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fast sequential Markov coalescent simulation of genomic data under complex evolutionary models

benchmarks

We have performed a few comparisons of fastsimcoal with ms, simcoal2 or MaCS

speed comparison of fastsimcoal (January 2013), ms, simcoal2 and MaCs

datasets

The following test data sets were used in our speed comparisons

	No. of populations	Diploid population size	Migration rate (gen-1)	Mutation rate (gen-1 × bp-1)	Recombination rate (gen-1 × bp-1)	Sample size per population (no. of genes)
1popNoRec	1	12500		2×10-8	0	2000
1popSmallSample	1	12500		2×10-8	1.2×10-8	20
1popLargeSample	1	12500		2×10-8	1.2×10-8	2000
2popNoRec	2	6250	0.001	2×10-8	0	1000
2popSmallSample	2	6250	0.001	2×10-8	1.2×10-8	10
2popLargeSample	2	6250	0.001	2×10-8	1.2×10-8	1000

The population, mutation and recombination parameters correspond to those used by Chen et al. (2009) in their comparison of ms to MaCS.

results

The results reported below are average CPU time per run expressed in seconds. All runs were run on a Linux cluster made up of 2.6GHz AMD Opterons with 4 GB of RAM and 74 GB HD.

n=2000, no recombination

Data set	No. of replicates	Sequence length	Program
			ms	MaCS	fastsimcoal
1popNoRec	1000	1 Mb	1.1	11.1	9.5
	100	10 Mb	9.6	107.0	72.9
	100	100 Mb	147.9	1319.5	1038.1
2popNoRec	1000	1 Mb	1.2	12.5	9.3
	100	10 Mb	8.9	128.1	71.5
	100	100 Mb	161.2	1513.2	1099.9

Without recombination, ms is much faster than the two other programs based on the SMC’ approximation, and fastsimcoal is becomes increasingly faster than MaCS with larger recombination rates and with migration.


n=20, recombination

Data set	No. of replicates	Sequence length	Program
			ms	MaCS	fastsimcoal
1popSmallSample	1000	1 Mb	0.344	0.242	0.095
	100	10 Mb	159.246	2.618	0.460
	100	100 Mb	x	26.124	4.364
2popSmallSample	1000	1 Mb	0.378	0.907	0.152
	100	10 Mb	165.507	9.094	1.080
	100	100 Mb	x	97.876	10.559

x : ms crashed

For small sample sizes (total n=20) and with recombination, the SMC’ based programs are becoming much faster than ms, which fails to run for 100Mb sequences. For such small sample sizes, fastsimcoal is 2.5 to 9.3 times faster than MaCS. For MaCS and fastsimcoal, computing time increases approximately linearly with sequence length, as expected.

n=2000, recombination

Data set	No. of replicates	Sequence length	Program
			ms	MaCS	fastsimcoal
1popLargeSample	1000	1 Mb	3.7	28.1	25.2
	100	10 Mb	x	327.5	235.7
	100	100 Mb	x	3700.8	2635.4
2popLargeSample	1000	1 Mb	3.9	33.3	25.9
	100	10 Mb	x	393.5	240.6
	100	100 Mb	x	4311.1	2684.7

x : ms crashed

For large sample sizes (total n=2000), ms is actually faster than the two other programs for a “small” sequence of 1Mb, but failed to run successfully for longer sequences. For these large sample sizes, fastsimcoal is 1.2 to 1.8 times faster than MaCs. fastsimcoal computing time still increases approximately linearly with sequence length, which is not the case ofMaCS, which becomes slightly penalized by larger sequences. Note however, that for 1Mb and 10Mb, we used fastsimcoal options allowing it to keep all simulated sites in memory before writing them to the output file, which was not possible for 100Mb sequences, which would use up too much memory.

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patterns of molecular diversity

Number of pairwise difference

We report below a comparison of the patterns of diversity within and between populations simulated by ms, MaCs and fastsimcoal.

ms results are shown with a black line, MaCs with a red line, and fastsimoal, with a blue line. In all cases, the empirical distributions of the number of pairwise differences were computed from 100,000 simulations of the coalescent of 2 genes. The 2 genes were drawn from a single population for the one-population case, and were drawn each in a different population in the two-island model case. We used the following population parameters: for the one population case; and for the two-island case; and was varied between 0 and 1000, as shown above. In all cases, MaCS and fastsimcoal lead to identical distributions, which is expected as they are both based on the same SMC’ approximation.

In absence of recombination MaCS and fastsimcoal give also exactly the same distributions as ms, but are just running 7-10 times slower, as was seen in the previous section. With very high recombination rates, the SMC-based approximation of MaCS and fastsimcoal is extremely close to the ancestral recombination graph (ARG) implemented in ms, in keeping with previous results (McVean and Cardin, 2005). For "intermediate" recombination rates (R=10, R=100), some slight differences do emerge between ARG- and SMC-based programs, and these differences are slightly more pronounced in the 2-island model. However, it seems that these differences are much less than differences due to the choice of different demographic, mutation, or recombination parameters.

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patterns of linkage disequilibrium

simcoal2 vs fastimcoal ver 1

Here, we report a comparison of the average LD (as measured by  r²) between the ARG-based simcoal2 program and fastsimcoal ver 1.0 (SMC'-based) between two SNP markers located at a given recombination distance expressed in R units.

The results are based on 20,000 simulations and confirm that average r² values are virtually undistinguishable between simcoal2 (ARG-based) and fastsimcoal (SMC-based).

simcoal2 vs fastimcoal ver 2.51

Here, we report a new comparison of the average LD (as measured by  r²) between the ARG-based simcoal2 program and fsc251  (SMC'-based) between two SNP markers located at a given recombination distance expressed in R units.

The results are based on 40,000 simulations and confirm that average r² values are virtually undistinguishable between simcoal2 (ARG-based) and fatssimcoal ver 2.5.1, which has a faster implementation of the SMC'-based algorithm (see benchmark below)

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speed comparison of fastsimcoal ver 2.5 (July 2014) and fastsimcoal21 (December 2013)

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speed comparison for different number of threads (-c) and batches (-B) in fsc25

./$fsc25 -i 1PopDNAnoRec10Mb.par -n10 -I -x --seed 1234 10 simulations of 100,000 segments of 100 bp

./$fsc -t 1PopExpInst20Mb.tpl -e 1PopExpInst20Mb.est -d -M0.001 –n200000 –N200000 -I –l5 –L5 --seed 1234 –q

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speed comparison : from fastsimcoal ver 1.0 to ver 2.5.1

We report here the total computation time taken to do a given number of simulations in 1 or 2 populations of samples size 10 or 1000 gene copies.  We simulate DNA sequences with or without recombination, with a mutation rate of 2e-8 per bp.

Other parameters:

• Population sizes N=12500 diploids
• Migration rate between populations: 0.001 per gene copy per generation
• All simulations were performed with option -k200000, and using a single thread (-c1) and a single batch (-B1) for versions 2.5 and 2.51
  

No recombination case (r=0)

	Num. Sims	n	Seq. Length	fsc v.1	fsc v2.1	fsc v 2.5	fsc v 2.51
1pop	1000	10	1Mb	1.67s	1.61s	2.79s	2.57s
1pop	1000	10	10Mb	15.64s	16.88s	31.15s	29.08s
1pop	100	10	100Mb	17.45s	27.74s	16.78s	16.60s
1pop	10	1000	1Mb	9.39s	9.02s	6.23s	5.54s
1pop	10	1000	10Mb	1m25s	1m35s	1m40s	1m38s
1pop	3	1000	100Mb	5m51s	7m12s	4m56s	4m42s
2pop	100	10	1Mb	7.29s	7.44s	4.42s	6.78s
2pop	100	10	10Mb	1m08s	1m16s	1m06s	1m08s
2pop	10	10	100Mb	1m58s	2m08s	1m11s	1m10s
2pop	10	1000	1Mb	6m38s	7m11s	7m23s	6m42s
2pop	10	1000	10Mb	65m21s	77m14s	73m31s	67m06s
2pop	3	1000	100Mb	87m00s	92m04s	74m31s	69m00s

Recombination case (r=1.2e-8 between bp)

	Num. Sims	n	Seq. Length	fsc v.1	fsc v2.1	fsc v 2.5	fsc v 2.51
1pop	100	10	1Mb	1.69s	1.28s	1.45s	0.56s
1pop	100	10	10Mb	13.04s	12.68s	13.52s	5.57s
1pop	10	10	100Mb	14.26s	13.83s	11.96s	5.09s
1pop	10	1000	1Mb	46.82s	49.17s	44.92s	16.38s
1pop	10	1000	10Mb	7m52s	7m53s	8m17s	3m06s
1pop	3	1000	100Mb	27m42s	26m36s	26m33s	9m22
2pop	100	10	1Mb	22.86s	23.59s	19.36s	14.55s
2pop	100	10	10Mb	3m57s	3m58s	2m03s	1m58s
2pop	10	10	100Mb	3m55s	3m57s	3m12s	2m31s
2pop	10	1000	1Mb	3m52s	3m54s	3m51s	1m34s
2pop	10	1000	10Mb	38m41s	39m07s	38m19s	15m45s
2pop	3	1000	100Mb	122m23s	123m16s	116m26s	53m20s

Main changes:

• Version 1 was limited to the pure simulation of genetic data
  
• With version 2, we introduced the possibilty to infer parameters from the site frequency spectrum, making many objects a bit more complex
• With version 2.5, we introduced multi-threading, removing many static object members, implying some cost for monothreaded computations.
• With version 2.5.1, we introduced a new implementation of recombination under the SMC' algorithm, making is drastically faster (2-3x performance gain).
  

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Last updated by L. Excoffier on 08.10.2014

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