Perform demographic model optimizations and comparisons with this accessible and flexible tool called moments_pipeline. This tool is a direct translation of the dadi_pipeline tool that allows it to be used with the package moments (as opposed to dadi).
This tool is designed to work with the Python package moments and assumes you already have the package installed. This pipeline can be run using Python 2 or 3, but moments is now intended to be run with Python 3 only. You'll need to be familiar with how moments works, and some of the basic syntax for writing moments scripts with python. Unfortunately there do not appear to be many community resources for getting help with moments. However, given the strong similarity between moments and dadi, you can take advantage of the abundance of resources available for dadi, including the dadi user group. Alternatively, you can also email the authors of moments directly, as they have been very helpful. Before attempting to use these scripts, please read over the user manual for moments and try running the program with the example files.
In this main repository of moments_pipeline is a general use script (moments_Run_Optimizations.py) that can be used to run moments to fit any model on an allele frequency spectrum/joint-site frequency spectrum containing one to three populations. This script will perform a general optimization routine proposed by Portik et al. (2017), which was originally written for dadi, and will produce associated output files. To use this workflow, you'll need a SNPs input text file to create an allele frequency or joint site frequency spectrum object. Alternatively, you can import a frequency spectrum of your own creation, editing the script appropriately (see moments manual). The user will have to edit information about their allele frequency spectrum, and a #************** marks lines in the moments_Run_Optimizations.py that will have to be edited. Any custom model can be used, and below are several examples of how to use various arguments to control the model optimizations.
The moments_Run_Optimizations.py script and Optimize_Functions.py script must be in the same working directory to run properly.
If you'd like to use the optimization routine of this script to analyze larger sets of published 2D models, please look in the nested repository Two_Population_Pipeline. The Two_Population_Pipeline workflow is a modified version of the moments_Run_Optimizations.py script that are designed to perform the optimization routine across the available 2D models. Many of the 2D models available in the dadi_pipeline are available here, including all the diversification models. However, due to differences in how discrete admixture events are implemented in moments, the 2D island diversification model set has not yet been translated for use in the moments_pipeline.
If you'd like to assess the goodness of fit for your demographic model, please look in the Goodness_of_Fit repository.
For information on how to cite moments_pipeline, please see the Citation section at the bottom of this page.
The moments_Run_Optimizations.py and associated 2D and 3D population pipelines are components of moments_pipeline that each were designed to implement the optimization routine proposed by Portik et al. (2017). This optimization routine includes fitting the model using particular settings for a given number of replicates, then using the parameters from the best scoring replicate to seed a subsequent round of model fitting using updated settings. This process occurs across multiple rounds, which improves the log-likelihood scores and generally results in convergence in the final round.
In the moments_Run_Optimizations.py script, the optimization routine contains a user-defined number of rounds, each with a user-defined or default number of replicates. The starting parameters are initially random, but after each round is complete the parameters of the best scoring replicate from that round are used to generate perturbed starting parameters for the replicates of the subsequent round. The arguments controlling steps of the optimization algorithm (maxiter) and perturbation of starting parameters (fold) can be supplied by the user for more control across rounds. The user can also supply their own set of initial parameters, or set custom bounds on the parameters (upper_bound and lower_bound) to meet specific model needs. This flexibility should allow these scripts to be generally useful for fitting any model to any data set.
Let's assume you've supplied the correct information about your SNPs input file, population IDs, projection sizes, and are using the model in the script (sym_mig).
I will show several ways to use the main function for model fitting to highlight different options.
We will use always use the following function from the Optimize_Functions.py script, which requires some explanation:
Optimize_Routine(fs, outfile, model_name, func, rounds, param_number, fs_folded, reps=None, maxiters=None, folds=None, in_params=None, in_upper=None, in_lower=None, param_labels=" ")
Mandatory Arguments:
- fs: spectrum object name
- outfile: prefix for output naming
- model_name: a label help name the output files; ex. "no_mig"
- func: access the model function from within
dadi_Run_Optimizations.pyor from a separate python model script, ex. after importing Models_2D, calling Models_2D.no_mig - rounds: number of optimization rounds to perform
- param_number: number of parameters in the model selected (can count in params line for the model)
- fs_folded: A Boolean value indicating whether the empirical fs is folded (True) or not (False)
Optional Arguments:
- reps: a list of integers controlling the number of replicates in each of the optimization rounds
- maxiters: a list of integers controlling the maxiter argument in each of the optimization rounds
- folds: a list of integers controlling the fold argument when perturbing input parameter values
- in_params: a list of parameter values
- in_upper: a list of upper bound values
- in_lower: a list of lower bound values
- param_labels: list of labels for parameters that will be written to the output file to keep track of their order
The mandatory arguments must always be included when using the Optimize_Routine function, and the arguments must be provided in the exact order listed above (also known as positional arguments). The optional arguments can be included in any order after the required arguments, and are referred to by their name, followed by an equal sign, followed by a value (example: reps = 4). The usage is explained in the following examples.
Let's use the function to run an optimization routine for our data and this model. We always need to specify the eight required arguments (in order) in this function, but there are other options we can also use if we wanted more control over the optimization scheme. We'll start with the basic version here. The argument explanations are above. This would perform three rounds of optimizations, using a default number of replicates for each round. At the end of each round, the parameters of the best-scoring replicate are used to generate the starting parameters for the replicates of the next round, and so on. This will help focus the parameter search space as the rounds continue.
#create a prefix to label the output files
prefix = "V1"
#make sure to define your extrapolation grid size
pts = [50,60,70]
Optimize_Functions.Optimize_Routine(fs, prefix, "sym_mig", sym_mig, 3, 4, fs_folded=True)
It is a good idea to include the labels of the parameters so they can get written to the
output file, otherwise you'll have to go back to the model each time you wanted to see their order. The optional arguments require using the = sign to assign a variable or value to the argument.
prefix = "V2"
pts = [50,60,70]
#here are the labels, given as a string
p_labels = "nu1, nu2, m, T"
Optimize_Functions.Optimize_Routine(fs, prefix, "sym_mig", sym_mig, 3, 4, fs_folded=True, param_labels = p_labels)
Here is the same example but also including your own custom parameter bounds. Notice the optional arguments can be placed in any order following the mandatory arguments.
prefix = "V3"
pts = [50,60,70]
p_labels = "nu1, nu2, m, T"
#Here are the custom bounds
upper = [20,20,10,15]
lower = [0.01,0.01,0.01,0.1]
Optimize_Functions.Optimize_Routine(fs, prefix, "sym_mig", sym_mig, 3, 4, fs_folded=True, param_labels = p_labels, in_upper = upper, in_lower = lower)
You can also be very explicit about the optimization routine, controlling what happens across each round. Let's keep the three rounds, but change the number of replicates, the maxiter argument, and fold argument each time. We'll need to create a list of values for each of these, that has three values within (to match three rounds).
prefix = "V4"
pts = [50,60,70]
p_labels = "nu1, nu2, m, T"
upper = [20,20,10,15]
lower = [0.01,0.01,0.01,0.1]
#Here are the optional arguments
reps = [10,20,50]
maxiters = [5,10,20]
folds = [3,2,1]
Optimize_Functions.Optimize_Routine(fs, prefix, "sym_mig", sym_mig, 3, 4, fs_folded=True, param_labels = p_labels, in_upper=upper, in_lower=lower, reps = reps, maxiters = maxiters, folds = folds)
Using these arguments will cause round one to have 10 replicates, use 3-fold perturbed starting parameters, and a maxiter of 5 for the optimization algorithm steps. Round two will have 20 replicates, use 2-fold perturbed starting parameters, and a maxiter of 10 for the optimization algorithm steps, and etc. for round three.
It's also good run the optimization routine multiple times. Let's write a short loop to do the above optimization routine five times. We will name the prefix based on which point we are at, and include it within the looping. Note that when you use the range argument in python it will go up to, but not include, the final number. That's why I have written a range of 1-6 to perform this 5 times.
pts = [50,60,70]
p_labels = "nu1, nu2, m, T"
upper = [20,20,10,15]
lower = [0.01,0.01,0.01,0.1]
reps = [10,20,50]
maxiters = [5,10,20]
folds = [3,2,1]
for i in range(1,6):
prefix = "V5_Number_{}".format(i)
Optimize_Functions.Optimize_Routine(fs, prefix, "sym_mig", sym_mig, 3, 4, fs_folded=True, param_labels = p_labels, in_upper=upper, in_lower=lower, reps = reps, maxiters = maxiters, folds = folds)
In the Example Data Folder you will find a SNPs input file that will run with the moments_Run_Optimizations.py script.
You will only need to edit the path to the file in the script, and then you will be able to run all five examples above. The
outputs for these examples are also contained within the Example Data Folder, in a separate folder labeled Example_Outputs.
Please test the script using these data to ensure everything is working properly before examining your own empirical data.
For each model run, there will be a log file showing the optimization steps per replicate and a summary file that has all the important information.
Here is an example of the output from a summary file, which will be in tab-delimited format:
Model Replicate log-likelihood AIC chi-squared theta optimized_params(nu1, nu2, m, T)
sym_mig Round_1_Replicate_1 -1684.99 3377.98 14628.4 383.04 0.2356,0.5311,0.8302,0.182
sym_mig Round_1_Replicate_2 -2255.47 4518.94 68948.93 478.71 0.3972,0.2322,2.6093,0.611
sym_mig Round_1_Replicate_3 -2837.96 5683.92 231032.51 718.25 0.1078,0.3932,4.2544,2.9936
sym_mig Round_1_Replicate_4 -4262.29 8532.58 8907386.55 288.05 0.3689,0.8892,3.0951,2.8496
sym_mig Round_1_Replicate_5 -4474.86 8957.72 13029301.84 188.94 2.9248,1.9986,0.2484,0.3688
To change whether the frequency spectrum is folded vs. unfolded requires two changes in the script. The first is where the spectrum object is created, indicated by the polarized argument:
#Convert this dictionary into folded AFS object
#[polarized = False] creates folded spectrum object
fs = moments.Spectrum.from_data_dict(dd, pop_ids=pop_ids, projections = proj, polarized = False)
The above code will create a folded spectrum. When calling the optimization function, this must also be indicated in the fs_folded argument:
#this is from the first example:
Optimize_Functions.Optimize_Routine(fs, prefix, "sym_mig", sym_mig, 3, 4, fs_folded=True)
To create an unfolded spectrum, the polarized and fs_folded arguments in the above lines need to be changed accordingly:
#[polarized = True] creates an unfolded spectrum object
fs = moments.Spectrum.from_data_dict(dd, pop_ids=pop_ids, projections = proj, polarized = True)
#and the optimization routine function must also be changed:
Optimize_Functions.Optimize_Routine(fs, prefix, "sym_mig", sym_mig, 3, 4, fs_folded=False)
It will be clear if either argument has been misspecified because the calculation of certain statistics will cause a crash with the following error:
ValueError: Cannot operate with a folded Spectrum and an unfolded one.
If you see this, check to make sure both relevant arguments actually agree on the spectrum being folded or unfolded.
The optimization routine arguments offer a lot of flexibility, but the default settings can also be used. If only the number of rounds is changed, here are the defaults for the optional arguments (reps, maxiters, folds) based on the number of rounds selected:
Three rounds (as in Examples 1-3):
| Argument | Round 1 | Round 2 | Round 3 |
|---|---|---|---|
| reps | 10 | 10 | 20 |
| maxiter | 5 | 5 | 5 |
| fold | 3 | 2 | 1 |
Two rounds:
| Argument | Round 1 | Round 2 |
|---|---|---|
| reps | 10 | 20 |
| maxiter | 5 | 5 |
| fold | 2 | 1 |
X Rounds (>3):
| Argument | Round 1 | Round 2 | Round 3 | Round X-1 | Round X |
|---|---|---|---|---|---|
| reps | 10 | 10 | 10 | 10 | 20 |
| maxiter | 5 | 5 | 5 | 5 | 5 |
| fold | 3 | 3 | 3 | 2 | 1 |
When fitting demographic models, it is important to perform multiple runs and ensure that final optimizations are converging on a similar log-likelihood score. In the 2D, 3D, and custom workflows of moments_pipeline, the default starting parameters used for all replicates in first round are random. After each round is completed, the parameters of the best scoring replicate from the previous round are then used to generate perturbed starting parameters for the replicates of the subsequent round. This optimization strategy of focusing the parameter search space improves the log-likelihood scores and generally results in convergence in the final round.
Below is a summary of the log-likelihood scores obtained using the default four-round optimization settings present in the 2D pipeline. This analysis was conducted for a particular model (nomig, the simplest 2D model) using the example data provided. You can clearly see the improvement in log-likelihood scores and decrease in variation among replicates as the optimization rounds progress.
Please understand that it is possible for a single execution of the pipeline to get stuck on a local optima for any given model! This is why I strongly recommend running the pipeline multiple times for a given model. If several independent runs for this model each converge on similar log-likelihood scores in their last optimization rounds, you can be mostly confident that analyses are not getting trapped on local optima, and that the true log-likelihood has been obtained.
For various reasons, sometimes an analysis can crash. In some cases, it is not desirable to re-start a model optimization routine from scratch. You can essentially pick up where you left off through a couple of simple actions. First, you will need to find the highest scoring replicate that occurred during the round that crashed. These parameter values will be used as input parameters. Second, the number of rounds and corresponding reps, maxiters, and folds arguments will need to be adjusted to start in the later rounds.
For example, let's say the program crashed fitting a model during round 2 (of 4). You can quickly sort the output file to find the best scoring replicate:
Model Replicate log-likelihood AIC chi-squared theta optimized_params(nu1, nuA, nu2, nu3, m1, m2, T1, T2, T3)
refugia_adj_1 Round_2_Replicate_1 -2227.89 4473.78 14271.56 180.26 0.7541,2.1299,12.2678,0.8252,0.6424,0.6868,0.3189,1.3291,0.9736
refugia_adj_1 Round_2_Replicate_7 -2283.95 4585.9 3131.07 182.59 0.6738,3.0342,5.7909,0.8692,0.3357,0.346,0.2572,2.2233,1.1109
refugia_adj_1 Round_2_Replicate_9 -2297.34 4612.68 4517.14 185.11 0.798,0.9479,6.9163,2.5229,0.3895,0.235,0.2362,1.2066,0.5539
In this example above, we want the parameters from Round_2_Replicate1:
0.7541,2.1299,12.2678,0.8252,0.6424,0.6868,0.3189,1.3291,0.9736
In the script running this model, we will need to change the following arguments:
#**************
#Set the number of rounds here
rounds = 4
#define the lists for optional arguments
#you can change these to alter the settings of the optimization routine
reps = [10,20,30,40]
maxiters = [3,5,10,15]
folds = [3,2,2,1]
These need to be changed to reflect the fact that we want to 'start' in round 3 and continue to round 4. We also want to use the best parameters from round 2 to seed round 3, so we will need to add a params variable. The arguments can be adjusted like so:
#**************
#Set the number of rounds here
rounds = 2
#define the lists for optional arguments
#you can change these to alter the settings of the optimization routine
reps = [30,40]
maxiters = [10,15]
folds = [2,1]
params = [0.7541,2.1299,12.2678,0.8252,0.6424,0.6868,0.3189,1.3291,0.9736]
Finally, in the actual call for the model we will need to add the optional flag in_params=params to let the routine know we are supplying the starting parameters to seed the replicates.
For example, add the in_params=params argument to this:
Optimize_Functions.Optimize_Routine(fs, prefix, "refugia_adj_1", Models_3D.refugia_adj_1, rounds, 9, fs_folded=fs_folded, reps=reps, maxiters=maxiters, folds=folds, param_labels = "nu1, nuA, nu2, nu3, m1, m2, T1, T2, T3")
so that it looks like this:
Optimize_Functions.Optimize_Routine(fs, prefix, "refugia_adj_1", Models_3D.refugia_adj_1, rounds, 9, fs_folded=fs_folded, reps=reps, maxiters=maxiters, folds=folds, in_params=params, param_labels = "nu1, nuA, nu2, nu3, m1, m2, T1, T2, T3")
That will allow you to more or less pick up where you left off. Please note that if running multiple models in a given script, changing the rounds, reps, maxiters, and folds arguments will affect all of them. So, it is best to isolate a single model to jump-start a crashed analysis.
If you encounter any issues while using moments_pipeline, it could be the result of a moments-specific problem or an error in moments_pipeline. If you believe the issue is specific to moments_pipeline, please post the error along with the relevant details of the analysis in the issues page in the repository.
The likelihood and AIC returned represent the true likelihood only if the SNPs are unlinked across loci. For ddRADseq data where a single SNP is selected per locus, this is considered true, but if SNPs are linked across loci then the likelihood is actually a composite likelihood and using something like AIC is no longer appropriate for model comparisons. See the discussion group for more information on this subject.
This demographic modeling pipeline is a direct translation of the dadi_pipeline of Portik et al. (2017). This allows their multi-round optimization routine, original models, and custom output files to be used by the program moments. Because of these important features, the dadi_pipeline and moments_pipeline are not 'wrappers' for dadi or moments, but rather additional packages. The dadi_pipeline was published as part of Portik et al. (2017) and the moments_pipeline was published as part of Leache et al. (2019). If you have used moments_pipeline to run your analyses, please indicate so in your publication. Here is an example of how you can cite this workflow:
To explore alternative demographic models, we used moments (Jouganous et al. 2017) to analyze joint site frequency spectra. Moments uses differential equations to simulate the evolution of allele frequency distributions over time and is closely related to the diffusion approximation method used in the program dadi (Gutenkunst et al. 2009). We fit 15 demographic models using moments_pipeline (Leache et al. 2019), which allows the demographic modeling pipeline of Portik et al. (2017) to be implemented with moments.
The main motivation behind the creation of this workflow was to increase transparency and reproducibility in demographic modeling. In your publication you should report the key parameters of the optimization routine. The goal is to allow other researchers to plug your data into moments_pipeline and run the same analyses. For example:
For all models, we performed consecutive rounds of optimizations (Portik et al. 2016; Leache et al. 2019). For each round, we ran multiple replicates and used parameter estimates from the best scoring replicate (highest log-likelihood) to seed searches in the following round. We used the default settings in dadi_pipeline for each round (replicates = 10, 20, 30, 40; maxiter = 3, 5, 10, 15; fold = 3, 2, 2, 1), and optimized parameters using the Nelder-Mead method (optimize_log_fmin). Across all analyses, we used the optimized parameter sets of each replicate to simulate the 3D-JSFS, and the multinomial approach was used to estimate the log-likelihood of the 3D-JSFS given the model.
The above example explains all the parameters used to run the analyses. If you change any of the default options, you should report them here in your methods section. This can include changes to the number of rounds, replicates, maxiters, folds, or other optional features (such as supplying parameter values or changing the default parameter bounds).
Here is a list of the publications mentioned above, for easy reference:
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Gutenkunst, R.N., Hernandez, R.D., Williamson, S.H., and C.D. Bustamante. 2009. Inferring the joint demographic history of multiple populations from multidimensional SNP frequency data. PLoS Genetics 5: e1000695.
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Jouganous, J., Long, W., Ragsdale, A. P., and S. Gravel. 2017. Inferring the joint demographic history of multiple populations: Beyond the diffusion approximation. Genetics 117: 1549-1567.
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Portik, D.M., Leache, A.D., Rivera, D., Blackburn, D.C., Rodel, M.-O., Barej, M.F., Hirschfeld, M., Burger, M., and M.K. Fujita. 2017. Evaluating mechanisms of diversification in a Guineo-Congolian forest frog using demographic model selection. Molecular Ecology 26: 5245-5263. https://doi.org/10.1111/mec.14266
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Leache, A.D., Portik, D.M., Rivera, D., Rodel, M.-O., Penner, J., Gvozdik, V., Greenbaum, E., Jongsma, G.F.M., Ofori-Boateng, C., Burger, M., Eniang, E.A., Bell, R.C., and M.K. Fujita. 2019. Exploring rain forest diversification using demographic model testing in the African foam-nest tree frog Chiromantis rufescens. Journal of Biogeography, Early View. https://doi.org/10.1111/jbi.13716
- Leache, A.D., Portik, D.M., Rivera, D., Rodel, M.-O., Penner, J., Gvozdik, V., Greenbaum, E., Jongsma, G.F.M., Ofori-Boateng, C., Burger, M., Eniang, E.A., Bell, R.C., and M.K. Fujita. 2019. Exploring rain forest diversification using demographic model testing in the African foam-nest tree frog Chiromantis rufescens. Journal of Biogeography, Early View. https://doi.org/10.1111/jbi.13716
For a complete list of publications that have used the dadi version of the demographic modeling workflow (dadi_pipeline), please see here.
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