# Function for estimating indel rates while accounting for missing data.

### Description

This is the function used for running the four gene gain/loss rate models. The four models being run are "M1", "M2", "M3", and "M4". The first model only estimates indel rates where both the insertion and deletion rates are the same. The second model tries to account for possible missing data while estimating indel rates. The third model estimates insertion and deletion rates separately. The fourth model tries to account for possible missing data while estimating insertion and deletion rates separately. See modelnames in the arguments below.

### Usage

1 2 3 4 5 6 7 | ```
indelrates(verbose = FALSE, usertree = NULL, userphyl = NULL,
matchtipstodata = FALSE, datasource = "user", seed = 1, taxa = 5,
brlensh = c(1, 4), mu = 1, nu = 1, phyl = 5000,
pmiss = 0, toi = 1, bgtype = "listofnodes", bg = NULL,
zerocorrection = TRUE, rootprob = "stationary", rpvec = NULL,
optmethod = "nlminb", init = 0.9, lowlim = 0.001, uplim = 100,
numhessian = TRUE, modelnames = c("M1", "M2", "M3", "M4"),...)
``` |

### Arguments

`verbose ` |
If TRUE, will print out estimates and standard errors from each model. Note that the order of printing is the deletion rate followed by the insertion rate. Default value is FALSE. |

`usertree ` |
Used with datasource = "user". Rooted binary tree of class "phylo". Read in Newick tree using read.tree() from package ape before passing this argument. The branch lengths must be in expected substitutions per site. Popular tree estimation programs like MrBayes and BEAST, for instance, yield branch lengths on that scale. |

`userphyl ` |
Used with datasource = "user". Matrix of gene phyletic patterns. Matrix entries denote presence (1) or absence (0) of a specific gene (rows) for an individual taxon (columns). |

`matchtipstodata` |
The default is FALSE, which means that the user must ensure that the ordering of the taxa in the data matrix must match the internal ordering of tip labels of the tree. Set to TRUE, if the column names of the data matrix, i.e., the taxa names, are all present, with the same spelling and notation in the tip labels of the tree provided, in which case, the restriction on ordering is not necessary. |

`datasource ` |
"simulation" or "user". Default is "user". |

`seed ` |
seed number for replication (default is 1). |

`taxa ` |
Used with datasource = "simulation". Total number of taxa (default is 5). Tree is generated using ape package. |

`brlensh ` |
Used with datasource = "simulation". Branch lengths are simulated from a beta distribution. The shape parameters can be provided as a vector (default = c(1, 4)). For simulating closely related sequences (i.e., with smaller branch lengths more important in trees with more taxa), use something like c(1, 8). |

`mu ` |
(unstandardized) deletion rate (default is 1). Used with datasource = "simulation". Sequences given the trees are generated after the rate matrix is standardized such that one unit of time is what we expect to see one change per gene site in. (cf. Equation 13.14 in Felsenstein, 2004.) |

`nu ` |
(unstandardized) insertion rate (default is 1). Used with datasource = "simulation". An example of the conversion that phangorn implements is simulating with mu = 0.6 and nu = 3 when given mu = 1 and nu = 5. Similarly, phangorn simulates with mu = 0.67 (0.75) and nu = 2 (1.5) when given mu = 1 (1) and nu = 3 (2). |

`phyl ` |
Used with datasource = "simulation". Total number of gene phyletic patterns (default is 5000). |

`pmiss ` |
Proportion of present genes to remove in the taxa of interest for the purpose of simulating "missingness". Primarily provided for used with datasource = "simulation" but can be used with datasource = "user" as well. |

`toi ` |
A vector of tiplabels for taxa of interest as determined by using ape::tiplabels() function while plotting a tree of class "phylo". Models "M2" and "M4" will account for possible missing data for these taxa. Using toi = "all" specifies all tips (although this often leads to over-parameterization). Default value is tip 1. |

`bgtype ` |
If clade-specific insertion and deletion rates are required to be estimated, specify as "ancestornodes". If, on the other hand, a group of branches (not in a clade) are hypothesized to follow the same rates, use argument option "listofnodes". |

`bg ` |
A vector of nodes can be given here if the "ancestornodes" option was chosen for argument "bgtype". If "listofnodes" was chosen, a list should be provided with each element of the list being a vector of nodes that limit the branches that follow the same rates. See examples. |

`zerocorrection` |
Felsenstein's correction for unobserved data. The results are conditional on observing the gene present in at least one taxa. This accounts for the sampling bias. Default is TRUE. |

`rootprob ` |
Four options are available for the prior probability of character state frequencies at the root. The "equal" option makes gene absence and presence contribute equally to the likelihood calculation at the root of the tree. The "stationary" option will weight the contributions by the averaged equilibrium frequencies of all different branch groupings. The "maxlik" option estimates the probability of gene family absence at the root. Default is "stationary". If "user" is supplied here (e.g., for empirical frequencies), a vector of root frequency parameters can be provided to argument "rpvec". |

`rpvec ` |
If option "user" is specified for argument "rootprob", supply a vector of length two, representing the root frequency parameters. |

`optmethod ` |
"nlminb" (default) or "optim". The "indelrate" model being a one-dimensional problem always uses "nlminb". The "optim" option is provided purely as a fall-back; in most cases, "nlminb" will converge to the correct solution more stably and quickly as compared to "optim". |

`init ` |
Initial value for the rates. The default value is 0.9. |

`lowlim ` |
For finer control of the boundaries of the optimization problem. The default value is 0.001. This usually suffices if the branch lengths are in expected substitutions per site. However, if branch lengths are in different units, this should be changed accordingly. |

`uplim ` |
For finer control of the boundaries of the optimization problem. The default value is 100. This usually suffices if the branch lengths are in expected substitutions per site. However, if branch lengths are in different units, this should be changed accordingly. |

`numhessian ` |
Set to FALSE if standard errors are not required (or standard errors are being calculated using bootstrapping). This speeds up the algorithm. Default is TRUE. |

`modelnames ` |
Default is all models. The four options are "M1", "M2", "M3", and "M4". A vector of these values can be given. The first model only estimates indel rates where both the insertion and deletion rates are the same. The second model tries to account for possible missing data while estimating indel rates. The third model estimates insertion and deletion rates separately. The fourth model tries to account for possible missing data while estimating insertion and deletion rates separately. |

`... ` |
Passing other arguments of the optimization algorithms used. See "nlminb" or "optim" documentation. For example, control = list(trace = 5) with method = "nlminb" will print progress at every 5th iteration. |

### Details

Gene presence/absence should be coded as 1/0. By default, any datapoints (in the data supplied) greater than 1 are changed to 1 and any rows consisting of zeros only are removed. Gene presence/ absence patterns should be ordered by the tips of the tree.

### Value

All arguments used while calling the indelrates function are attached in a list. Moreover, the following components are also returned:

`call ` |
Function call used. |

`conv ` |
A vector of convergence indicators for each model run. 0 denotes successful convergence. |

`time ` |
Time taken in seconds. |

`tree ` |
The phylogenetic tree used. |

`bg ` |
List of group of nodes modelled with individual insertion and deletion rates. |

`results ` |
List of results including modelname, parameter estimates: insertion ("nu") and deletion ("mu") rates and proportion of missing data ("p"), standard errors, number of parameters fit, and AIC and BIC values. For the models with missing data proportions, an estimate (rounded off) of the number of genes missing for the taxa of interest specified is also provided. Furthermore, details from the optimization routine applied are also available. |

`data_red ` |
Gene phyletic patterns observed. |

`w ` |
Number of times each gene phyletic pattern was observed. |

### Author(s)

Utkarsh J. Dang and G. Brian Golding

### See Also

See also `print.indelmiss`

, `plot.indelmiss`

, and `plottree`

.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 | ```
###User supplied tree and data###
#Simulate data
#library(phangorn)
#set.seed(1)
#usertree <- rtree(n = 7, br = rbeta(n = 7, shape1 = 1, shape2 = 7))
#data <- simSeq(usertree, l = 5000, type = "USER", levels = c(0, 1),
#bf = c(1/(1 + 5), 5/(1 + 5)), Q = 1) #1 and 5 correspond to
#unstandardized rates. See item help descriptions on mu and nu.
#datab <- matrix(as.numeric(as.character(data)), nrow = 7)
#userphyl <- t(datab)
#Run the models.
#indel_user <- indelrates(datasource = "user", usertree = usertree,
#userphyl = userphyl, toi = 1, zerocorrection = TRUE, rootprob = "stationary",
# modelnames = c("M3", "M4"), optmethod = "nlminb",
#control = list(trace = 10))
#print(indel_user)
#####Simulation#####
#Simulate a dataset with default options and run algorithm.
#indel1 <- indelrates(verbose = TRUE, datasource = "simulation",
#control = list(trace = 5))
#print(indel1)
#Estimate insertion/ deletion rates from gene presence/absence
#data simulated on a simulated five taxon tree.
#indel2 <- indelrates(datasource = "simulation", seed = 1, taxa = 5,
#brlensh = c(1, 8), mu = 1, nu = 5, phyl = 5000, pmiss = 0, toi = 1,
#zerocorrection = TRUE, rootprob = "stationary",
#modelnames = c("M1", "M2", "M3", "M4"), optmethod = "nlminb",
#control = list(trace = 5))#1 and 5 correspond to unstandardized rates.
#See item help descriptions on mu and nu.
#print(indel2)
#With toi="all"
#indel3 <- indelrates(datasource = "simulation", seed = 1, taxa = 5,
#brlensh = c(1, 8), mu = 1, nu = 5, phyl = 5000, pmiss = c(0, 0.15, 0.25, 0, 0), toi = "all",
#zerocorrection = TRUE, rootprob = "maxlik", modelnames = c("M3", "M4"),
#optmethod = "nlminb")
#print(indel3)
#Compare with
#indel3 <- indelrates(datasource = "simulation", seed = 1, taxa = 5,
#brlensh = c(1, 8), mu = 1, nu = 5, phyl = 5000, pmiss = c(0.15, 0.25), toi = c(2, 3),
#zerocorrection = TRUE, rootprob = "maxlik", modelnames = c("M3", "M4"),
#optmethod = "nlminb")
#print(indel3)
#Here, a vector of ancestor nodes specify the nodes which
#along with all their descendants have unique indel rates.
#indel4 <- indelrates(datasource = "simulation", seed = 1, taxa = 10,
#brlensh = c(1, 8), mu = 1, nu = 5, phyl = 5000, pmiss = 0, toi = 1,
#bgtype = "ancestornodes", bg = c(15), zerocorrection = TRUE, rootprob =
#"maxlik", modelnames = c("M3", "M4"), optmethod = "nlminb")
#print(indel4)
#plot(indel4, model = "M4")
#Above command prints two plots that can be obtained individually.
#These are confidence intervals based on asymptotic normality
#of the maximum likelihood estimators.
#Different confidence interval levels can be specified with the cil option.
#plotrates(indel4, model = "M4", ci = TRUE, cil = 95)
#plotp(indel4, model = "M4", ci = TRUE, cil = 95)
#This is an alternate (more flexible but potentially less user-friendly)
#way to specify groups of nodes which have unique indel rates.
#A list of nodes is used here.
#indel5 <- indelrates(verbose = TRUE, datasource = "simulation", seed = 1,
#taxa = 5, brlensh = c(1, 8), mu = 1, nu = 3, phyl = 5000, pmiss = 0,
#toi = 1, bgtype = "listofnodes", bg = list(c(7, 1, 2),
#c(6, 8, 3, 7, 9, 5, 4, 9)), zerocorrection = TRUE, rootprob = "maxlik",
#modelnames = c("M1", "M2", "M3", "M4"), optmethod = "nlminb")
#Mycobacterium data example
# data(mycobacteriumdata1)
# indel_myco <- indelrates(verbose = TRUE, usertree = mycobacteriumdata1$tree, modelnames = "M4",
# userphyl = mycobacteriumdata1$phyl, matchtipstodata = TRUE,
# datasource = "user", toi = c(3:4, 6:10), bgtype = "listofnodes",
# zerocorrection = TRUE, rootprob = "stationary", optmethod = #"nlminb",
# numhessian = TRUE, control = list(eval.max = 50000, iter.max = 50000))
``` |