rfitness {OncoSimulR} | R Documentation

## Generate random fitness.

### Description

Generate random fitness landscapes under a House of Cards, Rough Mount Fuji (RMF), additive (multiplicative) model, Kauffman's NK model, Ising model, Eggbox model and Full model

### Usage

    rfitness(g, c = 0.5, sd = 1, mu = 1, reference = "random", scale = NULL,
             wt_is_1 = c("subtract", "divide", "force", "no"),
             log = FALSE, min_accessible_genotypes = NULL,
             accessible_th = 0, truncate_at_0 = TRUE,
             K = 1, r = TRUE, i = 0, I = -1, circular = FALSE, e = 0, E = -1,
             H = -1, s = 0.1, S = -1, d = 0, o = 0, O = -1, p = 0, P = -1,
             model = c("RMF", "Additive", "NK", "Ising", "Eggbox", "Full"))

### Arguments

`g` | Number of genes.
`c` | The decrease in fitness of a genotype per each unit increase in Hamming distance from the reference genotype for the RMF model (see `reference`).
`sd` | The standard deviation of the random component (a normal distribution of mean `mu` and standard deviation `sd`) for the RMF and additive models .
`mu` | The mean of the random component (a normal distribution of mean `mu` and standard deviation `sd`) for the RMF and additive models.
`reference` | The reference genotype: in the RMF model, for the deterministic, additive part, this is the genotype with maximal fitness, and all other genotypes decrease their fitness by `c` for every unit of Hamming distance from this reference. If "random" a genotype will be randomly chosen as the reference. If "max" the genotype with all positions mutated will be chosen as the reference. If you pass a vector (e.g., `reference = c(1, 0, 1, 0)`) that will be the reference genotype. If "random2" a genotype will be randomly chosen as the reference. In contrast to "random", however, not all genotypes have the same probability of being chosen; here, what is equal is the probability that the reference genotype has 1, 2, ..., g, mutations (and, once a number mutations is chosen, all genotypes with that number of mutations have equal probability of being the reference).
`scale` | Either NULL (nothing is done) or a two- or three-element vector. If a two-element vector, fitness is re-scaled between `scale[1]` (the minimum) and `scale[2]` (the maximum) and, later, if you have selected it, `wt_is_1` will be enforced. If you pass a three element vector, fitness is re-scaled so that the new maximum fitness is `scale[1]`, the new minimum is `scale[2]` and the new wildtype is `scale[3]`. If you pass a three element vector, none of the `wt_is_1` options apply in this case, to ensure you obtain the range you want. If you want the wildtype to be one, pass it as the third element of the vector. As a consequence of using a three element vector, the amount of stretching/compressing (i.e., scaling) of fitness values larger than that of the wildtype will likely be different from the scaling of fitness values smaller than that of the wildtype. In other words, this argument allows you to change the spread of the positive and negative fitness values (and you can make this difference extreme and make most fitness values less than wildtype be 0 by using a huge negative number –huge in absolute value– for `scale[2]` if you then truncate at 0 –see `truncate_at_9`). Using a three element vector is probably the most natural way of changing the scale and range of fitness. See also `log` if you want the log-transformed values to respect the scale.
`wt_is_1` | If "divide" the fitness of all genotypes is divided by the fitness of the wildtype (after possibly adding a value to ensure no negative fitness) so that the wildtype (the genotype with no mutations) has fitness 1. This is a case of scaling, and it is applied after `scale`, so if you specify both "wt_is_1 = 'divide'" and use an argument for `scale` it is most likely that the final fitness will not respect the limits in `scale`. If "subtract" (the default) we shift all the fitness values (subtracting fitness of the wildtype and adding 1) so that the wildtype ends up with a fitness of 1. This is also applied after `scale`, so if you specify both "wt_is_1 = 'subtract'" and use an argument for `scale` it is most likely that the final fitness will not respect the limits in `scale` (though the distorsion might be simpler to see as just a shift up or down). If "force" we simply set the fitness of the wildtype to 1, without any divisions. This means that the `scale` argument would work (but it is up to you to make sure that the range of the scale argument includes 1 or you might not get what you want). Note that using this option can easily lead to landscapes with no accessible genotypes (even if you also use `scale`). If "no", the fitness of the wildtype is not modified. This option has no effect if you pass a three-element vector for `scale`. Using a three-element vector for `scale` is probably the most natural way of changing the scale and range of fitness while setting the wildtype to a value of your choice.
`log` | If TRUE, log-transform fitness. Actually, there are two cases: if `wt_is_1 = "no"` we simply log the fitness values; otherwise, we log the fitness values and add a 1, thus shifting all fitness values, because by decree the fitness (birth rate) of the wildtype must be 1. If you pass a three-element vector for scale, you will want to pass `exp(desired_max)`, `exp(desired_min)`, and `exp(desired_wildtype)` to the `scale` argument. (We first scale values in the original scale and then log them). In this case, we ignore whatever you passed as `wt_is_1`, setting `wt_is_1 = "no"` to avoid modifying your requested value for the wildtype.
`min_accessible_genotypes` | If not NULL, the minimum number of accessible genotypes in the fitness landscape. A genotype is considered accessible if you can reach if from the wildtype by going through at least one path where all changes in fitness are larger or equal to `accessible_th`. The changes in fitness are considered at each mutational step, i.e., at each addition of one mutation we compute the difference between the genotype with `k + 1` mutations minus the ancestor genotype with `k` mutations. Thus, a genotype is considered accessible if there is at least one path where fitness increases at each mutational step by at least `accessible_th`. If the condition is not satisfied, we continue generating random fitness landscapes with the specified parameters until the condition is satisfied. (Why check against NULL and not against zero? Because this allows you to count accessible genotypes even if you do not want to ensure a minimum number of accessible genotypes.)
`accessible_th` | The threshold for the minimal change in fitness at each mutation step (i.e., between successive genotypes) that allows a genotype to be regarded as accessible. This only applies if `min_accessible_genotypes` is larger than 0. So if you want to allow small decreases in fitness in successive steps, use a small negative value for `accessible_th`.
`truncate_at_0` | If TRUE (the default) any fitness <= 0 is substituted by a small positive constant (a random uniform number between 1e-10 and 1e-9). Why? Because MAGELLAN and some plotting routines can have trouble (specially if you log) with values <=0. Or we might have trouble if we want to log the fitness. This is done after possibly taking logs. Noise is added to prevent creating several identical minimal fitness values.
`K` | K for NK model; K is the number of loci with which each locus interacts, and the larger the K the larger the ruggedness of the landscape.
`r` | For the NK model, whether interacting loci are chosen at random (`r = TRUE`) or are neighbors (`r = FALSE`).
`i` | For de Ising model, i is the mean cost for incompatibility with which the genotype's fitness is penalized when in two adjacent genes, only one of them is mutated.
`I` | For the Ising model, I is the standard deviation for the cost incompatibility (i).
`circular` | For the Ising model, whether there is a circular arrangement, where the last and the first genes are adjacent to each other.
`e` | For the Eggbox model, mean effect in fitness for the neighbor locus +/- e.
`E` | For the Eggbox model, noise added to the mean effect in fitness (e).
`H` | For Full models, standard deviation for the House of Cards model.
`s` | For Full models, mean of the fitness for the Multiplicative model.
`S` | For Full models, standard deviation for the Multiplicative model.
`d` | For Full models, a disminishing (negative) or increasing (positive) return as the peak is approached for multiplicative model.
`o` | For Full models, mean value for the optimum model.
`O` | For Full models, standard deviation for the optimum model.
`p` | For Full models, the mean production value for each non 0 allele in the Optimum model component.
`P` | For Full models, the associated stdev (of non 0 alleles) in the Optimum model component.
`model` | One of "RMF" (default) for Rough Mount Fuji, "Additive" for Additive model, "NK", for Kauffman's NK model, "Ising" for Ising model, "Eggbox" for Eggbox model or "Full" for Full models.

### Details

When using `model = "RMF"`, the model used here follows the Rough Mount Fuji model in Szendro et al., 2013 or Franke et al., 2011. Fitness is given as

f(i) = -c d(i, reference) + x_i

where d(i, j) is the Hamming distance between genotypes i and j (the number of positions that differ) and x_i is a random variable (in this case, a normal deviate of mean `mu` and standard deviation `sd`).

When using `model = "RMF"`, setting c = 0 we obtain a House of Cards model. Setting sd = 0 fitness is given by the distance from the reference and if the reference is the genotype with all positions mutated, then we have a fully additive model (fitness increases linearly with the number of positions mutated), where all mutations have the same effect.

More flexible additive models can be used using `model = "Additive"`. This model is like the Rough Mount Fuji model in Szendro et al., 2013 or Franke et al., 2011, but in this case, each locus can have different contributions to the fitness evaluation. This model is also referred to as the "multiplicative" model in the literature as it is additive in the log-scale (e.g., see Brouillet et al., 2015 or Ferretti et al., 2016). The contribution of each mutated allele to the log-fitness is a random deviate from a Normal distribution with specified mean `mu` and standard deviation `sd`, and the log-fitness of a genotype is the sum of the contributions of each mutated allele. There is no "reference" genotype in the Additive model. There is no epistasis in the additve model because the effect of a mutation in a locus does not depend on the genetic background, or whether the rest of the loci are mutated or not.

When using `model = "NK"` fitness is drawn from a uniform (0, 1) distribution.

When using `model = "Ising"` for each pair of interacting loci, there is an associated cost if both alleles are not identical (and therefore 'compatible').

When using `model = "Eggbox"` each locus is either high or low fitness, with a systematic change between each neighbor.

When using `model = "Full"`, the fitness is computed with different parts of the previous models depending on the choosen parameters described above.

For `model = "NK" | "Ising" | "Eggbox" | "Full"` the fitness landscape is generated by directly calling the `fl_generate` function of MAGELLAN (http://wwwabi.snv.jussieu.fr/public/Magellan/). See details in Ferretti et al. 2016, or Brouillet et al., 2015.

For OncoSimulR, we often want the wildtype to have a mean of 1. Reasonable settings when using RMF are `mu = 1` and `wt_is_1 = 'subtract'` so that we simulate from a distribution centered in 1, and we make sure afterwards (via a simple shift) that the wildtype is actuall 1. The `sd` controls the standard deviation, with the usual working and meaning as in a normal distribution, unless `c` is different from zero. In this case, with `c` large, the range of the data can be large, specially if `g` (the number of genes) is large.

### Value

An matrix with `g + 1` columns. Each column corresponds to a gene, except the last one that corresponds to fitness. 1/0 in a gene column denotes gene mutated/not-mutated. (For ease of use in other functions, this matrix has class "genotype_fitness_matrix".)

If you have specified `min_accessible_genotypes > 0`, the return object has added attributes `accessible_genotypes` and `accessible_th` that show the number of accessible genotypes under the specified threshold.

### Note

MAGELLAN uses its own random number generating functions; using `set.seed` does not allow to obtain the same fitness landscape repeatedly.

### Author(s)

Ramon Diaz-Uriarte for the RMF and general wrapping code. S. Brouillet, G. Achaz, S. Matuszewski, H. Annoni, and L. Ferreti for the MAGELLAN code. Further contributions to the additive model and to wrapping MAGELLAN code and documentation from Guillermo Gorines Cordero, Ivan Lorca Alonso, Francisco Muñoz Lopez, David Roncero Moroño, Alvaro Quevedo, Pablo Perez, Cristina Devesa, Alejandro Herrador.

### References

Szendro I.~G. et al. (2013). Quantitative analyses of empirical fitness landscapes. Journal of Statistical Mehcanics: Theory and Experiment\/, 01, P01005.

Franke, J. et al. (2011). Evolutionary accessibility of mutational pathways. PLoS Computational Biology\/, 7(8), 1–9.

Brouillet, S. et al. (2015). MAGELLAN: a tool to explore small fitness landscapes. bioRxiv, 31583. http://doi.org/10.1101/031583

Ferretti, L., Schmiegelt, B., Weinreich, D., Yamauchi, A., Kobayashi, Y., Tajima, F., & Achaz, G. (2016). Measuring epistasis in fitness landscapes: The correlation of fitness effects of mutations. Journal of Theoretical Biology\/, 396, 132–143. https://doi.org/10.1016/j.jtbi.2016.01.037

MAGELLAN web site: http://wwwabi.snv.jussieu.fr/public/Magellan/

### See Also

`oncoSimulIndiv`, `plot.genotype_fitness_matrix`, `evalAllGenotypes` `allFitnessEffects` `plotFitnessLandscape` `Magellan_stats`

### Examples

    ## Random fitness for four genes-genotypes,
    ## plotting and simulating an oncogenetic trajectory

    ## NK model
    rnk <- rfitness(5, K = 3, model = "NK")
    plot(rnk)
    oncoSimulIndiv(allFitnessEffects(genotFitness = rnk))

    ## Additive model
    radd <- rfitness(4, model = "Additive", mu = 0.2, sd = 0.5)
    plot(radd)

    ## Not run:
    ## Eggbox model
    regg = rfitness(g=4,model="Eggbox", e = 2, E=2.4)
    plot(regg)

    ## Ising model
    ris = rfitness(g=4,model="Ising", i = 0.002, I=2)
    plot(ris)

    ## Full model
    rfull = rfitness(g=4, model="Full", i = 0.002, I=2,
                     K = 2, r = TRUE,
                     p = 0.2, P = 0.3, o = 0.3, O = 1)
        plot(rfull)

    ## End(Not run)

[Package OncoSimulR version 3.2.0 Index]