A clade is all the living descendants of a single common ancestor.
In general, it is an objective of the branch of biology called cladistics to define each taxonomical unit (species, genus, family, and so on) so that it is a clade. We'll see how this works in the diagram below.
__________ Alpha | | | ____ Beta Z___ | | | | | | V_____| | |____ Gamma _______ | | | | |_______________ Delta Lucky ____| | | |________________________ Epsilon
Let's say Lucky is extinct, and the endpoints Alpha through Epsilon are all species alive today. What are the clades in this tree?
Obviously, the whole thing is a clade: all the living descendants of Lucky. Another clade is Beta plus Gamma: all the living descendants of V. Alpha, Beta, and Gamma constitute another clade: all the living descendants of Z. Any endpoint by itself is also a clade: not just Epsilon, but also Beta.
But Alpha plus Gamma is not a clade. The most recent common ancestor of Alpha and Gamma is Z, but Beta is also a descendant of Z, so it must be in any clade including both Alpha and Gamma.
Notice that if the inconvenient Beta did not exist, Alpha + Gamma would become a clade, even though the two biological units themselves were unchanged. This shows that being a clade is not something intrinsic to a group of individuals, but depends on relationships outside the group.
Suppose that Alpha and Gamma are well-known, but Beta is unknown. Alpha + Gamma is a clade. Now an intrepid adventurer brings back a specimen of Beta. Whoops! Suddenly Alpha + Gamma is no longer a clade.
The clade concept also assumes a single-ancestor tree, which is not always a safe assumption. It is reasonably clear that a certain number of species (some estimates as high as 10% of all plant species) have originated by hybridization.
[It should be mentioned that Radical Cladistics 1.01 rejected the use of the word "ancestor" completely, concentrating on relationships instead of descent, and creating clusters of related individuals and groups. Cladistics 2.00 has mellowed.]
Despite these logistical issues, the clade concept has proven very handy in analyzing the relationships among organisms. Note that it entirely dispenses with taxa, such as species, genus, and family. It is only concerned with relationships, not with assigning importance to groupings and especially not with naming things. This independence of the Linnaean tyranny (what you call it is what it is) is a great advantage.
The above discussion may have sounded very abstract, but here are two examples of clade reorganization from current research, showing how it reflects our changing understanding of relationships among living creatures.
It used to be, way back in the primitive days of the twentieth century, that the origin and development of the flowering plants was visualized as follows:
________________ Magnolias, etc. | _______ Dicots ____| | | ______ Gesneriads, etc. | |_________| Flo #1 ____| | | |______ Other dicots | |___________________________________ Monocots
Both the dicots and monocots were clades, because Flo #1 was conveniently extinct.
But recent genetic research has revised this picture. The monocots didn't come right out of Flo #1. Instead...
______ Most dicots (including gesneriads) | [now called "eudicots"] _________| | |______ Monocots __________| | | | |________________ Nymphaeas (water lilies) & Friends Flo #1 ____| | | |__________________________ Austrobaileya & a few friends
The inconvenient result: the dicots (which include Austrobaileya and Nymphaea but not the monocots) are not a clade. So a new term ("eudicots") had to be invented for the clade at the top of the diagram ("Most dicots (including gesneriads)").
Note: Austrobaileya scandens, the only species in its genus and family, is a climber of the south Pacific. Its flowers smell like rotting fish. Despite its scientific interest, there probably won't be a big horticultural market for this plant.
Some authorities believe that we should stop using the term "dicot". Although it is well-defined (dicots are all flowering plants minus the monocots), the term no longer describes a clade. Horrors. These same authorities grumble about our continuing use of other non-clade terms, such as in the case of...
_____ Jawless fishes | | Backbone #1 ____| | | _____ Sharks and rays |_____| | ____ Most fish |_____ Bony fishes ____| | |____ Amphibians
The vertebrates are the descendants of Backbone #1. Fish are the descendants of Backbone #1 minus the amphibians and their descendants. Result: fish = not a clade. Stop using the word.
_____ Most amphibians (frogs, salamanders, etc.) | | Amphibian #1 ____| | | |_____ Amniotes (egg-laying vertebrates + descendants)
Once again: amphibian = not a clade (it's all the descendants of Amphibian #1 minus the amniotes).
_____ Mammal-like reptiles _____ Mammals | | Reptile #1 ____| | | _____ "Regular" reptiles (snakes, crocodiles, turtles, etc.) |_____| | |_____ Dinosaurs (including birds)
Yet again: reptile = not a clade. It's the descendants of Reptile #1 minus the birds and mammals.
This last chart is an oversimplification. I believe that the current majority view is that the turtles branched before the reptile/dinosaur split, and that crocodilians are sister to the dinosaurs:
_____ Mammal-like reptiles _____ Mammals | | Reptile #1 ____| | | _____ Turtles |_____| | | | ____ Snakes and lizards |_____| | | | ____ Crocodilians |____| | |____ Dinosaurs and birds
Are we going to stop using the words fish and reptile? Of course not. They are not ambiguous terms, even though not cladish. Similarly, we can continue to use the word dicot.
Back in the twentieth century, life was so simple. Either the cell had its DNA packed into a compartment called the nucleus, and was therefore a eukaryote, or it didn't, and was a prokaryote. The family tree was easy:
________ Prokaryotes | | Free Cell ____| | | |________ Eukaryotes
Even the discovery of the "archaebacteria", single-celled organisms that lived in extreme environments like mid-oceanic hot spots and sulfurous geysers, only changed the diagram a little:
______ Bacteria ____ Prokaryotes ___| | | | |______ Archaebacteria Free Cell ____| | | |___________________________ Eukaryotes
But here came those inconvenient facts again. Even disregarding the fact that eukaryotes originated from the failed digestion of one prokaryote cell by another, the above diagram just didn't stand up to the spotlight of molecular genetics. Instead...
______ Bacteria _____________| | | | |______ Eukaryotes Free Cell ____| | | |____________________ Archaea
So the old term prokaryote is, unfortunately, exposed as a non-clade. It's the bacteria plus the archaea, which isn't all the descendants of anything. Still it is a useful term for all organisms without a cell nucleus, so people continue to use it.
Until the next big bombshell. Just so you won't get caught by surprise, here it is:
______ Bacteria __________________| | | | |______ Eukaryotes | ___________| | |_________________________ Archaea | Free Cell ____| | |_____________________________________ Lindsay Lohan