Prev: How to model complex systems (Major transitions)
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TODO List:
  • REF Lotka volterra
  • REF Gardener & Aschby + CLARIFICATION
  • REF De Boer & Hogeweg 1985? immune influx system
  • REF Hubble 2001?
  • REF Higgs & Derida?
  • REF koza
  • REF Lynch small pops?
  • REF Kimura Waddington
  • REF Kauffmann: robustness maintained while making novelty

Ecosystem complexity, selection and insights

  • Equilibrium of a system? But what property of that system should be then consider? Which species, how many species? Often it is much easier studying transients.
  • Replicator versus influx systems
    • entities self-replicating, versus autocatalytic (not self-replicating)
  • neutrality versus selection
  • levels of complexity

Ecosystem complexity

  • In the 60's the main idea was that diversity leads to stability. This was an emergent truth, but a misinterpretation of Lotka-Volterra models.
  • In the 70's the likes of Gardener and Ashby, and May studied systems with arbitrary interactions:
    • here diverse systems were less likely to be stable
    • close to equilibrium of the random Jacobian matrices:
      • sigma*root(species*connectivity) < diagonal in almost all cases (??)
      • if get bigger (??) term hold, there is less chance of being stable
    • very little biological knowledge inputed, only equilibrium analysis
  • Later, more biological structure included: this gave a similar trend but showed much more stability
  • But: are equillibria so important or relevant for real ecosystems? The are only valid in settings with pre-defined non-changing species

Replicator versus Influx

This is based on a study by de Boer and Hogeweg 1985 (REF) on immune system diversity to study the postulate that in an influx driven system like the immune-system, complexity is different from an ecosystem case. Using a similar analysis as above (70's case):
  • replicator system: on diagonal -a + Ecijnj: to be stable, negative, harder with greater N
  • influx system: on diagonal: -b - Ecijnj, always negative, the more stable
Bottomline: self- or non-self replicator dynamics are quite different
  • problem in out competition (hard to stabilize diversity and stability), which is not a problem in influx case
  • this is important for autocatalytic to self-replicator transition!

Ecosystem stability

We saw that:
  • interlocking timescales: the evolutionary timescales can be important for stabilizing diversity! (adapting polymorphism)
  • population-based diversity: co-evolution of populations (virus and host), may blow up complexity of system!
  • eco-system based information accumulation: (ecosystem based problem solving, hypercycles) all sorts of side-effects, creates new niches, based on selection
  • neutral theory (Hubble 2001): diversity simply due to randomness of birth death and dispersal. Species abundance patterns in "equilibrium", but what is there is changing.
    • so non-functional niches? no, but should take into account as "baseline" expectation
    • does function niche disturb species abundance as we should expect from random process? (now combined with Tilman niche differentiation)
    • cf Cordero: random process genes generates a number of observation in gene regulatory networks, but we conclude that FFL are not functional

Neutrality and speciation

  • quasi-species variation:
    • mutants are close in genotype but not in phenotype
    • depends on geno-pheno mapping variants can be quite different in phenotypes (cf Critters)
    • these are "shapes in the shadow" on the neutral path
    • on flat landscape (finite): clustering due to gyneology, simple random births and deaths (Higgs and Derida?), cf neutral path
  • standard speciation:
    • allopatric (could be selection) and mating, incompatability after neutral drift (e.g. via duplications and network attractors)
    • population - individual-based diversity: the bistability between them
  • alternative:

Thus about the elephant:
  • information threshold (not arbitrary amount of information)
  • side-effect of evolution (versus fixed target) (cf Koza)
  • side-effect of small populations (Lynch): contradicts information threshold
    • "constructive neutral evolution": effective population size is much smaller of complex organisms
    • they may be over information threshold: selected genome, population shrinks, suboptimal genotypes will arise, longer in population because mechanism by sub-functionalization
    • e.g. chaperones there because proteins loose independent protein, more freedom to evolve (chaperones, with stress work less well, more variation in proteins, way to rescue system?).
  • genetic operators (duplication, gcr, transposons)
  • structuring gene regulation networks
  • evolutionary signatures (only information local)
  • as alternative to population based diversity
  • as alternative to mutation priming, red Queen
  • study how to solve different tasks? qualitative insights what can be done
  • study as multi-level system:
    • critters: genes and system with dynamics of own, multiple side-effects
  • automatic orchestration of multiple features
  • interface with self-organization
  • robustness

Neutrality and evolvability

  • important for adaptation in evolution
  • long neutral paths and networks
  • there is a short way to go to better solution (many solutions 1% of all protein sequences do have enzyme function)
  • phenotype-first evolution (pre-pattern): Kimura, Waddington
  • mutational priming: needs nothing other than previous evolutionary history
  • evolutionary robustness (versus evolvability): fixed versus variable target, do not hinder each other, explore genotype space. Kauffmann: robust attractors can remain while making novelty

Next: Models of explanation (and end)

De Boer & Hogeweg (1985)
Lynch ??
Higgs & Derida ??
Hubble 2001?
Tilman ?
Kimura ?
Waddington ?
Gardener & Ashby (197?)