Hoyle's Fallacy - Analysis

Analysis

Hoyle's fallacy derives from disregarding everything about sequence space other than its size. Two factors are conflated: the probability of getting a 'first sequence' (abiogenesis or novel function) and the probability of going anywhere else (evolution). This may be illustrated by dissection of Hoyle's argument made in relation to myoglobin. Any sequence of repeated elements – for example, DNA or protein – generates a sequence space for n positions and v different values at each position of vn possibilities. Therefore myoglobin, a protein of 153 amino acids, has a probability, in a 'random-amino-acid machine', of 20−153 of occurring in one step. For this to have any evolutionary significance, the number of useful myoglobins in that sequence space would have to be exactly 1. Further, any space of vn elements includes all lower-order spaces: {{vn-1, n-2, n-3 ...},{(v-1)n, n-1 ...} ... }. A probabilistic analysis must consider the smallest such space that contains a functional myoglobin. Neither n=153 nor v=20 can be accepted as minimal requirements, a priori.

Myoglobin function is in fact a property of the folded protein, not the amino acid sequence, per se. Protein folding is indeed determined by its amino acids, but activity is determined within a three-dimensional space. Certain key functional groups require suspension in a tightly-specified spatial orientation, but many different sequences may perform the scaffolding task of holding these in place. Even an imperfect arrangement may be superior to its predecessor, while adaptive evolution has the capacity to channel random processes along paths of optimization. If multiple functional sequences and adaptive gradients exist, then the total size of a sequence space delimited by a single modern instance does not set an upper bound on the probability of achieving a functional arrangement.

The minimum sequence of a functional myoglobin, the distributions of functional sequence within the total space, and the adaptive benefit of variant sequences within organisms are all unknown. Without such information, the probability of generating a functional myoglobin cannot be calculated.