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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.

imrobert
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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.

Bryan Krause
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    So if I find a new mold, how am I supposed to know if it's a fungus or something else? – imrobert Nov 02 '23 at 20:14
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    @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. – Bryan Krause Nov 02 '23 at 20:15
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    If I find an organism of any kind that I suspect to be a fungus, how am I supposed to determine whether it is or not... – imrobert Nov 02 '23 at 20:19
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    @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. – Bryan Krause Nov 02 '23 at 20:31
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    @imrobert: It might be worth asking a followup question, something like “What phenotypic characteristics distinguish fungi from other similar organisms?” This answer gives the correct theoretical answer to your original question as written — that the formal definition of fungi is cladistic, not phenotypic. But asking about distinguishing characteristics is also a valid and important question, and it sounds like that’s more the question you care about and maybe meant to originally ask, you just didn’t quite hit a technically correct phrasing of it. – PLL Nov 03 '23 at 13:12
  • @PLL I'd like to leave my question open to a cladistic definition but "The monophyletic group where true fungi go" is obviously not a definition – imrobert Nov 03 '23 at 16:26
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    @imrobert "Fungi" is the name for that monophyletic group; that's the definition. – Bryan Krause Nov 03 '23 at 16:31
  • @BryanKrause What defines that monophyletic group? – imrobert Nov 03 '23 at 17:14
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    @imrobert Phylogenetics: common descent. They share an ancestor. That's what "monophyletic" means. – Bryan Krause Nov 03 '23 at 17:19
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    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. – Bryan Krause Nov 03 '23 at 17:25
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    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. – Bryan Krause Nov 03 '23 at 17:28
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    If you want a definition, here is a not very formal cladistic one: If you found an organism and determine that the most recent common ancestor of that organism and a mushroom is neither your ancestor nor the ancestor of a potato, that organism is a fungus (probably the potato part of the definition can be discarded as redundant). – Pere Nov 03 '23 at 18:33
  • Thanks guys, I understand the concept of a monophyletic group. My question is, how can I determine if an organism is inside the group Eumycota? If you don't know it's okay – imrobert Nov 03 '23 at 18:52
  • It's hard to be sure. You need to reconstruct a tree using the available features of that organism and other members of the taxon (and also other non-member), and that features can be of all kinds, although nowadays genetic ones are the most useful when available. From here: https://evolution.berkeley.edu/phylogenetic-systematics/reconstructing-trees-cladistics/reconstructing-trees-parsimony/ – Pere Nov 03 '23 at 18:59
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    Of course, if the organism you found is of a known species or at related to know taxa, it becomes a lot easier. For example, if you found a mushroom with all the parts mushrooms usually have, you can be sure that it's a fungus. – Pere Nov 03 '23 at 19:01
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    @imrobert You can see my comment above about using phenotype to get a pretty good idea but if a definitive answer is needed you'll need to look at the genome. As far as which phenotypic characteristics, the Wikipedia page you previously rejected is a good place to start (for example the "characteristics" section). Fungi are a huge group with a lot of variety, so it's not as if you'll be able to just check one or two boxes to decide. Like Pere suggests it might make more sense to start more focused e.g. to ask "is this a mushroom?" - if yes, it's a fungus, too. – Bryan Krause Nov 03 '23 at 19:29
  • @BryanKrause "how am I supposed to determine whether it is (a fungus) or not"? Didn't there used to be books where they asked questions about what you saw, and it sent you to a different page? Eventually, after X number of questions, you got your answer. I remember doing this once in high school at an insectarium: catch a bug, and then identify it using a huge book. – RonJohn Nov 03 '23 at 20:45
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    @RonJohn Sounds like a "dichotomous key". It's a lot like following a phylogenetic tree: each time the tree branches, there is some characteristic that is different in one branch from the other, though as a practical tool they don't necessarily need to follow phylogeny at all, just go through enough characteristics within a limited group (usually limited by geography as well as overall "type" of organism, a literal tree perhaps). The thing is, fungi are a huge group many many steps removed from the common ancestor, so they don't necessarily look very much like that ancestor. – Bryan Krause Nov 03 '23 at 20:52
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    @RonJohn at the end of the day, the ancestry-based definition means that kind of thing only works as an approximation. If it walks like a duck, talks like a duck, but (e.g.) its DNA tells us its ancestry branched off earlier, when then, its not a duck. – mbrig Nov 03 '23 at 23:13
  • @mbrig in practice, how far does DNA move creatures? For example, moving the Giant Panda from Ursidae to Ailuridae then back again seems reasonable, but "We thought this was a really weird bat, but DNA says it's really a bird" seems a bit extreme. – RonJohn Nov 03 '23 at 23:44
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    @RonJohn I think that's partly a question of how "bad" the initial identification is and partly how close convergent evolution comes. You could imagine that somebody guessing that some Multituberculata is part of Rodentia, but obviously people try not to make that kind of mistake (and its harder when the thing is extinct and you have less evidence to go off of). Maybe more realisticly, I could definitely see some kind of bacteria getting reassigned to Archaea based on DNA, and that's a whole nother domain! – mbrig Nov 04 '23 at 00:04
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    @RonJohn Adding to what mbrig wrote, some initial classifications were extremely wrong (eg: archaea used to be classified as bacteria), and have been revised substantially as various new information is available, and there are still open debates about fairly substantial parts of the overall tree, especially around microorganisms. But, mostly what keeps things consistent are the closer relatives; every time you discover a new bat, you can see how it relates to other bats and that immediately tells you roughly where it falls, you don't have to start from scratch. – Bryan Krause Nov 04 '23 at 01:05
  • does anyone know the genetic data required to classify something as a fungus, or where i can find out? – imrobert Nov 04 '23 at 23:25
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    @imrobert: As per my first comment, I really suggest asking that as a new followup question. I appreciate your disappointment with this answer — it’s technically absolutely correct, but it’s also kind of a gotcha, saying “you phrased your question technically wrong” and explaining how, but never answering the actual question you wanted an answer to. But you’re much more likely to get a useful answer by asking a new question, now you know a technically more correct wording for it, rather than going on in comments here. – PLL Nov 05 '23 at 11:58
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    thanks @PLL i'm going to ask a new question. do you have a suggestion on specific wording to include to make sure i get what i'm looking for in the answers – imrobert Nov 07 '23 at 21:52