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Fungi are immotile eukaryotes that do not have chloroplasts or perform photosynthesis. Yet there are other organisms that fit this definition that are not fungi, for example slime molds. What is the formal definition of a fungus? Wiktionary, Wikipedia, and other dictionaries provide informal definitions.

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    $\begingroup$ Some fungi produce zoospores, which are motile. $\endgroup$ Nov 2, 2023 at 19:21
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    $\begingroup$ A fungus is formally a fungus, a base divergence of Eukaryote, a plant is a plant. An animal is an animal. $\endgroup$ Nov 3, 2023 at 2:51

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Formal definitions aren't really a thing in Biology or anywhere outside of mathematics.

For cladistics, the closest you will get is that species are arranged based on common ancestry. Fungi are a group of organisms sharing a common ancestor. This is present, not absent, in the definition on Wikipedia:

These and other differences place fungi in a single group of related organisms, named the Eumycota (true fungi or Eumycetes), that share a common ancestor (i.e. they form a monophyletic group), an interpretation that is also strongly supported by molecular phylogenetics.

If you have some organism and you want to convince other biologists that it should or should not be classified as a fungus, you would want to make arguments about its ancestry.

Before modern molecular biology techniques, these groupings were entirely based on phenotype. Linnaeus is the individual most recognized for classifying organisms this way and many of his conventions and groupings are still used today (though many others have changed, as well). Darwin's contribution to biology was recognizing that the groupings based on phenotypic similarity originate from common descent (that is, shared ancestry). But, even with that knowledge, it's possible to make mistakes in classification based on phenotype alone. When you hear about some organism previously classified one way whose classification has changed, it's likely that the previous classification was based on assumed relationship based on phenotype, but molecular phylogenetic methods have since suggested a different ancestry and therefore a different classification is more appropriate. Because we do not have all the ancestors (or, really, any of them) to examine, these relationships have to be inferred.

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    $\begingroup$ @imrobert New to you, or new to science? How do you know it's a mold? If you're sure it's a mold, for whatever reason, then congratulations, you have a fungus! If it's a slime mold, well, that isn't a mold at all, any more than a bat is a bird. $\endgroup$
    – Bryan Krause
    Nov 2, 2023 at 20:15
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    $\begingroup$ @imrobert You can probably assume it's a fungus if it shares the phenotypic characteristics of other fungi. It's helpful to know about other types of organisms that you might possibly confuse with a fungus so you can consider or dismiss those alternatives. If you have a key for identifying species, and you can use it to classify what you've observed, you'll have a better answer. If a definitive answer is critical you could sequence the genome and use that to either identify the species or find which known species it is most closely related to. $\endgroup$
    – Bryan Krause
    Nov 2, 2023 at 20:31
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    $\begingroup$ @imrobert Phylogenetics: common descent. They share an ancestor. That's what "monophyletic" means. $\endgroup$
    – Bryan Krause
    Nov 3, 2023 at 17:19
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    $\begingroup$ Not liking an answer doesn't make it wrong... Life evolves from previous life. We can organize all life into a "tree" of related organisms. It's useful to name parts of that tree to refer to groups of organisms together. Fungi are one of those groups. There are no features that make something a fungus or not besides being in that related part of the tree. If you find something that seems to share every characteristic you can think of, but then find out it's not actually related, then it's not in that group. $\endgroup$
    – Bryan Krause
    Nov 3, 2023 at 17:25
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    $\begingroup$ Similarly, if you find a member of that "family tree" of organisms within that group that has some feature that you didn't think any fungus has, you wouldn't declare it "not a fungus", instead you would say "aha, this particular fungus has a new feature we didn't think any fungi had". There is no definition, besides membership in that clade, that describes it and would not change with new discovery. $\endgroup$
    – Bryan Krause
    Nov 3, 2023 at 17:28

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