Summary of the paper:
In this paper, the authors proposed a deep learning-based eDNA ordination method, known as the ORDination via Deep Neural Algorithm (ORDNA). In particular, the proposed ORDNA method involves training a deep neural network using self-supervised learning (SSL) to map an eDNA sample to a lower-dimensional representation. To do so, the authors used the triplet loss from deep metric learning, which encourages an "anchor" to be closer to a "positive" instance than to a "negative" instance by at least some pre-defined margin -- the "anchor" here refers to a subsample of 1000 eDNA sequences; a "positive" instance is another subsample of 1000 eDNA sequences from the same eDNA sample as the "anchor"; and a "negative" instance is a subsample of 1000 eDNA sequences from an eDNA sample that is different from the sample where the "anchor" comes from. Once the deep neural network is trained, to obtain an embedding of a given eDNA sample, the authors proposed to pass all subsets of 1000 eDNA sequences from the sample through the trained network, and then to average their embeddings into a single embedding for the sample. The authors compared the (two-dimensional) embeddings obtained from ORDNA with traditional bioinformatics methods (in particular, PCoA) and concluded that ORDNA's embeddings generally correlate better with geographical and environmental variations than PCoA.

Strengths:
- The use of deep metric learning to embed eDNA samples and to analyze eDNA samples is novel.
- The proposed ORDNA method can advance eDNA analysis techniques beyond traditional bioinformatics pipelines.
- The embeddings produced by the ORDNA do exhibit stronger correlations with geographical and environmental factors, than the competing PCoA method.
- The paper is very well written, and very easy to follow.

Weaknesses:
- Currently, subsamples of 1000 sequences from an eDNA sample are used to train an ORDNA network. The authors should perform an ablation study with various subsample sizes to empirically compare the quality of the resulting embeddings.
- The authors only compared their ORDNA method with PCoA. The authors should also compare their method with more commonly used baseline methods, such as PCA.