Overall title: The geometry of macro-evolution: steps towards a
postmodern synthesis

Lecture 1: On integrative biology, adaptive dynamics, and mesoscale
evolutionary patterns

Adaptive Dynamics (AD) is a recently developed framework geared towards
making the transition from micro-evolution to macroevolution based on a
time scale separation approximation. This assumption allows defining the
(invasion) fitness of a mutant as the rate constant of initial
exponential growth of the mutant population in the environment created by
the attractor of the resident community dynamics. This definition makes
that all resident types have fitness zero. If in addition it is assumed
that mutational steps are small, evolution can be visualised as an uphill
walk in a fitness landscape that keeps changing as a direct result of the
evolution it engenders. One of the intriguing consequences from studying
the singular points of the resulting dynamical systems is the existence
of a fairly ubiquitous type of singularity that engenders what is now
called adaptive speciation. Another type of singular points are the
so-called Evolutionarily Stable Strategies, characterised by the fact
that in the environment created by such a strategy no mutants has
positive fitness. Contrary to what is suggested by their name ESSes may
still repel; attracting ESSes are called CSSes.
Within the AD framework the following macroevolutionary predictions
follow from geometric genericity arguments:
1. When an empty habitat is colonised and the physical environment stays
roughly constant for a sufficiently long time, then initially speciation
occurs very frequently but the overall speciation rate decreases quickly.
2. Initially in the phases of directional selection in between speciation
events a lot of random, non-adaptive, variability is incorporated, most
of which will be weeded out at later stages.
3. Speciation is rare in environments that fluctuate on time scales
between that of directional evolution and speciation (where the latter
tends to be much slower than the former).
4. Given the observed speeds of directional evolution we may expect that
most slow change in the fossil record is due to the tracking of changing
adaptive equilibria, punctuated by rare short periods of fast directional
evolution. The punctuation events are of two types, coupled to
speciation, when a CSS changes into a branching point, and "just so", due
to the collision of a CSS and an evolutionary repellor.

Lecture 2:  Geometric considerations about internal selection: the
selection side of Evo-Devo

The AD arguments are largely local in character. The second part of the
talk looks at general morphological and developmental arguments that bear
on the larger scale geometry of fitness landscapes. From this enlarged
perspective the low dimensional fitness landscapes studied in AD can be
seen as the surfaces of ridges in a much higher dimensional landscape of
potential morphologies, with the abyss around the ridges created by the
lack of a proper development, or functioning, of the corresponding
morphologies. The location of the ridges and abysses is grossly the same
for large sets of possible environmental conditions. Biological parlance
expresses this constancy by referring to the corresponding selective
processes as internal selection. The high dimension combined with the
ridgyness conspire in a number of ways:
1. Developmental systems leading to mutation distributions that are in
some way aligned with the ridges evolve much faster than systems where
such is not the case.
2. The stabilising selection in the off-ridge directions has a great
robustness of the developmental system as inevitable consequence. Yet,
the high dimension of genotype space makes that this robustness can never
lead to a lack of suitable mutational variation, and thereby to the
conservation of features. The fact that evolution largely proceeds
through the quantative variation in the size and shape of homologous
parts is due only to the stabilising internal selection that arises as a
consequence of the organisation of multicellular organisms.
3. So-called allopatric speciation supposedly occurs by separated
populations wandering around in the high fitness maze, so that after a
while their mixed offspring, having intermediate properties, ends up in
the abyss. However, it is not easy to make this idea work.
4. Large mutational steps far more often than not make an individual land
in the abyss, and only the much rarer very small steps keep it on the
top. This provides a justification for the assumption made in AD.

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  J.A.J. Metz  (Hans)

  Section Theoretical Biology, Institute of Biology, Leiden University

  Van der Klaauw Laboratorium, Kaiserstraat 63, NL-2311 GP Leiden
  P.O. Box 9516, NL-2300 RA Leiden, the Netherlands

  tel:  +31-71-5274937       home:  +31-10-4297995
  secr: +31-71-5275180       faxh:  +31-10-4953070
  faxw: +31-71-5274900       Email: metz@rulsfb.leidenuniv.nl

2nd affiliation:
  Adaptive Dynamics Network, IIASA, A-2361 Laxenburg, Austria
  tel:  +43-2236-807 546     fax:   +43 2236 807 466
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