1 intro Flashcards
Evolutionary modelling
*concerned with understanding the change over generations of the heritable traits in biological populations
- Evolutionary modelling aims at describing how populations made of discrete entities (individuals, animals, genes, cells, bacteria) evolve, i.e. change in time. The main processes underlying evolutionary modelling are: reproduction, selection, mutations, migration and randomness. Dealing with these processes requires various mathematical tools.
Darwin’s evolution theory by natural selection rests on the following principles:
(1) Not all produced offspring can survive. (2) Traits vary among individuals. (3) Rates
of survival/reproduction differ. (4) Trait differences are heritable. (5) Offspring of parents
better adapted to environment replace deceased members of the population.
The main objection to his theory
troubled Darwin himself
if a selected variety spreads under blending inheritance, species diversity should rapidly decline, but natural selection needs variability to operate otherwise there is no evolution. The puzzle then is: how can natural selection be compatible with the
maintenance of population’s diversity
According to these “inheritance laws”, during mating the discrete genotypes of individuals get reshuffled and paired, not blended, which allows genetic
variability via chance events
Lamarck’s theory,
theory of “heritability of acquired characteristics” of Lamarck (1744-1829)1 which was based on the belief that organisms have an inherent drive to evolve into more complex forms. The underlying idea was that during its life an organism may adapt to its environment, leading to better adapted individuals by the inheritance of acquired characters producing offspring with continuously improved adaptation
the more an organ is used, the more adapted and developed it becomes. Hence, for Lamarck giraffes would develop long necks by stretching to reach leaves high up on trees: giraffes would keep stretching their neck and would all develop longer necks, a character that they would pass on to next generations, see Fig. 1.3. However, Lamarck’s
theory is disproved by facts: there is no ability to pass on traits obtained during lifetime. On
the other hand, Darwin’s theory says that a group of giraffes with different neck length will
evolve in such a way that natural selection favours those with longer necks that will be more
likely to pass on their genes to the next generations in which there are giraffes of various
neck lengths, with a general increase in the neck length from one generation to the next,
What is evolution and what are the mechanisms underpinning evolution?
Evolution occurs in entities having heredity and requires variability. Evolution is about how
populations change in time due to reproduction, selection, mutations, migration, and chance:
Reproduction
Selection:
Mutations
Migration:
Chance fluctuations:
reprodcution
some growth processes, typically some cells division, happen in synchrony at regular intervals of time. When this happens, the population growth process
is modelled in terms of a discrete-time version of differential equations called difference
equations or maps (Chapter 2). However, it is often appropriate to assume that the time
flows continuously and there is asynchrony in the reproduction. In this case, evolutionary
processes can be modelled with differential equations (Chapter 3).
selection
different types of individuals (species) have different reproduction rates,
and typically compete for resources. The fitness of an individual is proportional to its
reproduction rate: those with higher reproduction rate have higher fitness and spread
faster. The fitness is not constant but varies in time with the population’s composition.
Game theory and evolutionary game theory will allow us to model the effect of selection
when species’ fitness depends on the fitness of the others (Chapters 5-6, 9).
- Mutations:
reproduction is never a perfectly replication process, as errors may occur.
These errors are called mutations; they lead to slightly modified sequences DNA and
therefore enhance genetic variability (Chapter 4).
Migration:
Individuals move and migrate, e.g. to improve their nutrient intake or due
to environmental conditions. Movement enhances genetic variation by allowing genetic
exchanges between separate sub-populations. The process of migration is often modelled
by diffusion-like equations (Chapter 10).
- Chance fluctuations
- Chance fluctuations: Populations have a finite size, and individuals have discrete
genotypes that get reshuffled during mating. Chance, or randomness, therefore matters
in evolution! Often different types have a comparable fitness and in this case chance
preserves genetic variation. In Chapters 7-9 and 11, we will model processes in finite
populations with Markov chains. We shall see that the smaller the population size the
larger the fluctuations.
Luria-Delbr¨uck fluctuation test experiment
- to understand whether mutations in bacteria may randomly occur at any time (spontaneous mutations), or if they are an adaptive response (induced mutations).
*bacteria (E-coli) exposed to viral infection T1 phage, After the infection most of the bacteria die, but due to mutations leading to resistant individuals, the population can recover and contain mostly
resistant bacteria (with mutations),
*the mutation-induced scenario corresponds
to Lamarck’s theory in which individuals acquire some needed characteristics (virus resistance), and pass them on to their offspring; whereas the mutation-spontaneous scenario corresponds to Darwinian theory which assumes that randomness and variation are always present, and selection favours it if the new characteristics leads to a fitness advantage.
*In Luria-Delbr¨uck experiment, the number of resistant colonies on each plate varied greatly
and the variance was considerably greater than what the induced activation scenario predicted
Luria-Delbr¨uck experiment demonstrates that genetic mutations arise spontaneously and randomly, rather than being a direct response to environmental stress.
