We have been looking at Christoph Adami’s book, The Evolution of Biological Information. Previous posts have considered his problematic definition of information as well as the failure of his Maxwell’s demon argument for increasing biological information. Today, we will be looking at his attempt to show a pattern of increasing information along the line of biological descent.
Adami analyzes two different proteins. One is the homeodomain, or homeobox, protein, which is essential in controlling the pattern of development in animals. The other is the cytochrome c oxidase subunit II (COX2), which is a gene in the mitochondria that plays an important role in aerobic respiration. From this, he derives two figures intended to show the evolution of information over evolutionary time.
From Eukaryotes to Animals
Adami’s Figure 3.6 shows the evolution of the homeobox proteins. According to it, the homeobox protein increased in information during the transition from eukaryotes to animals. Arthropods increased in information, while chordates and bony vertebrates lost information. Mammals lost further information while fish gained it.
Adami’s Figure 3.7 shows the evolution of the COX2 sequence. Across most lineages there was a striking increase in information. The exception is bacteria, which lost a large amount of information. This example leads Adami to say that the evolution of information “most likely reflects the adaptive value of the protein for each family.”
Do Adami’s figures actually show an evolutionary history of information? To answer that, we must ask another question. How did Adami measure the entropy of long-gone ancestral genes? He gestures at using phylogenetic techniques that attempt to reconstruct ancestral proteins. But he does not actually make use of those techniques.
Instead, Adami estimates the entropy of sequences by taking all sequences within a clade and treating them as a single collection. For example, in order to determine the eukaryotes’ sequence entropy, he takes all eukaryote sequences. But the collection of all present-day eukaryote sequences would be expected to be nothing like the sequence found in the eukaryote ancestor. He is rather computing a meaningless quantity.
Furthermore, the features of these graphs are simply consequences of how that quantity is computed. Firstly, when multiple groups of sequences are combined, the entropy is effectively averaged. The entropy will thus tend to be in the middle of the two groups. That is why in many cases across the graphs, one clade will show an increase in information while the other shows a decrease. That is because the inferred parental information or entropy is simply an average of the two subclades and thus will tend toward the middle.
A Nonsensical Quantity
However, when two subclades differ on part of a sequence, combining them will not simply average the entropy but rather increase it. This tends to cause ancestral groups to show more entropy than more recent groups. This is responsible for the tendency in the figures, especially Figure 3.7, to show decreasing entropy and thus increasing information over time.
In the end, Adami’s method has not shown anything about the entropy or information content of ancestral sequences. His method computes a nonsensical quantity and the results he shows are simply the artifacts of how this quantity is computed.