Note that while bootstrapping has an element of randomness to it, there is fairly large difference between those nodes that are well-supported and the others.
What it means that the bootstrap has an element of randomness?
Only six of the 18 nodes have good support values. By this I mean that good values are above 90 due to the problem of multiple branches. Another three have only marginal support (between 70 and 90). The rest are unresolved with no support.
See the attached pdf version where I have marked 6 branches with high support with a black dot on the respective node and a black line showing support for the monophyly of the group (but not necessarily the internal relationships within the clade. Orange lines indicate marginal support for a clade but not for the interanal relationship within the clade.
The tree has now support for the deep nodes in the tree so the relationship among the six subclasses cannot be deduce.
This common for trees and is only a problem if the relationships of interest do not have good support.
For example the five P. marinas and Synechococcus sp. 78211568 taxa form a monophyletic group. The placement within this subclass of the Synechococcus sp. is not clear from this tree.
Synechococcus sp. appears to join the five P. marinas sequences to the exclusion of the two S. elongatus and the other Synechococcus sp. 16329170.
As a whole the deep clades are unresolved and the tree seems polyphyletic with respect to the Genus names.
Sorry. I missed the second part of the question. You probably already knew the first.
This is the tricky bit. It helps to know how the bootstrap is calculated. In statistics we often do not have known distribution (Normal, Poisson, etc.). And that is definitely the case with the distribution of all possible trees that might fit our sequence data. In the absence of a known distribution, statisticians use nonparametric methods. Most of these methods are excellent as is the nonparametric bootstrap.
The randomness refers the random sampling (with replacement) of the observed data. This means that the computer takes a random sampling of (say 60%) of the same length as the original sequence. So some of the sites are randomly not sampled at all and some are repeated to produce the same length as the original. Then a tree is inferred from that data (using likelihood or parsimony, etc.). That tree is sample one.
The whole process of random sampling (using different random num generators for each one) and tree inferences is repeated many times. At the very least 100 sampled trees for a small number of sequences, but much better is thousands of random samples from the original tree.
The next step is to make a consensus tree of all these randomly sampled trees. The consensus tree branches are then labelled with the percentage (probability) of times that each branch appears in the large sample.
So in your case, you can see that some branches appear in 100% of your trees. Some appear in 90% or more of the sampled trees.
Any sequence has some sites that provide no information whatsoever about the relationships among the taxa. Many provide weak support because only a very few sites support the branch. Others appear in 100% of the trees because enough sites support the branch that some are appear in every single random sample (be it 100 or 1000 samples with replacement).
The original sequence is simply a population level sample of the true tree. The process of evolution is stochastic and so cannot be estimated from a single sample. The bootstrap sampling gives us an idea of which branches are supported with many informative sites and which have just a few or none.
A caution: the bootstrap value is only as good as the method you choose for analysis. Some methods can be biased and all methods will not give you a good estimate of the real tree unless your chosen model of sequence evolution is realistic. Failing to choose the very best method can and does result in a spuriously well-supported but false tree.
The bootstrap will tell you what is in your data but will not tell you if your analysis has properly modeled the process of sequence evolution that gave rise to your 'slice of time' sample.
Thanks for the clarification. So adding the "the bootstrap has an element of randomness " Note, will not affect the answer to the question regarding the number of well-supported nodes. Is this right?