How are phylogenetic trees read?
See below.
Phylogenetic trees show the evolutionary relationships between organisms or taxa. The root is the ancestral lineage and the tips of the tree are the descendants. The descendants may be living or extinct. The descendants may be individual species but they do not have to be.
Node -Represent common ancestors. Speciation events happen at nodes*
Branches -Represent the evolutionary history or lineage. In some instances, but not all, the branch length represents the amount of time
Clade -An ancestor and all of its descendants (see fourth image)
Root -The ancestral lineage
Sister group -Two descendants that split from the same node are considered in one sister group
Outgroup -A lineage that falls outside of the clade or sister groups of interest
Basic example of an evolutionary tree with five descendants:
What can be said about last common ancestors and evolutionary relationships when reading trees:
A is more closely related to B than it is to C because it shares a more recent common ancestor with B when compared to C.
Phylogenetic trees do not need to be read from top to bottom. The same descendants can be displayed in different orders as long as their positions in relation to nodes is correct. Both of the trees below show the exact same information and are both correct:
Examples of what clades are and what a clade is not:
*While in phylogenetic trees speciation events happen at nodes, the reality is that speciation may not be an abrupt, obvious change that can be narrowed down to a single event or year. Speciation may occur very slowly.
For more information, see another explanation and example here and learn about the pitchfork specifically here.
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Tracing the branches of phylogenetic trees from the roots to the tips indicates the evolutionary relationships between organisms, with closely related species having more recent common ancestors than distantly related species.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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