Surely.
This was a post I made on phylogenetics, which is one small aspect of science that supports the modern synthesis (by the way you may want to clarify what "Darwinism" is because I don't know a biologist alive today who follows all of Darwin's ideas)
No worries, my fault in the assumption. Let's digress from eye evolution for a moment and speak of phylogenetics, as it is key to understandng evolution and how we derive these "chains" as you have called them. Let's first explain some basics of phylogenetics then maybe you will see how this is evidence, these "chains"
Phylogenetics is the study of infered relationships among organisms, particularly the evolutionary relationships and history of specific lineages. That is to say the study of Darwin's "common descent". Phylogenetics seeks to identify the historical communities of descent through shared features, which well call nested sets. The relationships can be described in two basic ways: Branching (cladogenesis) and Linear (anagensis). We can choose any number of visual representations to display these relationships; trees, circles etc, it makes no difference. The information represented is the same in both examples below.
So the question then becomes,
where and
how do we arrive at these relationships?
The answer is in the math. If we study organisms and characterize their variation we can array this in a matrix. We can then analyze many matrices and find these nested sets that pertain to the groups. Today, we use computer programs that use clustering algorithms. There is mathematical proofs such sets arise, but let's skip the math for now while we cover basics (if you wish to come back to it at a later time let me know).
These shared features can look similar because of chance, convergences or common histories (homologies). We can see a simple example of homologies in limb bones.
So what kind of evidence to support homologous structures? We have lots of genetic evidence, in the form of genes, ultraconserved non-coding regions etc. We can construct trees based up phenotypical traits and test them against the genes that code for these traits. Do we know though this is the absolutely 100% correct tree? No, like all science we can only say this is the tree that best represents the data.
We can talk of groups in 3 basic ways. The first is a
monophyletic group. That being all the descendants of a common ancestor. Seen in this example:
The next type of grouping is paraphyly this includes some, but not all descendants of a common ancestor. In this case (for the example below) its saying, "Dinosaurs but not birds"
Finally we have polyphyly, which is distantly related groups lumped together.
(Bare with me there is some points in all this)
So what kind of errors can we make interpretation of group relations? Or chains as you called them.
We see with paraphyletic relationships that we exclude some members of the lineage. In the case of polyphyletic relationships we make the mistake of of including unrelated organisms. Easy to do with convergent features such as the eye.
So how do we minimize error? By sampling an extremely high number of attributes and the associated variations.
So, as a few people here are fond of claiming "Evolution is not testable" or "Evolution is belief and not science". If evolution is a science, in particular the science of phylogenetics, then it should not only be testable, but it should help us ask questions and make predictions.
What kind of questions can we ask with phylogenies? Things like; What is the evolutionary origin of a particular group, trait, feature, structure? What adaptations accompany changes of life history or habitat? Are particular attributes unique to the specimen or are they characterized by a broader group?
In formulating these questions we can form hypothesis that we can then test against fossil, genetic, protein etc data.
Lets look at an example with mammals, everyones favorite
.
We can ask the question are mammals a monophyletic group?
We can then build a tree based on the attributes of mammals. Using matrices we can derive some commonalities which we have deemed above, nested sets. These we can order on our tree as per their value in the matrices and we come up with something like this:
One would expect if what you and others who argue against the many sciences involved in evolution are true ("chains of comparisons prove"that simple evolved to complex is a leap of faith, as you said), then we ought to find violations to the nested hierarchies inherent in the system. Meaning, we should find placental mammals which lack ear bones on the skull, or monotremes with pouches. If was a leap of faith made and we simply assume all these things, then why is this what data supports? There should be evidence to the contrary.
We then can use common descent as a null hypothesis for similarity in the progression of "simple to complex" (yuck, that is gross misrepresentation to life on earth but I am trying to keep this simple). When we see similar attributes, we can then assume they are the same, that is they represent the same basis for testing. Homology then becomes our null hypothesis we are testing.
Now lets come full circle, you said:
"* You showed how the eyes of the simpler creatures are simpler in construction,
* and more complex in more complicated creatures.
You show that there is a "chain" -- simpler lead on to more complex."
Then you claimed the leap is made when we say it evolved. As you can hopefully see now, there has been no leap of faith, nor untestable/unfalsifiable science being done. All we have done is to construct a tree based on the shared attributes of specific animals and groups of animals, albeit it is much more complex than the simple illustrations I have highlighted above. What is certainly interesting, as I noted in my original post, is not only do we have structural evidence to support our evolutionary relationships, but genetics and molecular (cellular) as well.
If you are at all confused by this, please respond so that we may resolve any complications you see with it.
~Regards
My apologies for simply reposting but you asked for some evidence for it (NS and evolution) and so I figured this would suffice.
