Complexity, Self-organization, and Evolution

1
Complexity, Self-organization,and Evolution

• Rich Strauss

Alice laughed There's no use trying,' she
said 'one can't believe impossible things.'
'I daresay you haven't had much practice,' said
the Queen. 'When I was younger, I always did it
for half an hour a day. Why, sometimes I've
believed as many as six impossible things before
breakfast.' Lewis Carroll Alice in
Wonderland
2
Outline

• Evolution and natural selection can it work?
• Emergent properties and complexity.
• Genetic networks
• Boolean N-K networks
• CAS complex adaptive systems
• Life at the edge of chaos
• Autocatalytic systems
• Artificial life
• Whats the point?

3
Theory of evolution

• Mayr theory of evolution can be divided into
  five distinct subtheories.
• Somewhat independent of one another.
• Explains why parts of the theory can be so
  divisive among those who dont question other
  parts.
• Subtheories
• Evolution, as such, occurs.
• Common descent every group of organisms is
  descended from common ancestor, including all of
  life.
• Multiplication of species speciation.
• Gradualism accumulation of small changes.
• Natural selection genetic variation
  differential reproduction.

4
Natural selection

• Model originated with Darwin as a verbal
  argument process to account for pattern.
• Augmented during the New Synthesis with
  quantitative models from population genetics.
• Basic model of Darwinian natural selection
• Natural selection is the inevitable outcome of 4
  features of organisms.
• Proposed as four postulates by Darwin.
• Now understood as basic facts about the natural
  world.

5
Natural selection

• (1) Organisms vary no two living things are
  exactly alike.
• DNA and mutations.
• Sexual reproduction
• Independent assortment.
• Crossing-over and recombination.
• Combining two unique haploid genotypes into a
  novel diploid genotype.
• (2) Variation among organisms is heritable
• Many differences are due to environmental
  variation, but many (most?) are due to
  differences in genotypes.
• Genetic differences among adult organisms in any
  generation will produce differences among their
  offspring.

6
Natural selection

• (3) Excess progeny are produced
• Organisms face a struggle for existence
  (Malthus).
• In every generation, far more offspring are born
  than ever survive to reproduce, due to
• Overproduction more offspring than the
  environment can support.
• Biotic interactions
• Competition within and among species for common
  resources.
• Predation, parasitism, pathogenesis.
• Selective mating via sexual selection not all
  individuals are suitable as mates.

7
Natural selection

• (4) Reproductive output varies among individuals
  based on their heritable differences
• Survival and reproduction are non-random
  processes (at least in part)
• Some individuals have traits that allow them to
  survive and reproduce better than do others in
  the population.
• Individuals with the most favorable traits will,
  on average, produce more offspring than do others
  in the population.
• Variation in competence might be due to
• Different abilities in competition with other
  genotypes.
• Differential survival under onslaught of
  parasites, predators, diseases, changes in
  physical environment.
• Variable reproductive competence.
• Variable ability to find and penetrate new
  habitats.

8
Natural selection

• If the four factors hold, the inevitable result
  is natural selection favorable traits will
  increase in frequency in the population over
  time.
• Accounts for much of what we observe in nature.
• Basis of agriculture and animal husbandry.
• Basis of highly successful optimization
  procedures genetic algorithms and evolutionary
  programming.
• "How extremely stupid not to have thought of
  that!
• Thomas Henry Huxley, 1865

9
Natural selection

• But selection cant be perfect
• Cant result in perfect adaptation because of
  several types of constraints or limitations
• Time lags
• Every generation of organisms is adapted to the
  conditions that existed in previous generations.
• Selection usually acts slowly relative to the
  rate of environmental change.
• Result organisms may not be perfectly adapted
  to existing conditions.
• Mechanical constraints
• Organisms are constructed of materials that
  have limits to their physical properties.
• Many phenotypes are physically impossible e.g.,
• Limits to insect body size because of external
  skeleton.
• Limits to the size of terrestrial vertebrates
  because of properties of bone.

10
Natural selection

• Genetic/epigenetic linkages between traits
• Complex genetic/biochemical/developmental/
  functional relationships among traits.
• Particular genetic variation may produce an
  adaptive change in one trait, but a deleterious
  change in another.
• Result often is a tradeoff (compromise) among
  traits.
• All heritable traits are filtered through the
  phenotype.
• Thousands of possible heritable traits.
• Mediated and buffered by development and other
  linkages.
• Number of successful offspring usually very
  small.
• Crude filter.

11
Natural selection

• So can natural selection, by itself, really
  work?
• Can it produce the extremely complex organisms
  currently living?
• Can it account for the amazingly detailed
  convergences of form and function in different
  groups of organisms?
• Many evolutionary biologists have thought not.
• Other processes proposed
• E.g., heterochrony, developmental canalization.
• Until recently, none satisfactorily accounted for
  biological complexity.

12
Emergent properties

• Consider ants simple nervous systems.
• Individual ants regarded as unconscious
  automatons.
• Interactions not very complex
• Signal in only a few (5-8) different ways.
• Yet behavior of ant colonies can be astounding.
• Colonies may contain 5,000-2,000,000 individuals.
• Behavioral repertoires include
• Elaborate nest construction and defense. E.g.
• Columnar or arch-shaped structures.
• Wedge-shaped nests oriented N-S or E-W direction.
• Efficient foraging behavior.
• Slavery of other ant species.
• Farming of fungi and aphids.
• Emergent properties collective properties not
  predictable from examining individual organisms.

13
Emergent properties

• Long known from inanimate objects e.g.,
• Vortex spontaneously forms above drain in tub.
• Small perturbations of water and air determine
  direction of rotation (hallmark of chaotic
  behavior).
• Properties described by laws of fluid dynamics.
• Cant be predicted from knowledge of properties
  of water molecules and their interactions.
• Reductionist approach doesnt work.
• Emergent properties seen almost everywhere
• Avalanches, stream flow, air turbulence, weather
  patterns, formation of spiral galaxies.
• Living cells, ecological systems, human
  societies.

14
Emergent properties

• Studies of emergent properties lead to basic
  principles
• Emergent properties are characteristic of complex
  systems.
• System of sufficient complexity will typically
  have properties that cant be explained by
  breaking the system down into its elements.
• Complex systems are self-organizing.
• When system becomes sufficiently complex, order
  will spontaneously appear.
• Often have threshold effects.
• Till 20 yrs ago, little hope of understanding
  appearance of emergent properties in complex
  systems.
• Could be described analytically.
• But if couldnt be analyzed in reductionist
  manner, couldnt really be understood.

15
Emergent properties

• Advancement that led to change development of
  modern high-speed supercomputers.
• Possible to create models (simulations) of
  complex systems.
• Development of a mathematical field unknown
  20 yrs ago complexity theory.
• Applied to numerous disciplines
• Physics, astrophysics e.g. galaxy formation.
• Behavior of stock markets, traffic congestion,
  etc.
• Behavior of social insects ecological systems
  genomic organization.
• Relates to questions concerning the evolution of
  life.

16
Genetic networks

• Few traits caused by action of single gene.
• Most caused by many genes acting in concert.
• Many genes dont code for traits.
• Genes interact
• Turn one another on and off.
• Activation and inhibition control cellular
  development and activity.
• Generally not possible to find a gene for a
  certain trait.
• Most traits produced by networks of genes.
• Single gene may be part of gt1 network.
• May cause traits to be linked, functionally or
  fortuitously.
• E.g. white cats usually deaf.

17
Genetic networks

• Numbers of genes tend to be large
• 75,000 genes (?) in human genome.
• Bacteria have hundreds of genes.
• Number of possible interactions much greater.
• Genome of any organisms can be regarded as a
  complex system.
• Difficult to determine how 5 interconnected
  objects may behave.
• Hopeless to use reductionist methods to
  understand workings of genome.

18
Genetic networks

• Thus work in complex systems might shed light on
  problems of molecular biology, in the context of
  evolution.
• Stuart Kauffman
• Theoretical biologist, Santa Fe Institute.
• Seminal and influential work.
• Constructed computer models relating to
• Origin of life.
• Interconnections between genes.
• Evolvability of genomes that are interconnected
  in various ways.

19
Genetic networks

• Kauffman began work while a medical student in
  1960s.
• Based on Prigogine, hypothesized that
• Genetic networks would be self-organizing.
• Certain types of order should arise
  spontaneously.
• Should be possible to determine emergent
  properties.
• Properties would have nothing to do with natural
  selection.
• Once order appeared, might be subject to
  selection (exaptation).
• Worked on slow mainframe computers.
• Fortuitously began with very simple networks.
• Results exceeded his expectations.

20
Genetic networks

• Introduction to boolean N-K networks
• Simplifying assumptions
• N genes can turn each other on or off.
• Vary the mean number of inputs (K) to each gene.
  Extremes
• No gene has influence on any other (K0).
• Every gene influences every other gene (KN).

21
Genetic networks

• Basic results
• K1 network quickly freezes.
• All genes remain either on or off.
• Would result in cell death.
• K3 or more network becomes chaotic.
• System passes randomly through enormous number
  of states, without repeating.
• Behavior extremely sensitive to initial states of
  genes.
• Not good model for cell no coordination between
  states.
• K2 genes cycle through limited number of
  different states.
• Orderly activity, could serve as model for gene
  activity.

22
(No Transcript)
23
(No Transcript)
24
Genetic networks

• Responses to perturbations
• K1 stable.
• System quickly returns to original state.
• K3 or more chaotic.
• System usually moves to a completely different
  set of states.
• K2 stable adaptive.
• System often returns to original state, but
  occasionally jumps to a new stable state.
• Expected behavior under Wrights adaptive
  landscape model.

25
Genetic networks

• First characterization of emergent property of a
  network
• Out of many different kinds of configurations
  that a system might have, one has special
  properties.
• If K is variable, configuration can arise
  naturally.
• I.e., is a CAS complex adaptive system.
• N-K network models have been major source of work
  in complex systems for gt20 yrs.
• Generalization optimal number of inputs varies,
  depending on nature of network.
• For any network, there is always some optimum
  that defines borderline between frozen genetic
  activity and chaos.

26
Edge of chaos

• Kaufmann Life exists at the edge of chaos.
• Living systems seek the edge of chaos via
  natural selection.
• Effectiveness of natural selection depends on
  interconnectedness of genes.
• Nature of interconnectedness affects
  evolvability.
• Makes life and evolution possible.

27
Network theory for origin of life

• Life may be emergent property of certain kinds of
  complex systems autocatalytic.
• Observation certain biological molecules (e.g.,
  proteins) can catalyze the formation of other
  molecules.
• If reaction proceeds more rapidly when C is
  present, and C remains unchanged and available,
  then C is a catalyst.
• Can work in various ways, e.g. as template.
• Details arent important.
• In living cells, reaction rates can be 108-1011
  times faster in presence of catalyst.
• Action of catalysts is foundation for life.

28
Network theory for origin of life

• Model goes something like this
• Suppose chance that one molecule chosen at random
  will act as catalyst on second molecule chosen at
  random is 10-6.
• If few kinds of molecules are present, probably
  no catalytic action combination will be rare.
• As number of different kinds of molecules
  increases, number of interactions (possible
  catalytic reactions) increases exponentially.
• When certain degree of complexity is attained
  (e.g., 106 interactions), probability of
  catalysis increases suddenly threshold effect.
• Have inert system added a few kinds of elements
  system springs into life becomes autocatalytic.

29
Network theory for origin of life

• Autocatalytic systems are complex adaptive
  systems capable of mutating and evolving.
• Thus life and evolvability are emergent
  properties that arise when systems of biological
  chemicals attain certain degree of complexity.
• Combinatorial explosion.
• E.g., Cambrian explosion of basic body plans.
• Brain function in humans?

30
Artificial life

• Number of attempts to simulate evolution via
  computer.
• One of most successful
• Tierra Thomas Ray (1989)
• Organism is computer program, with three genes
  (function), 80 computer instructions.
• Replicate
• Mutate
• Feed on energy provided by CPU.
• Organisms reproduce, compete for common resources.

31
Tierra

• Within a few thousand generations, successful
  mutants appeared
• 79 computer instructions, reproduced more
  rapidly.
• Then smaller, more efficient organisms evolved.
• Parasites used reproductive genes of larger
  organisms.
• Hosts evolved defenses against parasites new
  forms of parasites evolved (arms race).
• Eventually was able to observe 29,000 different
  types of electronic organisms.
• About 300 different sizes.

32
Tierra

• Moved to different kinds of computers, changing
  the programming language.
• Much diversity among computers
• Digital evolution slow and gradual on some, rapid
  and punctuated on others, static on others.
• Difficult to account for differences.
• Ongoing work Network Tierra, using
  interconnected computers (different habitats).
• Ancestor introduced with 640 computer
  instructions 2 cell types, 10 cells (8 sensory,
  2 reproductive).
• Offspring produced from reproductive cells can
  migrate or not reaper at each computer node.
• Amazing results
• New forms, some of which couldnt interbreed
  (species).
• New cell types e.g., for more efficient
  reproduction and energy use.
• Tremendous diversity in evolvability.

33
So whats the point?

• Complexity networks represent simplified models
  of evolution.
• Similarities between artificial and real
  evolutionary patterns may reveal general
  principles about evolution and evolvability.
• Many complexity scientists view biological
  structure and evolution as complex adaptive
  systems that have predictable emergent
  properties.
• Account for, e.g., rampant convergence of
  strikingly similar form in very different groups
  of organisms.
• If so, life is not surprising.

34
So, whats the point?

• Principles of self-organization relieve us from
  having to view natural selection as operating
  separately on every small detail of an organism.
• Self-organization is present in almost every
  level of natural evolution
• Gene regulation networks
• Protein interaction networks
• Metabolic pathways
• Cellular organization, etc.
• Nature evolves instructions that produce
  organisms by a process of self-organization, and
  its the instructions that evolve.
• Issues of complexity and self-organization have
  not been integrated into standard evolutionary
  biology.

35
Darwinism vs complexity

• Neo-Darwinism
• Evolution chance mutations natural selection.
• Life may be a lucky accident.
• Complexity takes eons to develop.
• Structure is conditional upon history.
• Complexity
• Natural principles of self-organization create
  ordered patterns in complex systems.
• Evolution self-organization drive systems to
  the edge of chaos, where maximal adaptability
  is possible.
• Life is expected, and convergent properties are
  expected.
• We are At Home in the Universe (Kauffman, 1995).