advantage of the LPA approach? Is the effect of inhibitory substances dismissible?
l566-l568: Better: Following the ancient human DNA authentication of Orlando et al. (2021), …
l595-l608: Sounds more like an introduction than part of a discussion. Maybe move this part or rewrite with more focus on the discussion.
l609: I suggest adding a summary sentence before the start of the sentence in line 609, to have a better connection to the previous paragraph.