Download Selecting for Evolvability

Selecting for variation: the benefits of infidelity
Adam Hockenberry1
1
Interdepartmental Biological Sciences Graduate Program, Northwestern University, Chicago, IL U.S.A
RESULTS
ABSTRACT
Evolutionary theory posits that over time both genetic drift and natural
selection lead to a decrease in variation within a population. Variation is
maintained by other processes such as gene flow, mutation, and sexual
reproduction. However, mutation is not only a exogenous phenomenon.
Rates of mutation vary across individuals and between species leading to
speculation that the capacity to produce evolutionary change, heretofore
referenced as evolvability, is selectable at the individual level. Whether the
ability to evolve can itself be the subject of evolutionary pressures and
whether it has been in the past is, however, still an open question. Through
the use of agent based modeling, we show that the ability to maintain
replicative variation can be selected for under certain conditions. These
results add to the growing body of evidence which shows not only the
possibility, but the likelihood of selection for evolvability in extant lineages.
METHODS AND MODEL DESIGN
Environmental agents are stationary and simply grow food. They do, however, have maximum amounts of food
that they contain as well as adjustable nutrient production rates which gives the system a defined carrying
capacity. They also have an environmental `genome' which can be thought of as a binary representation of
several nutrients or toxins that they contain.
Bacterial agents have their own genomes which, unlike the binary environmental counter parts, are floating
point numbers between 0 and 1. At each time step bacteria move pseudo-randomly, eat to gain energy, and
lose a set amount of energy. If they have a threshold level of energy they reproduce and if they have zero
energy, they die.
Selection acts through their feeding as the individuals with genomes that more closely match the
environment are able to eat more at a given time step which will allow them to reproduce faster and
have a lower chance of dying. As an example:
let the environmental genome = 0, 1, 0, 1, 0
for a given bacterial genome = 0.32, 0.75, 0.47, 0.98, 0.22
the amount of energy harvested from the environment = 5 - 0.32 - 0.25 - 0.47 - 0.02 - 0.22 = 3.72
Bacteria pass their genome to their offspring with variation according to the value of their error-rate. Each
value is passed on according to a random-normal distribution centered around the current value with a
standard deviation equal to the value of the error-rate and there is an absolute floor set on error-rates (0.1) to
represent a maximum replicative fidelity that is achievable in a stochastic chemical system. The error-rate
parameter is crucially also passed on to offspring based on a random normal distribution described above.
In addition, the environmental genome can change over time. At each time step, there is a small chance that
one (or more) of the environmental `genes' will flip from a 1 to 0 or vice versa. In addition, the sharply peaked
fitness landscape can be varied by inserting various valleys of user defined depth and breadth. In effect, this
penalizes bacteria which have a range of specific values for certain genes making it difficult to move between
their current state and the optimum level.
An illustration of the model’s graphical user interface and run-time output
Replicating the basic features of evolution
Our system produces
population dynamics
illustrative of a defined
carrying capacity (a). (b)
Mean (black), min (green),
and max (red) generation
present in the population
during a representative
run. (c) Separate runs
showing the mean match
of individuals in the
population to the
environment at each time
step. (d) Separate runs
showing the mean errorrate across the population
over time.
Evolution in an unstable environment
(a) Population dynamics
for a representative run
with a 1:100 chance of a
magnitude 40%
environmental change
occurring at each time
step. (b) Trace of
generation time during the
same run shown in (a). (c)
Separate traces for the
same environmental
change showing the
oscillatory dynamics of
match to the environment.
(d) Separate traces
showing the error-rate
over time of the same 5
runs illustrated in (c).
Error-rates and environmental change
Histograms show the mean error-rates at each time step of 5 model simulations
of 10000 time steps each with a starting error-rate of 0.1. (a) For a given
magnitude of environmental change (40\%), increasing frequency of change
occurring shows increased time spent at higher error-rates. (b) For a given
frequency of environmental change (1:100) increasing magnitude of changes
pushes the population to spend more time at higher-error rates.
Features of a complex fitness landscape
(a) Schematic showing the
implementation of fitness
valleys which lead to local
fitness maxima. (b) Red
traces show error-rates
from separate runs under
conditions of
environmental stasis. Black
traces show separate runs
under conditions of
environmental change. (c)
For a set fitness valley
depth, breadth of valley
(0.1 red, 0.2
green)influences lag time
for population to reach
optimal match to the
environment. (d) For a set
fitness valley breadth,
depth of fitness valleys (0.5
blue, 1 green) influences
lag time for population to
reach optimal match to the
environment. (c) and (d)
show 5 representative runs
for each case. (e) For a
stable environment,
population levels and errorrate are relatively
consistent throughout
representative run. (f)
During periods of
environmental change,
population levels fluctuate
and correlate with
increases in mean
population error-rate.
CONCLUSIONS AND FUTURE DIRECTIONS
Results presented here hint that growing cultures of bacteria under
highly stable conditions for several thousand generations may lead to a
global decrease in error production whereas growing cells in highly
unstable environments can select for replicative infidelity. This could have
strong implications for biotechnology and cloning processes which rely
on bacteria to produce molecules. These bacteria frequently evolve ways
to circumvent the designers plans but perhaps evolving a strain with
decreased capacity for generation of variation would alleviate these
issues. Concurrently, for directed evolution experiments which try to
evolve bacteria to perform a non-native function, harsh and unpredictable
environments may produce quicker evolutionary change within the
population. This model represents a potential way forward for many
challenges of biological design that would benefit from the ability to tune
evolution.
A possible extension is to remove the 1-to-1 mapping between
bacterial and environmental genomes and include an error-prone
transcription/translation step. The dynamics of how this error-rate and the
existing replicative error-rate co-evolve may produce interesting results
with potential real world applications in fields attempting to use cellular
transcriptional and translational machinery for the production of novel
sequence defined drugs and materials.