The first way to treat this in the DAG paradigm that comes to mind is that the “quantitative” question is a question about a causal effect given a hypothesized diagram species→mycorrhyzal structure prevalence.
On the other hand, the “qualitative” question can be framed in two ways, I think. In the first, the question is about which DAG best describes reality given the choice of different DAGs that represent different sets of species having an effect. But in principle, we could also just construct a larger graph with all possible species as Ys having arrows pointing to $ X $ and try to infer all the different effects jointly, translating the qualitative question into a quantitative one. (The species that don’t effect $ X $ will just have a causal effect of $ 0 $ on $ X $.)
To your point about diversity in the wild, in theoretical causality, our ability to generalize depends on 1) the structure of the DAG and 2) our level of knowledge of the underlying mechanisms. If we only have a blackbox understanding of the graph structure and the size of the average effects (that is, $ P(Y \mid \text{do}(\mathbf{X})) $), then there exist [certain situations](https://ftp.cs.ucla.edu/pub/stat_ser/r372-a.pdf) in which we can “transport” our results from the lab to other situations. If we actually know the underlying mechanisms (the structural causal model equations in causal DAG terminology), then we can potentially apply our results even outside of the situations in which our graph structure and known quantities are “transportable”.
Thank you. It looks even more unfeasible than I thought (given the number of species of mycorrhizal and other root-inhabiting fungi); I’ll have to just explicitly assume that Y does not have an effect on X, in a given root system from the wild. At least things seem much cheaper to do now)))
The first way to treat this in the DAG paradigm that comes to mind is that the “quantitative” question is a question about a causal effect given a hypothesized diagram species→mycorrhyzal structure prevalence.
On the other hand, the “qualitative” question can be framed in two ways, I think. In the first, the question is about which DAG best describes reality given the choice of different DAGs that represent different sets of species having an effect. But in principle, we could also just construct a larger graph with all possible species as Ys having arrows pointing to $ X $ and try to infer all the different effects jointly, translating the qualitative question into a quantitative one. (The species that don’t effect $ X $ will just have a causal effect of $ 0 $ on $ X $.)
To your point about diversity in the wild, in theoretical causality, our ability to generalize depends on 1) the structure of the DAG and 2) our level of knowledge of the underlying mechanisms. If we only have a blackbox understanding of the graph structure and the size of the average effects (that is, $ P(Y \mid \text{do}(\mathbf{X})) $), then there exist [certain situations](https://ftp.cs.ucla.edu/pub/stat_ser/r372-a.pdf) in which we can “transport” our results from the lab to other situations. If we actually know the underlying mechanisms (the structural causal model equations in causal DAG terminology), then we can potentially apply our results even outside of the situations in which our graph structure and known quantities are “transportable”.
Thank you. It looks even more unfeasible than I thought (given the number of species of mycorrhizal and other root-inhabiting fungi); I’ll have to just explicitly assume that Y does not have an effect on X, in a given root system from the wild. At least things seem much cheaper to do now)))