• REF Boerlijst Hogeweg ???? Which one?
  • REF Hogeweg 19994?: feedback accumulated information
  • Wolbachia: clarify alpha parameter

Ecology and evolution: The fallacy of separation of timescales

The previous assessment of the value of group-level selection in solving the error threshold in individual sequences was not that successful. In this section we return to ecology based solutions of the error threshold (cf hypercycle). Eigen and Schuster's (1979) original approach to the hypercycle was in essence a purely ecological approach in the sense that mutations were ignored. Similarly, Boerlijst and Hogeweg (1991?) looked at the same system (based on similar assumptions), only in space, and results were that stability increased and spatial patterns led to new levels of selection. Paradoxically though, the whole point was to study the information threshold, i.e. what happens to information under high mutation rates. In sum we have therefore only approached this issue by studying invasion dynamics. However, evolution is an interplay of evolutionary and ecological dynamics. Although mutations were added (Boerlijst and Hogeweg, 1991?), the structure of possible interaction networks was always kept constant. This more or less still restricts the system to the invasion regime. Moreover, in all these models that assess a possible increase in information, the information is not used for anything.

Feedback of accumulated information

In that sense a better model would be one that incorporates the evolved information into the behaviour of the system. A hypothetical model (Hogeweg 1994?) could be one where 2 RNAs form duplexes (ligation) which then can catalyze the replication of (all) other RNAs (mutants and parasites alike). Such a system would form a star network. Results (Hogeweg 1994?) show that such networks are very stable because the interface where duplexes form is very narrow and it is difficult for parasites to persist:
  • parasites need to be where duplexes form
  • implicit trade-off between replication and being replicated, and a strong altruist loses the chance of being replicated
In evolution the strength of ligation therefore declines, but levels off. This minimizes ligation so that duplexes just manage to maintain themselves and thus gives them an advantage over parasites which is always below its criticality. The system therefore allows a dominance of 2 RNAs due to their isolation at their interface. Moreover, if there is diversity of replicases parasites cannot optimize at all. If parasites do get ligated, then newly evolved parasites are killed because the ligation product is not active due to mutant.

A crucial point here however is the assumption of a ligase product, i.e. extra information is assumed: an expandable matrix of who gives catalysis to who, and the mutant gets catalysis of the same things (but with (non-correlated) mutated parameters). It is however likely that there are implicit correlations which could have a profound impact on the system, but to obtain those requires a relationship between sequences based on their actual structure (see Takeuchi and Hogeweg 2008).

State of the art on information threshold: We don't know how to solve it! There is no satisfactory answer at this moment, although it would appear that the parasite problem can be solved.

Eco-evolutionary timescales

At this stage we further investigate the consequences of using ecology-based models to study evolutionary implications. It is therefore important to be explicitly conscious about the assumptions and inclusions (omissions) in standard ecological and evolutionary models:
  • ecological models: study ecological stability and dynamics of monomorphic populations.
  • evolutionary models: study invasion dynamics in populations with constant population size (e.g. quasi-species equation) or assumed QSS (i.e. population dynamics in attractor, parameter dependence). Invasion dynamics assumes low mutation rates and monomorphic populations.

An important underlying assumption for all of these models is the assumption of separation of timescales. Ecological models assume that evolution is slow enough that it will not impact ecological processes, and evolutionary models assume that ecology is fast enough that populations will be at equilibrium or in a QSS. However, we have seen in the host-parasite system (?) that separation of time scales from dynamics and fate of parasites depends on which timescale is used and we have seen that similar time-scales can occur in multi-level evolution, i.e. replicator vesicle dynamics should be the same. In these models, where ecology and evolution are not separated we see a clear interlocking of both processes.


A striking example of the danger of the separation of timescales is demonstrated by a study on Male Killers (Groenenboom & Hogeweg 2002). This study deals with Wolbachia bacterial parasites that are maternally inherited and kill males to further bias populations to their hosts (females). In a spatial finite population model results show that there are qualitatively different results according to a parameter α (???): either no infection, coexistence, or dying out (no more males). However, if the model had considered ratios of infected and uninfected individuals one would have concluded that there was still infection and coexistence because the ratio remains constant despite (atto-)extinction! This is a common error in theoretical papers which tend to use ratios! They assume they can keep population size constant despite not having a viable population!


Eigen M & Schuster P (1979) The Hypercycle: a principle of natural selforganisation. Springer, Berlin 92pp (also publised in Die Naturwiszenschaften, 1977:11, 1978:1 and 1978:7)
Groenenboom MAC & Hogeweg P (2002) Space and the persistence of male-killing endosymbionts in insect populations. Proc. R. Soc. Lond. B. Biol. Sci., 269: 2509-2518. MEDLINE. DownLoad PDF.
Hogeweg P (1994) Multilevel evolution: replicators and the evolution of diversity. Physica D 75, 275-291. PDF-file
Takeuchi N & Hogeweg P (2008) Evolution of complexity in RNA-like replicator systems. Biol. Direct., 3: 11. MEDLINE. DownLoad PDF.

Boerlijst M.A. and Hogeweg P. (1991) Spiral wave structure in pre-biotic evolution: Hypercycles stable against parasites. Physica D 48:17-28 pdf plate1 plate2
Boerlijst, M.A. and Hogeweg, P. (1991) Selfstructuring and Selection: Spiral waves as a substrate for prebiotic evolution. in: Artificial Life II. SFI Studies in the sciences of complexity Vol X (ed. C.G Langton) Addison Wesley pp 255-276 plate1 plate2 plate3
van der Laan JD and Hogeweg P (1995) Predator-prey coevolution: interactions among different time scales. Proc Royal Soc London B 259:35-42

Savill, N. J. , Rohani, P. and Hogeweg, P. (1997) Self-reinforcing spatial patterns enslave evolution in a host-parasitoid system J. theor. biol. 188:11-20 pdf
Savill, N.J. and Hogeweg, P. (1997) Evolutionary stagnation due to pattern pattern interactions in a coevolutionary predator prey model. Artificial Life 3: 81-100
(see also Laan, J.D. van der, Hogeweg. P (1995) Predator-prey coevolution: interactions among different time scales. Proc. R. Soc. Lond. B. 259: 35-42)

D.S. Wilson (1975) The theory of group selection. Proc. Nat. Acad. Sci USA 72:143-146


Return to ecological based solutions of error threshold:

In Eigen and Schusters original approach there was an approach by looking at ecology (i.e. mutations were ignored).
In Space (Hogeweg): the same assumptions were made and ecological dynamics were studied: results were that stability is increased and spatial patterns lead to new levels of selection.

However: the whole point was to study the information threshold: i.e. what happens under high muation rates: and these have now only been studied using invasion dynamics, however evolution is evolutionary + ecological dynamics.
So mutation was added, but the structure of possible networks was always kept constant which is more or less restricting the system to the INVASION REGIME => cheating
Moreover, in all these models we are trying to obtain more information, but it is not used for anything!

A nicer approach would be to included the evolved info into the behaviour of the system:
see model of 2 RNA's forming duplexes (ligation) which then catalyses replication of (all) other RNAs (mutants and parasites).
this forms a star network.
Results show that this is very stable! This is because the interface where duplex can form is very narrow and it is hard for parasites to persist because they need to be at that location. Moreover there is a an implicit parameter in trade-off between replication or to be replicated and strong altruist looses chance to be replicated.
In evolution: strength ligation goes down, but levels off. this minimizes ligation so that they can just exist themselves and this gives advantage over parasite which is always below this critcality (since it is hard for it to be at the interface!).
So there is a dominance of one or two RNAs due to their isolation at the interface
Moreover if there is diversity of replicases: parasites cannot optimize themselves at all!
Moreover if ligation of parasites: if newly evolved is killed because ligation product is not active due to mutant.
Crucial point here is assumption of ligase product: extra info!!!

So how was this modelled:
expandable matrix of who gives catalysis to who
AND mutant gets catalysis of same things, but changed parameters: no correlation
In order to get correlations requires a relationship solving according to its actual structure: i.e. implicit correlations, which might change system (NOBUTO IN PROGRESS!!!)

State of Art Info Threshold: WE DON'T KNOW! No satisfactory answer, but parasite problem can be solved!

Eco Evo Timescales

Eco models: monomorphic population and study ecological stability/ dyamics
Evo models: constant population size (quasi species equation) or assuming a QSS (i.e. population dynamics in attractor, parameter dependece) and studying invasion dynmaics (i.e. low mutation rates, monotypic population) (adaptive dynamics).

It is clear that separate time scales are assumed here!

Eco-Evo models:
-we saw that separation of time scales from dynamics and fate of parasites depends on which timescale used
-similar time scales in multi-level evolution: replicator vesicle dynamics should be the same
SO: interlocking: fitness on time dependent function.

How dangerous: separation of time scales: the case of Male Killers! (Groenenboom)

Wolbachia: parasite maternally inherited kills male offspring
(show model)
FInd qualitatively different results according to alpha parameter: no infection, coexistence, die out (no more males).
However if taken RATIO inf/uninfected one would have concluded that still infection/coexistence because the ration remains constant despite (atto-)extinction.
This is a common error in theoretical papers which tend to use ratio! I.e. assume they can keep population size constant despite not having a viable population!

Eco-Eco: van der Laan + Hogeweg

pred + prey evolution: many variants with probability on consumption depending on gaussian around optimum phenotype value.
non-spatial: with prey competing globally with sigma indicating width gaussian curve.
only in Shape-space: ordered variants with nearness relationship (wrapped).

Model started monomorphic and symmetrical initially (i.e pred + prey). Oberved in speciation into two prey-pred pairs (PIC).
However, pred are not on top of prey but in between + some evolutionary wiggles and population dynamics are pretty much stabilized
(if mutations stoppped, then get oscillations).

So how to characterize role of evolution?
stop mutations and see what happens:
-system dies out! but that depends on WHEN mutation rates are stopped
-diversity is lost when mutation rates put to zero: this is not just quasi-species but four species which are true species.

The wiggle shows that at all times you are being pushed. Indeed this is a very simple model, but it could be an important mechanism for ecosystem diversity: i.e. continuous adaptation through mutations.

In order to gain more understanding the system is now described using ODEs: to try and get parameters.
However, with no mutations the system dies out. But if done very carefully:
-measure parameters over long enough and avergae parameters over time: then YES, the four ODE system survives.
However, there are still differences:
-in ODE there are huge cycles and greater atto-fox problems.

-very narrow parameter range to make ODE viable at eco-time scale (i.e. when time scales separated)
-population dynamics of each species: period of system is much shorter that in eco model which is probably counter intuitive since EVO is generally thought of as a slow process. Instead EVO speeds up ECO: interlocking timescales.

What about MUTATION RATE?: here compare fullsimulation rates at different mutation rates and the derived ODE
- find that the effect of EVO on ECO is strongest for low mutation rates! (counter intuitve)
- this is because mutations affect how far pred and prey bands are away from each other: small mutations equals distance from prey, high mutations means more close to prey (more specialized).
- In eco equi-distant from prey means chaotic behaviour: here it is not chaotic and system organizes itself into stability
(incidentally, different non-wrapped boundary conditions do not significantly change the results at least in the middle)

So what about sigma (i.e. width interaction):
- if sigma gets higher wiggles get longer
- if lower, one gets red queen dynamics

This study shows:
- existence proof: counter example to eco fast, evo slow
- shows that evo could play an important (continuous) role in stabilizing ecosystems.

Note: we assumed prey and pred have same mutation rates, however allowing higher mutation rates in pred does not change much. This is because evolution is always mediated by competition (selection coefficient). Hence results hold for unequal mutation rates too.

SPACE-SPACE: what about the same analysis in space?
Most common behaviour is that of a prey diversifiying and pred remain constant and then pred suddenly switching (short period of two predators) and then staying the same again.
population dynamics show: stable pred and changing prey

space patterns: oscillations between:
- small scale patterns
- large scale patterns
in switches: small scale pattern where pred and prey are close enough, strong predation and large waves
when prey mutates enough then strength predation low, and can live amongst prey: specialize (larger waves)

Nicholson-Baily host-par: MAP

Debate on whether ODE or MAP would be better descriptor of evolution of parasite migration (beta)
Savill studied this in space: Lattice MAP (eco-evo)
in model
-parasitoid kills host
-study migration of parasite: B=1 all hosts get same amount of parasite: differentiation according to host density
-if B=0 differentiation is random and B>1 always to host with higest density
- add mutation of B

Results show spiral patterns and more chaotic regions
Moreover there a three levels of selection
- host / parasites
- spiral waves / chaotic waves
- regions of spiral waves / regions of chaotic waves

There is emergence of a life history of spirals:
- new spirals are born at interface spiral and chaotic with high B
- depends on which pattern to which B will evolve
- also: with high B chaotic and low B spirals

- spirals born at intervals due to spatial dynamics
- with relatively high B: descended from chaotic: rotate fast, active migration and increasing domains
- however when live as spiral: B decreases and domain is lost
- everyone comes from core
- low B has more chance to stay in core (others leave!)

So there are various selection pressures:
- inclusive fitness: how much fintness over generations
- over 50 generation: low B has least offspring whereever you are
- over 300 generations: low B wins in spiral core and dominates over other locations (spiral arms + chaotic) and wins over long term.
So everyone low B?
- no, during 300 generations, offspring mutates always to higher B

- no fixed fitness which remains the same
- moreover, fitness not fixed over longer time point
- at one time point: lower fitness may be the major source of offspring in system
- multiple time scales in system
- shouldn't look at good of species: but immediate fitness, but effect immediate fitness may be long term fitness!

Example: lions in serengeti
lions fighting: some always risk others dont: so why fight?
- signalling strength (nice males)
- others
all did not work
Conclusion of study: we cannot understand why males fight using darwinian selection: i.e. costs fighter benefit nonfighter
However: possible answer is group-level benefits
But this was TABOO:
in 1975 DS Wilson was not believed (vs EO Wilson), however now (2005), EO Wilson has admitted that DS was right (DS had long term fitness!)

So how to tear concepts kin selection and group selection apart?
DS used a separation (special case) in order to tear two processes apart in order to prove the case of group-selection. Kin selection then can just be seen as a parameter (how to make groups) in group-selection.