Based on your description of your study, I would say that you have a serious design problem: both SPECIES and TREATMENT are assigned to POOL (i.e., POOL is the experimental unit for these two factors), but you have no replicates of the SPECIES and TREATMENT combinations. You have only one pool for each combination.
If you assume that there is no interaction of SPECIES and TREATMENT, then you could use the 1 df for SPECIES*TREATMENT as the error for testing SPECIES and TREATMENT. Is that a legitimate approach? It depends upon the extent to which there actually is no SPECIES*TREATMENT. And with only 1 denom df, the tests would be of low power.
Unless you are willing to assume that there is no TIME effect and no PART effect, you cannot consider "repetition through time" or "through part" to be valid replications. You clearly think that there may be TIME and/or PART differences, so I doubt that you can find replicates in this fashion, apart from other concerns I would have about the validity of this.
Ignoring the lack of replication problem for the moment.... Plants (aka ID) are clustered within POOLs, and IDs are the experimental unit associated with the TIME factor. At this point, your design resembles a split plot where POOL is the whole plot unit, SPECIES and TREATMENT are the whole plot factors; ID is the subplot unit, and TIME is the subplot factor. If 3 plants in each pool were randomly assigned at the beginning of the study to be destructively sampled at different TIMEs, then you do not need anything fancy for the covariance structure: I'd consider either CS or CSH.
With respect to PART: Do you want to compare metal concentrations among PARTs, to do separate analysis of each PART, to analyze the mean over PARTs, or something else?
But back to lack of replication. You need to sort that problem out first, to your satisfaction and to the satisfaction of anyone who will be evaluating your work (committee, reviewers, etc.) before turning your attention to your other analysis questions. You could look into the methodologies presented here
https://www.amazon.com/Analysis-Messy-Data-Nonreplicated-Experiments/dp/0412063719
While searching for that link I noticed a symposium on the topic here
https://dl.sciencesocieties.org/publications/cs/tocs/46/6#h1-ANALYSIS OF UNREPLICATED EXPERIMENTS (SYMPOSIUM)
It may be that a descriptive approach would be best, no statistical inference tests.
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