StatsModels v0.6.0 compatibility; REQUIRE -> Project.toml

also:

- v0.9.1 and this commit not compatible with GLM v1.2.0+
  would need to cap v0.9.1 to use GLM v1.1.1.
- LinPredModel -> GLM.LinPredModel for compatibility with GLM v1.2.0+
- fitdiscrete:
  * better wrapper
  * empirical & stationary distributions
  * name change from fitDiscrete
  * rate variation: category median rates normalized
  * fixed SM traitlabels2indices error

Author: coraallensavietta

Project.toml

@@ -0,0 +1,49 @@
+name = "PhyloNetworks"
+uuid = "33ad39ac-ed31-50eb-9b15-43d0656eaa72"
+license = "MIT"
+version = "0.10.0"
+
+[deps]
+BioSequences = "7e6ae17a-c86d-528c-b3b9-7f778a29fe59"
+BioSymbols = "3c28c6f8-a34d-59c4-9654-267d177fcfa9"
+CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
+Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
+DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
+Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+GLM = "38e38edf-8417-5370-95a0-9cbb8c7f171a"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+NLopt = "76087f3c-5699-56af-9a33-bf431cd00edd"
+Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+StatsFuns = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
+StatsModels = "3eaba693-59b7-5ba5-a881-562e759f1c8d"
+
+[compat]
+BioSequences = "≥ 1.0.0"
+BioSymbols = "≥ 3.0.0"
+CSV = "≥ 0.4.0"
+Combinatorics = "≥ 0.7.0"
+DataFrames = "≥ 0.13.0"
+DataStructures = "≥ 0.9.0"
+Distributions = "≥ 0.15.0"
+GLM = "≥ 1.0.0"
+NLopt = "≥ 0.5.1"
+SpecialFunctions = "≥ 0.7.0"
+StaticArrays = "≥ 0.8.3"
+StatsBase = "≥ 0.26.0"
+StatsFuns = "≥ 0.7.0"
+StatsModels = "≥ 0.6.0"
+julia = "≥ 0.7.0"
+
+[extras]
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[targets]
+test = ["Test"]

REQUIRE

@@ -9,7 +9,7 @@ const SUITE = BenchmarkGroup()
 
 SUITE["nasm"] = BenchmarkGroup(["JC69", "HKY85"])
 SUITE["fitDiscreteFixed"] = BenchmarkGroup(["ERSM", "BTSM", "JC69", "HKY85"])
-SUITE["fitDiscrete"] = BenchmarkGroup(["ERSM", "BTSM", "JC69", "HKY85"])
+SUITE["fitdiscrete"] = BenchmarkGroup(["ERSM", "BTSM", "JC69", "HKY85"])
 
 # Add benchmarks to nasm group
 SUITE["nasm"]["JC69"] = @benchmarkable JC69([0.5])
@@ -20,8 +20,8 @@ SUITE["nasm"]["HKY85"] = @benchmarkable P!(P(m1, 1.0), m1, 3.0)
 net_dat = readTopology("(((A:2.0,(B:1.0)#H1:0.1::0.9):1.5,(C:0.6,#H1:1.0::0.1):1.0):0.5,D:2.0);")
 species_alone = ["C","A","B","D"]
 dat_alone = DataFrame(trait=["hi","lo","lo","hi"])
-SUITE["fitDiscreteFixed"]["ERSM"] = @benchmarkable fitDiscrete(net_dat, :ERSM, species_alone, dat_alone; optimizeQ=false, optimizeRVAS=false)
-SUITE["fitDiscreteFixed"]["BTSM"] = @benchmarkable fitDiscrete(net_dat, :BTSM, species_alone, dat_alone; optimizeQ=false, optimizeRVAS=false)
+SUITE["fitDiscreteFixed"]["ERSM"] = @benchmarkable fitdiscrete(net_dat, :ERSM, species_alone, dat_alone; optimizeQ=false, optimizeRVAS=false)
+SUITE["fitDiscreteFixed"]["BTSM"] = @benchmarkable fitdiscrete(net_dat, :BTSM, species_alone, dat_alone; optimizeQ=false, optimizeRVAS=false)
 
 fastafile = joinpath(@__DIR__, "..", "examples", "Ae_bicornis_Tr406_Contig10132.aln")
 dna_dat, dna_weights = readfastatodna(fastafile, true);
@@ -32,14 +32,14 @@ for edge in net_dna.edge #adds branch lengths
         setGamma!(edge, 0.5)
     end
 end
-SUITE["fitDiscreteFixed"]["JC69"] = @benchmarkable fitDiscrete(net_dna, :JC69, dna_dat, dna_weights; optimizeQ=false, optimizeRVAS=false)
-SUITE["fitDiscreteFixed"]["HKY85"] = @benchmarkable fitDiscrete(net_dna, :HKY85, dna_dat, dna_weights; optimizeQ=false, optimizeRVAS=false)
-
-## fitDiscrete benchmarks
-SUITE["fitDiscrete"]["ERSM"] = @benchmarkable fitDiscrete(net_dat, :ERSM, species_alone, dat_alone; optimizeQ=true, optimizeRVAS=true)
-SUITE["fitDiscrete"]["BTSM"] = @benchmarkable fitDiscrete(net_dat, :BTSM, species_alone, dat_alone; optimizeQ=true, optimizeRVAS=true)
-SUITE["fitDiscrete"]["JC69"] = @benchmarkable fitDiscrete(net_dna, :JC69, dna_dat, dna_weights; optimizeQ=true, optimizeRVAS=true)
-SUITE["fitDiscrete"]["HKY85"] = @benchmarkable fitDiscrete(net_dna, :HKY85, dna_dat, dna_weights; optimizeQ=true, optimizeRVAS=true)
+SUITE["fitDiscreteFixed"]["JC69"] = @benchmarkable fitdiscrete(net_dna, :JC69, dna_dat, dna_weights; optimizeQ=false, optimizeRVAS=false)
+SUITE["fitDiscreteFixed"]["HKY85"] = @benchmarkable fitdiscrete(net_dna, :HKY85, dna_dat, dna_weights; optimizeQ=false, optimizeRVAS=false)
+
+## fitdiscrete benchmarks
+SUITE["fitdiscrete"]["ERSM"] = @benchmarkable fitdiscrete(net_dat, :ERSM, species_alone, dat_alone; optimizeQ=true, optimizeRVAS=true)
+SUITE["fitdiscrete"]["BTSM"] = @benchmarkable fitdiscrete(net_dat, :BTSM, species_alone, dat_alone; optimizeQ=true, optimizeRVAS=true)
+SUITE["fitdiscrete"]["JC69"] = @benchmarkable fitdiscrete(net_dna, :JC69, dna_dat, dna_weights; optimizeQ=true, optimizeRVAS=true)
+SUITE["fitdiscrete"]["HKY85"] = @benchmarkable fitdiscrete(net_dna, :HKY85, dna_dat, dna_weights; optimizeQ=true, optimizeRVAS=true)
 
 # If a cache of tuned parameters already exists, use it, otherwise, tune and cache
 # the benchmark parameters. Reusing cached parameters is faster and more reliable

benchmark/benchmarks.jl

@@ -48,7 +48,7 @@ Pages = [
     "man/multiplealleles.md",
     "man/trait_tree.md",
     "man/parsimony.md",
-    "man/fitDiscrete.md"
+    "man/fitdiscrete.md"
 ]
 Depth = 3
 ```

docs/src/index.md

@@ -137,11 +137,11 @@ parsimonyGF
 Q
 randomTrait
 randomTrait!
-fitDiscrete
+fitdiscrete
 maxParsimonyNet
 nstates
-setrates!
-setalpha!
+stationary
+empiricalDNAfrequencies
 ```
 
 ```@meta

docs/src/lib/public.md

@@ -1,137 +1,142 @@
+```@setup traitevol_fixednet
+using PhyloNetworks
+using DataFrames
+mkpath("../assets/figures")
+```
+
 # Discrete Trait Evolution
 
 With a phylogenetic network structure inferred, we can now estimate how quickly traits
-have evolved over time using a likelihood model. These traits should be discrete 
-characteristics of a species such as feather color, diet type, or dna in aligned 
-genetic sequences.
+have evolved over time using a likelihood model. These traits should be discrete
+characteristics of a species such as feather color, diet type,
+or DNA in aligned genetic sequences.
 
 ## Discrete Trait Data
 
-As with continuous trait evolution, we assume a fixed network, correctly rooted, 
+As with continuous trait evolution, we assume a fixed network, correctly rooted,
 with branch lengths proportional to calendar time. We start with a network, then
 add data about the tips of this network. We allow data of two types.
-1. A vector of species names with a data frame of traits:
 
-```@setup fitDiscrete
-using PhyloNetworks, DataFrames
-mkpath("../assets/figures")
-```
-
-```@example fitDiscrete
-#read in network
-simple_net = readTopology("(A:3.0,(B:2.0,(C:1.0,D:1.0):1.0):1.0);");
-
-#read in trait data
-simple_species = ["C","A","B","D"]
-simple_dat = DataFrame(trait=["hi","lo","lo","hi"])
-```
-
-If your species names and trait data are in the same data frame, read in your data 
-frame then subset the data like this:
-```@example fitDiscrete
-dat = DataFrame(species=["C","A","B","D"], trait=["hi","lo","lo","hi"])
-simple_species = dat[:species]
-simple_dat = DataFrame(trait = dat[:trait])
-```
-
-2. To use dna data, read in the network structure then start with a fasta 
-file. Reading the data from this file using the `readfastatodna` function. This 
-creates a data frame of dna data and a vector of dna pattern weights.
-
-```@example fitDiscrete
-#read in network
-dna_net = readTopology("((((((((((((((Ae_caudata_Tr275:1.0,Ae_caudata_Tr276:1.0):1.0,Ae_caudata_Tr139:1.0):1.0)#H1:1.0::0.6,((((((Ae_longissima_Tr241:1.0,Ae_longissima_Tr242:1.0):1.0,Ae_longissima_Tr355:1.0):1.0,(Ae_sharonensis_Tr265:1.0,Ae_sharonensis_Tr264:1.0):1.0):1.0,((Ae_bicornis_Tr408:1.0,Ae_bicornis_Tr407:1.0):1.0,Ae_bicornis_Tr406:1.0):1.0):1.0,((Ae_searsii_Tr164:1.0,Ae_searsii_Tr165:1.0):1.0,Ae_searsii_Tr161:1.0):1.0):1.0)#H2:1.0::0.6):1.0,(((Ae_umbellulata_Tr266:1.0,Ae_umbellulata_Tr257:1.0):1.0,Ae_umbellulata_Tr268:1.0):1.0,#H1:1.0::0.4):1.0):1.0,((Ae_comosa_Tr271:1.0,Ae_comosa_Tr272:1.0):1.0,(((Ae_uniaristata_Tr403:1.0,Ae_uniaristata_Tr357:1.0):1.0,Ae_uniaristata_Tr402:1.0):1.0,Ae_uniaristata_Tr404:1.0):1.0):1.0):1.0,(((Ae_tauschii_Tr352:1.0,Ae_tauschii_Tr351:1.0):1.0,(Ae_tauschii_Tr180:1.0,Ae_tauschii_Tr125:1.0):1.0):1.0,(#H2:1.0::0.4,((((Ae_mutica_Tr237:1.0,Ae_mutica_Tr329:1.0):1.0,Ae_mutica_Tr244:1.0):1.0,Ae_mutica_Tr332:1.0):1.0)#H4:1.0::0.6):1.0):1.0):1.0,(((T_boeoticum_TS8:1.0,(T_boeoticum_TS10:1.0,T_boeoticum_TS3:1.0):1.0):1.0,T_boeoticum_TS4:1.0):1.0,((T_urartu_Tr315:1.0,T_urartu_Tr232:1.0):1.0,(T_urartu_Tr317:1.0,T_urartu_Tr309:1.0):1.0):1.0):1.0):1.0,(((((Ae_speltoides_Tr320:1.0,Ae_speltoides_Tr323:1.0):1.0,Ae_speltoides_Tr223:1.0):1.0,Ae_speltoides_Tr251:1.0):1.0):1.0,#H4:1.0::0.4):1.0):1.0):1.0,Ta_caputMedusae_TB2:1.0):1.0,S_vavilovii_Tr279:1.0):1.0,Er_bonaepartis_TB1:1.0):1.0,H_vulgare_HVens23:1.0);");
+1. A vector of species names with a data frame of traits:
 
-#read in dna data
-fastafile = joinpath(dirname(pathof(PhyloNetworks)), "..","examples",
-"Ae_bicornis_Tr406_Contig10132.aln")
-dna_dat, dna_weights = readfastatodna(fastafile, true);
-```
+   ```@example traitevol_fixednet
+   # read in network
+   net = readTopology("(A:3,((B:0.4)#H1:1.6::0.92,((C:0.4,#H1:0::0.08):0.6,D:1):1):1);");
+   # read in trait data
+   species = ["C","A","B","D"]
+   dat = DataFrame(trait=["hi","lo","lo","hi"])
+   ```
+
+   If your species names and trait data are in the same data frame,
+   read in your data frame then subset the data like this:
+   ```@example traitevol_fixednet
+   dat = DataFrame(species=["C","A","B","D"], trait=["hi","lo","lo","hi"])
+   species = dat[:species]
+   dat = DataFrame(trait = dat[:trait])
+   ```
+
+2. To use dna data, read in the network structure then start with a fasta
+   file. Reading the data from this file using the `readfastatodna` function.
+   This creates a data frame of dna data and a vector of dna pattern weights.
+
+   ```@example traitevol_fixednet
+   # read in network
+   dna_net = readTopology("((((((((((((((Ae_caudata_Tr275:1.0,Ae_caudata_Tr276:1.0):1.0,Ae_caudata_Tr139:1.0):1.0)#H1:1.0::0.6,((((((Ae_longissima_Tr241:1.0,Ae_longissima_Tr242:1.0):1.0,Ae_longissima_Tr355:1.0):1.0,(Ae_sharonensis_Tr265:1.0,Ae_sharonensis_Tr264:1.0):1.0):1.0,((Ae_bicornis_Tr408:1.0,Ae_bicornis_Tr407:1.0):1.0,Ae_bicornis_Tr406:1.0):1.0):1.0,((Ae_searsii_Tr164:1.0,Ae_searsii_Tr165:1.0):1.0,Ae_searsii_Tr161:1.0):1.0):1.0)#H2:1.0::0.6):1.0,(((Ae_umbellulata_Tr266:1.0,Ae_umbellulata_Tr257:1.0):1.0,Ae_umbellulata_Tr268:1.0):1.0,#H1:1.0::0.4):1.0):1.0,((Ae_comosa_Tr271:1.0,Ae_comosa_Tr272:1.0):1.0,(((Ae_uniaristata_Tr403:1.0,Ae_uniaristata_Tr357:1.0):1.0,Ae_uniaristata_Tr402:1.0):1.0,Ae_uniaristata_Tr404:1.0):1.0):1.0):1.0,(((Ae_tauschii_Tr352:1.0,Ae_tauschii_Tr351:1.0):1.0,(Ae_tauschii_Tr180:1.0,Ae_tauschii_Tr125:1.0):1.0):1.0,(#H2:1.0::0.4,((((Ae_mutica_Tr237:1.0,Ae_mutica_Tr329:1.0):1.0,Ae_mutica_Tr244:1.0):1.0,Ae_mutica_Tr332:1.0):1.0)#H4:1.0::0.6):1.0):1.0):1.0,(((T_boeoticum_TS8:1.0,(T_boeoticum_TS10:1.0,T_boeoticum_TS3:1.0):1.0):1.0,T_boeoticum_TS4:1.0):1.0,((T_urartu_Tr315:1.0,T_urartu_Tr232:1.0):1.0,(T_urartu_Tr317:1.0,T_urartu_Tr309:1.0):1.0):1.0):1.0):1.0,(((((Ae_speltoides_Tr320:1.0,Ae_speltoides_Tr323:1.0):1.0,Ae_speltoides_Tr223:1.0):1.0,Ae_speltoides_Tr251:1.0):1.0):1.0,#H4:1.0::0.4):1.0):1.0):1.0,Ta_caputMedusae_TB2:1.0):1.0,S_vavilovii_Tr279:1.0):1.0,Er_bonaepartis_TB1:1.0):1.0,H_vulgare_HVens23:1.0);");
+   # read in dna data
+   fastafile = joinpath(dirname(pathof(PhyloNetworks)), "..","examples","Ae_bicornis_Tr406_Contig10132.aln")
+   dna_dat, dna_weights = readfastatodna(fastafile, true);
+   dna_dat
+   dna_weights
+   ```
 
 ## Choosing a Substitution Model
 
-After reading in your data, choose a model to describe how evolutionary changes 
-(or substitutions, in the case of DNA) happened over time. We offer a selection 
-of Markov substitution models to describe the evolutionary process.
+After reading in your data, choose a model to describe how evolutionary changes
+(or substitutions, in the case of DNA) happened over time.
+Available Markov substitution models are described below.
 
-### Generic Trait Models  
+### Generic Trait Models
 
 These models works well for any type of trait we may want to model. For general
-trait types, use one of these three models:    
-`:ERSM` Equal Rates Substitution Model  
-`:BTSM` Binary Trait Substitution Model    
-`:TBTSM` Two Binary Trait Substituion Model    
-
-### DNA-Specific Models  
-
-The DNA-specific models are optimized for aligned sequence data. We offer JC69 
-and HKY85 models in both relative and absolute versions. The JC69 model was 
-developed by Jukes and Cantor in 1969 and uses one rate for all type of substitutions. 
-The HKY85 model was developed in 1985 by Hasegawa, Kishino, & Yano. It treats 
-transitions differently from transversions.    
-`:JC69` Jukes Cantor 69 Model    
-`:HKY85` Hasegawa, Kishino and Yano 1985     
-
-## Running FitDiscrete
-
-To infer evolutionary rates, run the `fitDiscrete` function on the network and data. 
-It will calculate the maximum likelihood score of a network given one or more 
-discrete trait characters at the tips. Along each edge, evolutionary changes
-are modeled with a continous time Markov model, with parameters estimated by 
-maximizing the likelihood. At each hybrid node, the trait is assumed to be 
-inherited from the immediate parent (or parents, in the case of a hybrid edge).
-If there is a hybrid edge, the trait is modeled according to the parents' weighted 
-average genetic contributions, as measured by inheritance gamma γ. The model 
-currently ignores incomplete lineage sorting.
+trait types, use one of these three models:
+- `:BTSM` Binary Trait Substitution Model (2 states, rates unconstrained)
+- `:ERSM` Equal Rates Substitution Model
+  (`k` states, all transitions possible with equal rates)
+- `:TBTSM` Two Binary Trait Substituion Model (though not fully implemented yet)
+
+### DNA-Specific Models
+
+The DNA-specific models are optimized for aligned sequence data.
+The 4 nucleotide states are from
+[BioSymbols](https://github.com/BioJulia/BioSymbols.jl)
+(listed [here](http://biojulia.net/BioSymbols.jl/stable/nucleicacids/)).
+Each model has a relative and an absolute version.
+- `:JC69` Jukes & Cantor 1969 model: one single rate for all transitions.
+  The relative version has values -1 along the diagonal of the rate matrix
+  (1 expected transition / unit of time). The absolute version has an extra
+  parameter to scale the rate matrix.
+- `:HKY85` Hasegawa, Kishino & Yano 1985: treats transitions differently
+  from transversions.
+
+## Fitting the model
+
+To infer evolutionary rates, run the `fitdiscrete` function on the network and data.
+It will calculate the maximum likelihood score of a fixed network
+given one or more discrete trait characters at the tips.
+Along each edge, evolutionary changes
+are modeled with a continous time Markov model, with parameters estimated by
+maximizing the likelihood. At each hybrid node, the trait is assumed to be
+inherited from the immediate parent (or parents, in the case of a hybrid node).
+At a hybrid node, the trait is assumed to be inherited from one or the other
+parent, with probabilities equal to the inheritance γ of each parent edge
+(which is given by the network).
+The model ignores incomplete lineage sorting (e.g. hemiplasy).
 
 ### General Trait Data
 
-```@example fitDiscrete
-s1 = fitDiscrete(simple_net, :ERSM, simple_species, simple_dat; optimizeQ=false, 
-optimizeRVAS=false)
-s2 = fitDiscrete(simple_net, :BTSM, simple_species, simple_dat; optimizeQ=false, 
-optimizeRVAS=false)
+```@repl traitevol_fixednet
+s1 = fitdiscrete(net, :ERSM, species, dat; optimizeQ=false)
+s2 = fitdiscrete(net, :BTSM, species, dat; optimizeQ=false)
 ```
-In this `fitDiscrete` call, we do not optimize rates or allow for rate variation
-across sites.
-
-If `optimizeQ = true`, the `fitDiscrete` function estimates the evolutionary rate
-or rates. Because we didn't allow for rate variation across sites in these models, 
-we do not optimize the way rates may vary across trait types.
-
-```@example fitDiscrete
-s3 = fitDiscrete(simple_net, :ERSM, simple_species, simple_dat; optimizeQ=true, 
-optimizeRVAS=true)
-s4 = fitDiscrete(simple_net, :BTSM, simple_species, simple_dat; optimizeQ=true, 
-optimizeRVAS=true)
+In this `fitdiscrete` call, we do not optimize rates or allow for rate variation
+across sites. The default rates (which act as starting value if rates
+were to be optimized) are chosen equal to the inverse of the total edge lengths
+in the network (or 1/ntax if all branch lengths are missing).
+
+If `optimizeQ = true` (which is the default), the `fitdiscrete`
+function estimates the parameters of the rate matrix.
+Because we didn't allow for rate variation across sites in these models,
+there is nothing to optimize in the way rates may vary across traits (sites).
+
+```@repl traitevol_fixednet
+s3 = fitdiscrete(net, :ERSM, species, dat)
+s4 = fitdiscrete(net, :BTSM, species, dat)
 ```
 
 ### DNA Data
 
-For DNA data, use `:JC69` or `:HKY85` models. 
-```@example fitDiscrete
-d1 = fitDiscrete(dna_net, :JC69, dna_dat, dna_weights, :RV; optimizeQ=false, 
-optimizeRVAS=false)
-d2 = fitDiscrete(dna_net, :HKY85, dna_dat, dna_weights, :RV; optimizeQ=false, 
-optimizeRVAS=false)
+For DNA data, use one of `:JC69` or `:HKY85`.
+To allow for rate variation across sites, use the `:RV` option.
+
+```@example traitevol_fixednet
+d1 = fitdiscrete(dna_net, :JC69, dna_dat, dna_weights, :RV; optimizeQ=false, optimizeRVAS=false)
+d2 = fitdiscrete(dna_net, :HKY85, dna_dat, dna_weights, :RV; optimizeQ=false, optimizeRVAS=false)
 ```
-In these `fitDiscrete` models, we do not optimize rates (`optimizeQ=false`), but
-we do allow for rate variation across sites.
+In these `fitdiscrete` models, we do not optimize rates (`optimizeQ=false`), but
+we do allow for rate variation across sites, with a default α of 1.
 
 ### Rate Variation Across Sites
 
-In its default version, `fitDiscrete` does not allow for rate variation across sites.
-To allow for rate variation across sites in your estimate of evolutionary rates 
-(or rate variation across trait types, in the case of general trait types), 
-include `:RV`. If you include `:RV` and `optimizeRVAS = true`, the model will 
-not only allow for rate variation, but it will also optimize how rates vary across 
-sites.
+In its default version, `fitdiscrete` does not allow for rate variation across sites.
+To allow for rate variation across sites in your estimate of evolutionary rates
+(or rate variation across traits in the case of general traits),
+include `:RV`. If you include `:RV` and `optimizeRVAS = true`,
+the model will allow for rate variation and
+also optimize the parameter α of the distribution of rates across sites.
 
 We optimize the evolutionary rates and the way rates vary across sites for the
-DNA data here:    
-```@example fitDiscrete
-d3 = fitDiscrete(dna_net, :JC69, dna_dat, dna_weights, :RV; optimizeQ=true, 
-optimizeRVAS=false)
-d4 = fitDiscrete(dna_net, :HKY85, dna_dat, dna_weights, :RV; optimizeQ=true, 
-optimizeRVAS=false)
-```
+DNA data here:
+```@repl traitevol_fixednet
+d3 = fitdiscrete(dna_net, :JC69, dna_dat, dna_weights, :RV; optimizeRVAS=false)
+d4 = fitdiscrete(dna_net, :HKY85, dna_dat, dna_weights, :RV)
+```