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Genome-wide forward simulations of evolving populations

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SelectionRegimes

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Attachments

CodeCogsEqn.png (2164 bytes)

dimret-example.png (22359 bytes)

directional-selection.png (21249 bytes)

dirsel-equation.gif (5645 bytes)

disruptive.png (25167 bytes)

gauss-example2.png (11219 bytes)

1 Files specific to mode qt
- truncating selection (--selection-regime)
  - selection for large phenotypic values
  - selection for small phenotypic values
2 Files specific to mode qff
- fitness function (--fitness-function)
- sex specific fitness function (--fitness-function)

1 Files specific to mode qt

truncating selection (--selection-regime)

selection for large phenotypic values

Per default MimicrEE2 performs truncating selection for the most pronounced phenotypic values (e.g the tallest individuals).

1   0.5
3   0.2

col1: generation
col2: selected fraction of individuals with the largest phenotypic values (i.e. fraction of individuals surviving truncating selection; these survivors will mate and the offspring will constitute the next generation)

Note A selection intensity must be provided for the first generation
Note For not provided generations the selection intensity of the next closest previous generation is used; This allows to provide short selection regime files;

selection for small phenotypic values

MimicrEE2 also allows performing truncating selection for the least pronounced phenotypic values (e.g. the smallest individuals). To select the small phenotypes simply provide negative values for the selected fraction.

1   -0.5
3   -0.2

col1: generation
col2: when multiplied with -1.0, the selected fraction of individuals with the smallest phenotypic values

Note It is also possible to mix selection for large and small phenotypic values.

2 Files specific to mode qff

fitness function (--fitness-function)

MimicrEE2 supports many different fitness functions.
The first line of the file is used to distinguish between these options.

stabilizing selection [stabilizing]

With stabilizing selection a Gaussian fitness function is used to map the phenotype to fitness.
This input file allows providing the shape for the Gaussian function for each generation. This allows simulating a moving optimum.

[stabilizing]
1       0.7     1.2     6       2
10      0.7     1.2     8       2
30      0.7     1.2     10      3

col1: generation
col2: min. fitness
col3: max. fitness
col4: mean of the fitness peak
col5: standard deviation of the fitness peak

Note a fitness function MUST be provided for the FIRST generation
Note a fitness function is valid for all following generations, until a new function is provided. In the above example the first entry is valid from generation 1-9 the second entry from generation 10-29 and the third from generation 30 onward.
Note per default the fitness function applies to all sexes

As an example the first entry of the file (0.7, 1.2, 6, 2) yields the following fitness function:

In this example only phenotypic values between 0 and 12 are shown. For very small and very large phenotypic values the fitness converges towards the minimum fitness (i.e. 0.7).
The highest fitness is 1.2 at the phenotypic value 0.6 and the standard deviation of the Gaussian is 2.

disruptive selection [disruptive]

Disruptive selection is similar to stabilizing selection. It also uses a Gaussian fitness function to map phenotype to fitness. Only difference the position of the fitness valley is provided instead of the peak.

[disruptive]
1       0.1     1.2     0       3
10      0.1     1.2     1       3
30      0.1     1.2     2       3

col1: generation
col2: min. fitness
col3: max. fitness
col4: mean of the fitness valley
col5: standard deviation of the fitness valley

Note a fitness function MUST be provided for the FIRST generation
Note a fitness function is valid for all following generations, until a new function is provided.

As an example the first entry of the file (0.1, 1.2, 0, 3) yields the following fitness function:

diminishing returns epistasis [dimret]

MimicrEE2 allows to simulate diminishing returns epistasis for a quantitative trait according to the following fitness function (similarly to Kosheleva and Desai 2017 MBE) :

Where f_min is the minimum fitness, f_max the maximum fitness, alpha the steepness of diminishing returns and beta the position of the function.

Note MimicrEE2 uses max(f, f_min), thus f_min will be used for f smaller than f_min

[dimret]
1       0.0     1.2     0.2       0
10      0.2     1.2     0.4       0
30      0.3     1.2     0.5       0

col1: generation
col2: min. fitness
col3: max. fitness
col4: alpha (influences the steepness of the curve)
col5: beta (shifts the position of the curve on the abszissa)

Note a fitness function MUST be provided for the FIRST generation
Note a fitness function is valid for all following generations, until a new function is provided. In the above example the first entry is valid from generation 1-9 the second entry from generation 10-29 and the third from generation 30 onwards.

As an example the first entry of the file (0.0, 1.2, 0.2, 0) yields the following fitness function:

directional selection [dirsel]

Similarly as implemented in quantiNemo (https://www.ncbi.nlm.nih.gov/pubmed/18450810) MimicrEE2 allows to simulate directional selection using the following equations:

The parameters of this equation may be provided in the fitness function

[dirsel]
1       0.3     1.2     1       -0.4     0
10      0.3     1.2     1       -0.6     0
30      0.3     1.2     1       -0.8     0

col1: generation
col2: min. fitness
col3: max. fitness
col4: s symmetry of the curve
col5: r growth rate
col6: beta (shift of the curve on the abszissa)

Note a fitness function MUST be provided for the FIRST generation
Note a fitness function is valid for all following generations, until a new function is provided.

As an example the first entry of the file (0.3, 1.2, 1, -0.4, 0) yields the following fitness function:

arbitrary fitness function [interpolate])

The Gaussian fitness function or diminishing returns epistasis only covers some specific cases of the infinitely many possible functions that could be used to map phenotypic values to fitness.
To enable more complex fitness functions we allow the user to provide as an approximation, arbitrary many pairs of phenotypic values and corresponding fitness values. Missing values will be interpolated linearly. This allows to approximate any fitness function with an arbitrary precision (e.g. increase precision with more dense data points).
For phenotypic values outside the range of provided values the fitness of the next closest phenotypic value will be used.

[interpolate]
1   0.0 1.2
1   0.5 1.1
1   1.0 1.05
1   1.5 1.2
1   2.0 1.3
5   0.0 1.2
5   0.5 1.1
5   1.0 0.8
5   1.5 1.2
5   2.0 1.3

col1: generation
col2: phenotypic value
col3: fitness (w) for the corresponding phenotypic value

No particular sorting of the entries is required.

Note a fitness function MUST be provided for the FIRST generation
Note a fitness function is valid for all following generations, until a new function is provided. In the above example the first entry is valid from 1-4 generations and the second entry from 5 onward.
Note the accuracy of the arbitrary fitness function may be increased by providing denser phenotypic values

sex specific fitness function (--fitness-function)

MimicrEE2 supports sex specific fitness function. Sex specific fitness functions are currently supported for stabilizing selection, disruptive selection, diminishing returns epistasis, directional selection and arbitrary fitness functions.

sex specific stabilizing selection [stabilizing]

To provide sex specific stabilizing selection it is just necessary to add more columns (13 columns in total).

[stabilizing]
1       0.7     1.2     6       2    0.7     1.2     8       2    0.7     1.2     6       2
10      0.7     1.2     8       2    0.7     1.2     6       2    0.7     1.2     6       2
30      0.7     1.2     10      3    0.7     1.2     10       2    0.7     1.2     6       2

col1: generation
col2: min. fitness - males
col3: max. fitness - males
col4: mean of the fitness peak - males
col5: standard deviation of the fitness peak - males
col6: min. fitness - females
col7: max. fitness - females
col8: mean of the fitness peak - females
col9: standard deviation of the fitness peak - females
col10: min. fitness - hermaphrodites
col11: max. fitness - hermaphrodites
col12: mean of the fitness peak - hermaphrodites
col13: standard deviation of the fitness peak - hermaphrodites

sex specific disruptive selection [disruptive]

To provide sex specific disruptive selection it is just necessary to add more columns (13 columns in total).

[disruptive]
1       0.1     1.2     0       3     0.1     1.2     3       3    0.1     1.2     0       3
10      0.1     1.2     1       3     0.1     1.3     2       3    0.1     1.2     0       3
30      0.1     1.2     2       3     0.1     1.4     1       3    0.1     1.2     0       3

col1: generation
col2: min. fitness - males
col3: max. fitness - males
col4: mean of the fitness valley - males
col5: standard deviation of the fitness valley - males
col6: min. fitness - females
col7: max. fitness - females
col8: mean of the fitness valley - females
col9: standard deviation of the fitness valley - females
col10: min. fitness - hermaphrodites
col11: max. fitness - hermaphrodites
col12: mean of the fitness valley - hermaphrodites
col13: standard deviation of the fitness valley - hermaphrodites

sex specific diminishing returns epistasis [dimret]