Poster on "population genetics of gene function", presented a Jacobs University, Bremen, during "Ecogrids" workshop in July 2012

1. POPULATION
GENETICS
OF
GENE
FUNCTION
Ignacio
Gallo
ANALYTIC NOVELTIES
We are interested in a situation where the “blue” and “green”
alleles schematically depicted in Fig. 1 are in a state of
dynamical equilibrium that may be characterized by a stable
distribution for the gene frequencies. Equilibrium is maintained
by reversible mutation acting jointly with the various selective
forces.
The two mode diagrams above give a summary of local
maxima (solid lines) and minima (dashed lines) for the gene
frequency distribution. Maxima and minima are plotted against
mutation rates: different curves correspond to different
intensities of reproductive selection.
The curve highlighted in red illustrates the qualitative change
caused by including life-span differentiation.
In the classical case (left) the random-drift regime ends
abruptly when the mutation rate equals one, whereas life-span
differentiation leads to bifurcations during the transition (right).
POSSIBLE IMPLICATIONS
The qualitative effect of considering life-time
differentiation in a population genetics model,
highlighted in the last section, is a relatively small one: it
clearly suggests, however, that the details of the
functional difference between alleles can lead to
population-dynamical consequences which are
potentially observable at a phenomenological level.
For instance, the peculiar bimodality of the equilibrium
distribution shown in Fig. 2 suggests the existence of
two clear time-scales for the dynamics of the
population: one time scale characterizing the fluctuation
around the modes, and another characterizing the
switch from one mode to the other.
This feature is potentially observable, and it implies the
possibility of identifying values of mutation, of the
selective coefficient, and of the life-span ratio by using
demographic statistics.
FUTURE DIRECTIONS
In order to help this simple toy model approach
empirical relevance, two research directions need to be
pursued.
One consists in looking for further insights coming from
the analytical form of the mapping going from the
genetic functional parameters to the population
features: these can be used as signatures against
which to check the relevance of the model.
The second concerns establishing a procedure allowing
to recover the model’s parameters from simulation
statistics, in order to prepare the model for an eventual
empirical application.
ACKNOWLEDGEMENTS
This model was partially inspired by a model drafted by
by Henrik Jeldtoft Jensen. The research was supported
by a Marie Curie Intra-European Fellowship within the
7th European Community Framework Programme.
INTRODUCTION
Population genetics can be used, in principle, to infer information
regarding the function of genes by observing the way genes are
distributed in a population in a state of dynamical equilibrium.
At a coarse level of description the function of a gene can be
characterized by its influence on the two dimensions of reproduction
and survival of an organism.
MODEL
We model the distribution of a gene’s alleles throughout a population.
The gene gives rise to only two phenotypes, but each phenotype
comprises many different genotypes which are selectively neutral with
respect to the other genotypes of the same phenotype.
This is the case of the alcohol dehydrogenase locus of Drosophila
melanogaster, for which a polymorphism of this type which has been
studied extensively.
The distribution can be represented schematically as follows:
We see that the demographic information available for a population of
this type includes the statistics of the relative population sizes for the
two phenotypes, as well as sample estimates for the number of
genotypes available for each phenotype.
As shown in Fig 1. the phenotype which is most abundant not
necessarily includes the largest number of genotypes.
The model presented here characterizes such discrepancy as arising
from the way mutation is balanced by the two separate selective
influences implied by differentiation in reproduction, and in life-span.
The latter relates to the organism potential for survival.
Fig. 1
relative frequency of “blue” alleles
Fig. 2
probabilitydensity
Having different average Life-
spans in the two the organisms
leads to regimes where the
equilibrium distribution exhibits
a shape which is a hybrid of
the random drift and the
mutation-selection regimes of
standard population genetics
models (Fig.2).
mutation rate mutation rate
relativefrequencyof“blue”alleles
relativefrequencyof“blue”alleles
€
T1
T2
=1
€
T1
T2
=
3
2
(life-spans are equal for the to types
of organism)
random drift mutation/selection balance