\name{rfitness}
\alias{rfitness}
\encoding{UTF-8}

\title{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{

\item{g}{Number of genes.}

\item{c}{The decrease in fitness of a genotype per each unit increase
in Hamming distance from the reference genotype for the RMF model
(see \code{reference}).}

\item{sd}{The standard deviation of the random component (a normal
distribution of mean \code{mu} and standard deviation \code{sd}) for
the RMF and additive models .}

\item{mu}{The mean of the random component (a normal distribution of
mean \code{mu} and standard deviation \code{sd}) for the RMF and

\item{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 \code{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., \code{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). }

\item{scale}{Either NULL (nothing is done) or a two- or three-element
vector.

If a two-element vector, fitness is re-scaled between
\code{scale[1]} (the minimum) and \code{scale[2]} (the maximum) and,
later, if you have selected it, \code{wt_is_1} will be enforced.

If you pass a three element vector, fitness is re-scaled so that the
new maximum fitness is \code{scale[1]}, the new minimum is
\code{scale[2]} and the new wildtype is \code{scale[3]}. If you pass a
three element vector, none of the \code{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 \code{scale[2]} if you
then truncate at 0 --see \code{truncate_at_9}).

Using a three element vector is probably the most natural way of
changing the scale and range of fitness.

the scale.
}

\item{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 \code{scale}, so if you specify both
"wt_is_1 = 'divide'" and use an argument for \code{scale} it is most
likely that the final fitness will not respect the limits in
\code{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 \code{scale}, so if you specify both
"wt_is_1 = 'subtract'" and use an argument for \code{scale} it is most
likely that the final fitness will not respect the limits in
\code{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 \code{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 \code{scale}).

If "no", the fitness of the wildtype is not modified.

This option has no effect if you pass a three-element vector for
\code{scale}. Using a three-element vector for \code{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.

}

\item{log}{If TRUE, log-transform fitness. Actually, there are two
cases: if \code{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
\code{exp(desired_max)}, \code{exp(desired_min)}, and
\code{exp(desired_wildtype)} to the \code{scale} argument. (We first
scale values in the original scale and then log them). In this case,
we ignore whatever you passed as \code{wt_is_1}, setting \code{wt_is_1
= "no"} to avoid modifying your requested value for the wildtype.}

\item{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 \code{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 \code{k + 1}
mutations minus the ancestor genotype with \code{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
\code{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.)
}

\item{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
\code{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 \code{accessible_th}.  }

\item{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.}

\item{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.}

\item{r}{For the NK model, whether interacting loci are chosen at random
(\code{r = TRUE}) or are neighbors (\code{r = FALSE}).}
\item{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.}

\item{I}{For the Ising model, I is the standard deviation for the cost
incompatibility (i).}

\item{circular}{For the Ising model, whether there is a circular arrangement,
where the last and the first genes are adjacent to each other.}

\item{e}{For the Eggbox model, mean effect in fitness for the neighbor
locus +/- e.}

\item{E}{For the Eggbox model, noise added to the mean effect in fitness (e).}

\item{H}{For Full models, standard deviation for the House of Cards model.}

\item{s}{For Full models, mean of the fitness for the Multiplicative model.}

\item{S}{For Full models, standard deviation for the Multiplicative model.}

\item{d}{For Full models, a disminishing (negative) or increasing
(positive) return as the peak is approached for multiplicative model.}

\item{o}{For Full models, mean value for the optimum model.}

\item{O}{For Full models, standard deviation for the optimum model.}

\item{p}{For Full models, the mean production value for each non 0
allele in the Optimum model component.}

\item{P}{For Full models, the associated stdev (of non 0 alleles) in the
Optimum model component.}

\item{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 \code{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

\deqn{f(i) = -c d(i, reference) + x_i}

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

When using \code{model = "RMF"}, setting \eqn{c = 0} we obtain a House
of Cards model. Setting \eqn{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 \code{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 \code{mu} and standard deviation \code{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 \code{model = "NK"} fitness is drawn from a uniform (0, 1)
distribution.

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

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

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

For \code{model = "NK" | "Ising" | "Eggbox" | "Full"} the fitness
landscape is generated by directly calling the \code{fl_generate}
function of MAGELLAN
(\url{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 \code{mu = 1} and \code{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 \code{sd} controls the standard deviation, with the
usual working and meaning as in a normal distribution, unless \code{c}
is different from zero. In this case, with \code{c} large, the range
of the data can be large, specially if \code{g} (the number of genes)
is large.

}

\value{

An matrix with \code{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 \code{min_accessible_genotypes > 0}, the return
object has added attributes \code{accessible_genotypes} and
\code{accessible_th} that show the number of accessible
genotypes under the specified  threshold.
}

\note{MAGELLAN uses its own random number generating functions; using
\code{set.seed} does not allow to obtain the same fitness landscape
repeatedly.}

\references{

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

Franke, J. et al. (2011). Evolutionary accessibility of mutational
pathways. \emph{PLoS Computational Biology\/}, \bold{7}(8), 1--9.

Brouillet, S. et al. (2015). MAGELLAN: a tool to explore small fitness
landscapes. \emph{bioRxiv},
\bold{31583}. \url{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. \emph{Journal of
Theoretical Biology\/}, \bold{396}, 132--143. \url{https://doi.org/10.1016/j.jtbi.2016.01.037}

MAGELLAN web site: \url{http://wwwabi.snv.jussieu.fr/public/Magellan/}

}

\author{ 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,

\seealso{

}
\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))

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

\dontrun{
## 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)
}
}
\keyword{ datagen }