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There is a theorem in the Intelligent Design literature called Basener's ceiling. It states that all evolutionary algorithms that attempt to optimize some fitness function will eventually reach a plateau where complexity no longer increases. This is seen in practice when engineers and computer scientists try to use algorithmic forms of evolution.

There are a number of standard models for the evolutionary process of mutation and selection as a mathematical dynamical system on a fitness space. We apply basic topology and dynamical systems results to prove that every such evolutionary dynamical system with a finite spatial domain is asymp- totic to a recurrent orbit; to an observer the system will appear to repeat a known state infinitely often. In a mathematical evolutionary dynamical system driven by increasing fitness, the system will reach a point after which there is not observable increase in fitness.

Biological evolution is the same as an evolutionary algorithm in the relevant aspects. It is a search to optimize reproductive fitness, where the fitness function is just the fact of survival or lack thereof.

How then is evolution able to make organisms continually increase in complexity, as history shows, despite Basener's ceiling?

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Four quick flaws:

1) Environments are always changing. The fitness space is dynamic, and includes both biological and non-biological players, the former which are also ever-changing. Given a sufficiently stable ecosystem, one would expect an equilibrium among species to develop (though it could be cyclical). However even if the environment stays constant, novel mutations could always increase the fitness of a given species, which could then affect the fitness of all the other species. Also, natural selection is not the only factor that influences evolution, and other factors can add dynamic instability.

2) You are conflating genetic algorithms with evolution. Genetic algorithms use selection to solve a minimization problem and are typically bounded within fairly rigid constraints. They are motivated by biology, not models for biology.

3) You are conflating complexity and fitness. Complexity can be more fit or it can be less fit. Evolution only selects for fitness, not for complexity.

4) Do organisms continually increase in complexity? Depending on how you define it, they may not. Thinking about humans as a "goal" of evolution or something like that is a feature of creationism or intelligent design, not biological evolution. Some of the most successful organisms on Earth in terms of number of individuals or even biomass are some of the simplest.

There may be others as well.

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  • $\begingroup$ Over time organisms have become more complex. Why is this not obvious? We start with the simplest single celled organisms and end up with a huge, diverse phylogenetic tree. It seems weird that this is the point of contention. $\endgroup$
    – yters
    Jun 14, 2017 at 20:53
  • $\begingroup$ @yters I'm referring to local/recent versus long term. Yes clearly there is more complex life now than when life first started. That doesn't mean that evolution is directed towards complexity, just that more complexity than it started with was advantageous for some individuals. Although the phylogenetic tree is huge, most individual organisms on earth and most of the diversity are still single-cellular. $\endgroup$
    – Bryan Krause
    Jun 14, 2017 at 21:14
  • $\begingroup$ Just because multicellularity took longer to evolve, for example, doesn't mean it is better. Becoming multicellular was good for some organisms, at some time, so the trait was maintained. Most unicellular organisms at the time the first multicellular organisms were originating stayed unicellular, and their descendants stayed unicellular over billions of generations. $\endgroup$
    – Bryan Krause
    Jun 14, 2017 at 21:16
  • $\begingroup$ The paper says we should not see this complexity increase, regardless of whether greater complexity is more advantageous or not to some individuals. $\endgroup$
    – yters
    Jun 14, 2017 at 21:35
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    $\begingroup$ But change doesn't cease, because organisms continue to mutate, which changes their fitness. In the paper you cite, the big flaw is that 1) Fitness is fixed for a given genotype, and 2) Genotypes are limited to just a couple possibilities. Yes, in that circumstance, you will get an equilibrium. Never in nature do those circumstances occur. Organisms aren't limited to X base pairs, evolution can both change and add or delete base pairs. $\endgroup$
    – Bryan Krause
    Jun 14, 2017 at 23:23

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