Download A threshold model for punctuated gradualism

Medical Hypotheses 17: Zlq-Zag, 1985
A THRESHOLD MODEL FOR PUNCTUATED GRADIIALISM
J.A. Kieser. Department of Orthodontics, School of Dcnti xtrq . Xi twatcrsrand
University, Johannesburg, South Africa.
H.T. Groencveld, Department of Biostatistics, Medica 1 Rcscarch i‘ouni, i I
Johannesburg, South Africa.
ABSTRACT
A model for continuous and discontinuous evolutionary chanec is pt~opo~~~d
that accommodates both punctuated equilibrium and phyletic gradualism.
Natural selection operating on a gaussian distribution of phcnotypc5
subjected to severe stress will result in a shewine of the normal dist-r-ihutIf a reproductive isiolation
ion in the direction of the favoured phenotype.
threshold is imposed upon this model. r a p i d crossing; of the t h r e s h o l d
by large numbers of individuals within the skewed distribution wi 11 r<~~ul t
in the sudden achievement of a critical descendant population ma\\.
Yild directional se1 ection however, w i l l result in gcntlc s h i f t s of’ the
qaussian mean thus leading us to suggest that stasis and incipient .pcciatio
are extremes of the same spectrum, defined by the rates of mran-shift
in response to varying severities of selection pressure.
Both pun\,tuated
and gradualistic evolution as accommoda.ted in our model may furthct- bc
described within Thorn’s cusp catastrophe theor->-.
Though the process of evolution is frequently employed b>- biomedical
scientists to address questions of phenotypic change and adaptation in
populations rangeing from micro-organisms to man, few have questioned
the underlying conceptual mechanisms of evolution. S i n c e ilhar-lcs D,~rwin
first stressed the importance of ‘I... slow and gradual accumulation of
numerous slight, yet profitable, variations” (1). the model of phylctik.
gradualism has survived the neo-Darwinian synthesis to gain asccndanc>
as the dominant model of evolutionary change (2. 3, 4. j, 6). Significant
questions concerning this mechanism have recently been raised with the
formulation of the model of punctuated equilibrium by Eldredge and Gould
( 7 , 3?, which has in turn prompted the “decoupling” of macro-cvslut i,>n
from micro-evolution (9, 10).
In this communication, we suggest a unitary model of evolution which
accommodates both gradual unidirectional phenotypic change and sudden
speciation followed by stasis.
THE THRESHOLD MODEL
The normal distribution density of phenotypes in a randomly mating population may be characterised by (or transformable to) a gaussian distrihution
with average phenotypes clustered about the mean and phenotypic divcre;ents
219
peripherally located in the tails. Anagenesis within this population
is governed by natural selection which tends to maintain symmetry around
the mean under stable environmental conditions. Gradual phenotypic change
due to progressive adaptation or to adjustments to gradual environmental
change are achieved simply by a shift in the gaussian mean. In order
to explain speciation however, it is necessary to impose a threshold
on the normal distribution such that only individuals who lie a given
distance from the mean (measured in standard deviation units) may achieve
reproductive isolation by crossing over the threshold (Fig. 1A). Phenotypic
peripherals that cross this reproductive isolation threshold under stable
environmental conditions perish because they fail to achieve the critical
population mass necessary for the establishment of a viable descendant
population (normalising selection). Crossed over individuals might be
considered as equivalent to Goldschmidt's hopeful monsters (ll), or
Schindewolf's grossmutants (12). Under environmentally stressful conditions,
the rapid accumulation of phenotypes that will allow their possessors
to survive in preference to those phenotypes that render them more liable
to extinction will skew the normal distribution in the direction of the
favoured phenotype (Fig. 1B).
(
I
A
B
Figure 1
A threshold model of speciation in a randomly mating population:
A - gaussian distribution of phenotypes under stable environmental conditions; B - skewing of the distirbution in response to severe environmental
stress.
If clustering is directed towards the threshold, a situation will be reached
where large numbers of phenotypic favourites will have accumulated just
short of the threshold, accompanied by very little movement in the population
mean (since the mean continues to be influenced by extreme values).
One result of this disproportionate accumulation of individuals is an
increase in the relative abundance of mutations short of the threshold,
a "genome in turmoil" (13). Further skewing spurred by the continuous
erosion in the numbers of unfavoured phenoytpes and possibly precipitated
by a rapid accumulation of mutants will result in the rapid crossing
over of large numbers of favoured individuals to reproductive isolation,
220
esulting in turn in the achievement of a critical population mas, cf‘tcn
shenotypically vastly different from its ancestral population (FiL:. 2).
Figure 2 Further skewing of the normal distribution as a result of nitural
selection results in rapid crossing of large numbers across the rcproductivc
isolation threshold and hence the establishment of a critical population
mass.
Whilst persistent or lethal stress will render the putative ancestral
population extinct, a progressive lessening threat will result in the
formation of two chronospecies. In the absence of a threshold. the entire
species may either become extinct or undergo gradua 1 phyletic change.
depending on the severity of the threat.
PUNCTUATION ANP GRAIXIALISM
The punctuation model holds that most evolutionary change is concentrated
in geologically instantaneous speciation events (7, S;, 14). Al though
the model thus defines the mark of origin of a species it offers no acrual
mechanism of speciation (15). Vrba has suggested that the spcciation
model favoured by punctuationalists is that of allopatric sprciation
in small isolates (10, 17). Against this sudden origin of species is
set the more conventional theory of phyletic gradualism which strcs\ch
the gradual transformation of one species into another (3) and ernphd?i<.eq
the lack of spatio-temporal discreteness of species (16. 15).
Punctuat ionalists originally based their model on the rapidity with which. mor-phological discontinuity had been shown to appear in the fossil record ,rnd
on the observed lack of transitional fossil forms. which has r-eccntlr
been underscored by studies on Ordovican trilobites, Mesozoic and Cenozoic
molluscs. radiolarians and hominids (19, 20). D e t r a c t o r s however , lia\rc
pointed out that the punctuation model is based upon negative rather
than empirical evidence (gaps in the fossil record) (Zl), that the model
is based on a temporal solipsistic definition of the graduality of “zraduat
(22) and that rapid phyletic speciation may be accounted for by Lewis’
saltation model or Whites’ stasipatric speciation model (10). Based
on Ozawas ’ observations G!.j)? we argue that time-dependent uniditol~tion;tl
221
phenotypic change (gradualism) coexists with rapid speciation as visualised
by the punctuation model. That punctuation and phyletic gradualism are
not mutually exclusive has recently been shown in Cretaceous ammonites
and Jurassic bivalves where a punctuated pattern of morphological discontin
uity coexists with gradual changes in size and sutural complexity (24, 25).
CUSP CATASTROPHE THEORY
Our punctuated gradualistic model may be better visualised using Rene
Thorn's qualitative catastrophe theory. Briefly stated, the model relates
to a system governed by a potential function V(QiAJ) where 83 is a set
of k externally controlled parameters and Q. a set of n state variables
or generalised coordinates. Whilst minimalivalues of Q. govern stability,
In a kstationary values of V with respect to Q. govern equilibrium.
dimensional space, surfaces may then be defined by the n equilibrium
equasions
av _
-_=u
aQi
whilst lack of equilibrium may be expected at critical states defined
by the vanishing stability determinant
a'v
(26, 27).
aQiaQj
A topological speciation model may then be plotted with the two control
parameters reproductive success and restraint as axes on a horizontal
plane which is referred to as the control surface (Fig. 3). For each
point on this surface the most probable behaviour of the species is
represented by a point directly above that on the control surface at
a height appropriate to the behaviour (28). Collectively, these behaviour
points present another surface above the control surface called the
behaviour surface. This surface is characterised by an overall slope
from high to low levels of reproductive success (Fig. 3). Rene' Thorn's
cusp catastrophe theory indicates that in the middle of this surface
there is a smooth double fold defined by the bimodality of behaviour
at some of the control points. The fold lines of this pleat define
catastrophes or sudden irreversible changes in behaviour. Consider path
1 in Figure 4, a species subjected to mild stress will experience a gradual
gaussian mean shift due to directional selection towards higher levels
of reproductive success (phyletic gradualism). Path 3 however, indicates
the behaviour of a threshold distribution. The stressed population moves
on the lower behaviour surface towards point B when it encounters the
fold line and jumps the gap towards the upper level of the behaviour
surface - completing a speciation catastrophe (punctuated equilibrium).
A reversal of this path (path 2) leads to a sudden extinction catastrophe.
HIERARCHIALISATION AND SPECIES SELECTION
The spatio-temporal individualisation of species offered by our threshold
model allows for the consideration of species as units of selection,
with favoured units exhibiting high speciation rates (7, 9, 14, 20, 29).
Within our model, species selection will favour specific variability
and the formation of interspecific thresholds, which in turn will lead
222
to higher speciation rates (considered to be the prime mechanism of specie?
selection) (14).
Renk Thorn’s generalised cusp catastrophe graph (see text for
Figure 3
explanation).
Figure 4 Continuous and discontinuous changes in speciation and extinction
shown as paths on the catastrophe graph (see text for explanation).
P<,th 1: phyletic gradual change, Path 2: extinction, Path ,?: p u n c t u a t e d
equilibrium.
223
MUTATIONS
According to our model, the sheer bulk of pre-threshold individuals within
the skewed gaussian curve will result in relatively high numbers of
mutations (gene - or chromosomal) available to the population prior to
speciation. Vrba has in fact suggested that the quality of change during
the speciation event may differ from that which characterises gradual
change (16). We hypothesise that this relative accumulation results
in a mutation pressure that enhances threshold crossing and may result
in the establishment of a descendant species that will differ quite
considerably from the ancestor-al phenotype. We further support the
hypothesis that selection will favour species that code their genetic
information so that mutations are more likely to result in viable individuals - selection for selectability - thus giving rise to a double feedback
loop cybernetic system (30). It is also suggested that the relative
increase in mutations in the pre-speciation distribution will result
in an increase in phenotypic variation during speciation, an effect that
has recently been documented in Cenozoic molluscs (31).
EXAPTATIONS
Gould has stressed the importance of those features that did not arise
as adaptations but are by-products of selection (14, 32). We suggest
that because of the high concentration of potential mutations in the
skewed pre-speciation gaussian curve, large numbers of exaptations (nonadaptive features) may be "piggy-backed" across the threshold, thus further
enhancing the phenotypic differences between descendant and ancestral
populations, and possibly providing a way out of Mivart's dilemma.
REFERENCES
1.
;:
4.
5.
6.
7.
8.
9.
10.
11.
Darwin C. On the Origin of Species by Means of Natural Selection.
Murray, London, p. 454, 1859.
Berry RJ. Neo-Darwinism. Edward Arnold, London, 1982.
Gingerich PD. Paleonology and phylogeny: patterns of evolution
at the species level in early Tertiary mammals. Am J Science 276:
1, 1976.
Boucot AJ. Rates of size increase and of phyletic evolution. Nature
261: 694, 1976.
Ayala F. Population and Evolutionary Genetics. Benjamin Cummings,
California, 1982.
Ayala F. The Mechanism of Evolution. In: Evolution, Freeman and
Sons, San Francisco, p. 14, 1978.
Eldredge N, Gould SJ. Punctuated equilibria: an alternative to
Phyletic Gradualism. In: Models in Paleobiology (Schopf, TJM,
ed), Freeman and Sons, San Francisco, 1972.
Gould SJ, Eldredge N. Punctuated equilibria: the tempo and mode
of evolution reconsidered. Paleobiol 3: 115, 1977.
Stanley SM. A theory of evolution above the species level. Proc
Nat1 Acad Science U.S.A. 72: 646, 1975.
Stebbins GL, Ayala FJ. Is a new evolutionary synthesis necessary?
Science 213: 967, 1981.
Goldschmidt R. The Material Basis of Evolution. Yale University
Press, New Haven, 1940.
224
12.
13.
14.
I’
2:
17.
1s.
19 *
20.
2 I.
22.
2,: .
34.
25.
26.
27.
3i .
20.
.30 .
il.
Schindewolf OH. PalaGntologie. Entwicklungslchre und Genctik.
Borntraeger, Berlin, 1936.
Pa leohiol
Schopf TJM. Punctuated equilibrium and evolutionary stn\is.
-.
156, i98l.
1.
Gould SJ. Darwinism and the expansion of evolutionary thcor\,.
Science 216:
~3890, 1982.
Sdturc ~;<W: 4171. 10~0.
Smith JM. Paleontology at the high tahlc.
Vrba ES. Evolution. species and fossils: how does lift, cv~~l\cY
S Afr J Science 76: 61) 1Q’QO.
Eldrcdge N. The allopatric model and phy1sgcn.v in Paleozoic
invertebrates.
Evolution 25:
156, 1971.
Rhodes FHT. Gradualism, punctuated equilibrium and the Origin ,\f
Species. Nature 305: 26?, 193.3.
Rhodes FHT. Darwin's gradualism and empiricism - a reply to i:inzcrich.
Nature 309:
116, 1984.
Stanley SM. Chronospccies' longevities. the origin of gcncI,a ;rnd
the punctuated model of evolution. Palcobiol 1:. 26, loT,*.
Gingcrich PD. Darwin's gradualism and empiricism. Nature 700:
116, 19x4.
Penny D. How gradual? Nature 207:
.: , 19s4.
Ozaw-a T.
Evolution of Lepidolina multiseptata in east Asia. Mcm
Fat SI-ionce Kyushu Univ 23:
117, 1?7.5.
Lister A. Evolutionary case histories from the fossil rcc.ord.
Nature 309:
114, 1984.
Hallam A. How rare is phyletic gradualism and what is its \>\:olutionary
significance?
Paleobiol 4:
16. 19785.
Thorn R. Structural Stability and Yorphogenesi\:
an Outline ~7f
a General Theory of Models. Benjamin, Reading. 19,7j.
Thompson JMT. Experiments in catastrophe. Nature 254: .?Q:! . 1975.
Zeeman EC. Catastrophe theory. Scicnt Amcr 2,74:
65, 19;h.
Arnold AJ, Fristrup K. The theory of evolution by natural selec.~ion:
a hierarchical expansion. Paleobiol q:
Il.?. 10*~2.
Pellgett P. Evolutionary unease. Nature 30';: 2,?0. I O"J .
Williamson Pg. Paleontological documentation of spcciation in
Cenozoic molluscs from Turcana Basin. Nature 29':
5.:7. lQ3l.
Gould SJ. Vrba ES. Exaptation - a missing term in the scicnl‘c of
form. Paleobiol 8: il_, 1982.
225