AbstractTrees interface

A BranchingProcessSolution is an AbstractTrees instance in which each node is represented by an AbstractSciMLSolution. Hence useful statistics of the sampled branching process trajectory can be obtained by combining features of these two types.

Tree statistics

Useful tree statistics can be obtained directly from the AbstractTrees interface. To illustrate this, consider the example of branching Brownian motion:

using DifferentialEquations, BranchingProcesses
f(u,p,t) = 0.0
g(u,p,t) = 1.0
u0 = 0.0
tspan = (0.0, 5.0)
bm = SDEProblem(f,g, u0, tspan)
λ = 1.0
nchild = 2
bbm = ConstantRateBranchingProblem(bm, λ, nchild)
sol = solve(bbm, EM(); dt=0.01)

BranchingProcessSolution{ConstantRateBranchingProblem{SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}, Exponential{Float64}, Int64}, RODESolution{Float64, 1, Vector{Float64}, Nothing, Nothing, Vector{Float64}, NoiseProcess{Float64, 1, Float64, Float64, Nothing, Nothing, typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST), typeof(DiffEqNoiseProcess.WHITE_NOISE_BRIDGE), Nothing, false, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, RSWM{Float64}, Nothing, Xoshiro}, Nothing, SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}, EM{true}, StochasticDiffEq.LinearInterpolationData{Vector{Float64}, Vector{Float64}}, SciMLBase.DEStats, Nothing, Nothing}}(ConstantRateBranchingProblem{SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}, Exponential{Float64}, Int64}(SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}(SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}(Main.f, Main.g, LinearAlgebra.UniformScaling{Bool}(true), nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, SciMLBase.DEFAULT_OBSERVED, nothing, nothing, nothing), Main.g, 0.0, (0.0, 5.0), SciMLBase.NullParameters(), nothing, Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}(), nothing, 0x0000000000000000), Exponential{Float64}(θ=1.0), 2), BranchingProcessNode{RODESolution{Float64, 1, Vector{Float64}, Nothing, Nothing, Vector{Float64}, NoiseProcess{Float64, 1, Float64, Float64, Nothing, Nothing, typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST), typeof(DiffEqNoiseProcess.WHITE_NOISE_BRIDGE), Nothing, false, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, RSWM{Float64}, Nothing, Xoshiro}, Nothing, SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}, EM{true}, StochasticDiffEq.LinearInterpolationData{Vector{Float64}, Vector{Float64}}, SciMLBase.DEStats, Nothing, Nothing}}(RODESolution{Float64, 1, Vector{Float64}, Nothing, Nothing, Vector{Float64}, NoiseProcess{Float64, 1, Float64, Float64, Nothing, Nothing, typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST), typeof(DiffEqNoiseProcess.WHITE_NOISE_BRIDGE), Nothing, false, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, RSWM{Float64}, Nothing, Xoshiro}, Nothing, SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}, EM{true}, StochasticDiffEq.LinearInterpolationData{Vector{Float64}, Vector{Float64}}, SciMLBase.DEStats, Nothing, Nothing}([0.0, 0.011279224313716437, -0.05567609549926506, -0.0634540842750384, -0.16595495440246544, -0.20741498758859833, -0.09163421774352495, -0.1458378524324478, -0.2654898863314643, -0.4080152163467406  …  -0.17638364582239438, -0.21218217163650308, -0.20300557994212792, -0.04810525464273868, 0.06774756472002545, 0.08987029359070359, 0.10204895722619611, -0.0974117490210061, -0.20336966233379922, -0.28617955248698745], nothing, nothing, [0.0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.060000000000000005, 0.07, 0.08, 0.09  …  1.0900000000000007, 1.1000000000000008, 1.1100000000000008, 1.1200000000000008, 1.1300000000000008, 1.1400000000000008, 1.1500000000000008, 1.1600000000000008, 1.1700000000000008, 1.1757716836348473], NoiseProcess{Float64, 1, Float64, Float64, Nothing, Nothing, typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST), typeof(DiffEqNoiseProcess.WHITE_NOISE_BRIDGE), Nothing, false, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, RSWM{Float64}, Nothing, Xoshiro}(DiffEqNoiseProcess.WHITE_NOISE_DIST, DiffEqNoiseProcess.WHITE_NOISE_BRIDGE, [0.0, 1.1757716836348473], [0.0, -0.28617955248698745], [0.0, -0.28617955248698745], nothing, 1.1757716836348473, -0.28617955248698745, nothing, 0.005771683634846481, -0.08280989015318825, nothing, -0.08280989015318825, nothing, 0.0, nothing, nothing, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}(Tuple{Float64, Float64, Nothing}[], 0, 0), ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}([(0.005771683634846481, -0.08280989015318825, nothing)], 1, 118), ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}(Tuple{Float64, Float64, Nothing}[], 0, 0), RSWM{Float64}(1.0e-15, :RSwM3), 0, 0, false, 118, Xoshiro(0xad4cc0aebcec01f4, 0x11b0307203caa791, 0xa8380551075a76a8, 0x34497c52371c0832, 0x6f87fbbedd2e6fda), true, true, true, nothing), nothing, SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}(SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}(Main.f, Main.g, LinearAlgebra.UniformScaling{Bool}(true), nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, SciMLBase.DEFAULT_OBSERVED, nothing, nothing, nothing), Main.g, 0.0, (0.0, 1.1757716836348473), SciMLBase.NullParameters(), nothing, Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}(), nothing, 0x0000000000000000), EM{true}(), StochasticDiffEq.LinearInterpolationData{Vector{Float64}, Vector{Float64}}([0.0, 0.011279224313716437, -0.05567609549926506, -0.0634540842750384, -0.16595495440246544, -0.20741498758859833, -0.09163421774352495, -0.1458378524324478, -0.2654898863314643, -0.4080152163467406  …  -0.17638364582239438, -0.21218217163650308, -0.20300557994212792, -0.04810525464273868, 0.06774756472002545, 0.08987029359070359, 0.10204895722619611, -0.0974117490210061, -0.20336966233379922, -0.28617955248698745], [0.0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.060000000000000005, 0.07, 0.08, 0.09  …  1.0900000000000007, 1.1000000000000008, 1.1100000000000008, 1.1200000000000008, 1.1300000000000008, 1.1400000000000008, 1.1500000000000008, 1.1600000000000008, 1.1700000000000008, 1.1757716836348473]), false, 0, SciMLBase.DEStats(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0), nothing, SciMLBase.ReturnCode.Success, 0x9638f7b8557cd282, nothing), BranchingProcessNode{RODESolution{Float64, 1, Vector{Float64}, Nothing, Nothing, Vector{Float64}, NoiseProcess{Float64, 1, Float64, Float64, Nothing, Nothing, typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST), typeof(DiffEqNoiseProcess.WHITE_NOISE_BRIDGE), Nothing, false, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, RSWM{Float64}, Nothing, Xoshiro}, Nothing, SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}, EM{true}, StochasticDiffEq.LinearInterpolationData{Vector{Float64}, Vector{Float64}}, SciMLBase.DEStats, Nothing, Nothing}}[BranchingProcessNode{RODESolution{Float64, 1, Vector{Float64}, Nothing, Nothing, Vector{Float64}, NoiseProcess{Float64, 1, Float64, Float64, Nothing, Nothing, typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST), typeof(DiffEqNoiseProcess.WHITE_NOISE_BRIDGE), Nothing, false, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, RSWM{Float64}, Nothing, Xoshiro}, Nothing, SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}, EM{true}, StochasticDiffEq.LinearInterpolationData{Vector{Float64}, Vector{Float64}}, SciMLBase.DEStats, Nothing, Nothing}}(RODESolution{Float64, 1, Vector{Float64}, Nothing, Nothing, Vector{Float64}, NoiseProcess{Float64, 1, Float64, Float64, Nothing, Nothing, typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST), typeof(DiffEqNoiseProcess.WHITE_NOISE_BRIDGE), Nothing, false, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, RSWM{Float64}, Nothing, Xoshiro}, Nothing, SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}, EM{true}, StochasticDiffEq.LinearInterpolationData{Vector{Float64}, Vector{Float64}}, SciMLBase.DEStats, Nothing, Nothing}([-0.28617955248698745, -0.33132622959829133, -0.44337043719315755, -0.47809085788482486, -0.36922357944028583, -0.23480263720782413, -0.12988099774636253, -0.29884734180135375, -0.2100735739231498, -0.11774647321047255  …  -0.7773579568419154, -0.7823676461630916, -0.7539033760086835, -0.735252999791049, -0.9044021317844265, -0.9236918089306343, -0.9166571962583107, -0.7899341354751921, -0.658166780815107, -0.6431604767932074], nothing, nothing, [1.1757716836348473, 1.1857716836348473, 1.1957716836348473, 1.2057716836348473, 1.2157716836348473, 1.2257716836348473, 1.2357716836348474, 1.2457716836348474, 1.2557716836348474, 1.2657716836348474  …  2.095771683634846, 2.105771683634846, 2.1157716836348457, 2.1257716836348455, 2.1357716836348453, 2.145771683634845, 2.155771683634845, 2.1657716836348446, 2.1757716836348444, 2.1841340473649624], NoiseProcess{Float64, 1, Float64, Float64, Nothing, Nothing, typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST), typeof(DiffEqNoiseProcess.WHITE_NOISE_BRIDGE), Nothing, false, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, RSWM{Float64}, Nothing, Xoshiro}(DiffEqNoiseProcess.WHITE_NOISE_DIST, DiffEqNoiseProcess.WHITE_NOISE_BRIDGE, [1.1757716836348473, 2.1841340473649624], [0.0, -0.35698092430621997], [0.0, -0.35698092430621997], nothing, 2.1841340473649624, -0.35698092430621997, nothing, 0.008362363730118005, 0.015006304021899595, nothing, 0.015006304021899595, nothing, 0.0, nothing, nothing, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}(Tuple{Float64, Float64, Nothing}[], 0, 0), ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}([(0.008362363730118005, 0.015006304021899595, nothing)], 1, 101), ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}(Tuple{Float64, Float64, Nothing}[], 0, 0), RSWM{Float64}(1.0e-15, :RSwM3), 0, 0, false, 101, Xoshiro(0xa02afbdd8ea7f56f, 0x91149f886f59587e, 0x15451f6db31c7e94, 0x0802ffddd20c7619, 0xfef71aaf233a1642), true, true, true, nothing), nothing, SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}(SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}(Main.f, Main.g, LinearAlgebra.UniformScaling{Bool}(true), nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, SciMLBase.DEFAULT_OBSERVED, nothing, nothing, nothing), Main.g, -0.28617955248698745, (1.1757716836348473, 2.1841340473649624), SciMLBase.NullParameters(), nothing, Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}(), nothing, 0x0000000000000000), EM{true}(), StochasticDiffEq.LinearInterpolationData{Vector{Float64}, Vector{Float64}}([-0.28617955248698745, -0.33132622959829133, -0.44337043719315755, -0.47809085788482486, -0.36922357944028583, -0.23480263720782413, -0.12988099774636253, -0.29884734180135375, -0.2100735739231498, -0.11774647321047255  …  -0.7773579568419154, -0.7823676461630916, -0.7539033760086835, -0.735252999791049, -0.9044021317844265, -0.9236918089306343, -0.9166571962583107, -0.7899341354751921, -0.658166780815107, -0.6431604767932074], [1.1757716836348473, 1.1857716836348473, 1.1957716836348473, 1.2057716836348473, 1.2157716836348473, 1.2257716836348473, 1.2357716836348474, 1.2457716836348474, 1.2557716836348474, 1.2657716836348474  …  2.095771683634846, 2.105771683634846, 2.1157716836348457, 2.1257716836348455, 2.1357716836348453, 2.145771683634845, 2.155771683634845, 2.1657716836348446, 2.1757716836348444, 2.1841340473649624]), false, 0, SciMLBase.DEStats(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0), nothing, SciMLBase.ReturnCode.Success, 0x30df42ece728d69f, nothing), BranchingProcessNode{RODESolution{Float64, 1, Vector{Float64}, Nothing, Nothing, Vector{Float64}, NoiseProcess{Float64, 1, Float64, Float64, Nothing, Nothing, typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST), typeof(DiffEqNoiseProcess.WHITE_NOISE_BRIDGE), Nothing, false, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, RSWM{Float64}, Nothing, Xoshiro}, Nothing, SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}, EM{true}, StochasticDiffEq.LinearInterpolationData{Vector{Float64}, Vector{Float64}}, SciMLBase.DEStats, Nothing, Nothing}}[BranchingProcessNode{RODESolution{Float64, 1, Vector{Float64}, Nothing, Nothing, Vector{Float64}, NoiseProcess{Float64, 1, Float64, Float64, Nothing, Nothing, typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST), typeof(DiffEqNoiseProcess.WHITE_NOISE_BRIDGE), Nothing, false, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, RSWM{Float64}, Nothing, Xoshiro}, Nothing, SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}, EM{true}, StochasticDiffEq.LinearInterpolationData{Vector{Float64}, Vector{Float64}}, SciMLBase.DEStats, Nothing, Nothing}}(RODESolution{Float64, 1, Vector{Float64}, Nothing, Nothing, Vector{Float64}, NoiseProcess{Float64, 1, Float64, Float64, Nothing, Nothing, typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST), typeof(DiffEqNoiseProcess.WHITE_NOISE_BRIDGE), Nothing, false, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, RSWM{Float64}, Nothing, Xoshiro}, Nothing, SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}, EM{true}, StochasticDiffEq.LinearInterpolationData{Vector{Float64}, Vector{Float64}}, SciMLBase.DEStats, Nothing, Nothing}([-0.6431604767932074, -0.6864420006686401, -0.7013489852442563, -0.5742249122712234, -0.6261128531068847, -0.5292404214558267, -0.4390724328777941, -0.49430534270197435, -0.5994355361948785, -0.6189527539062392  …  0.196469335864906, 0.18603998734896884, 0.27608323575673377, 0.3632196693532371, 0.4828564322173862, 0.5355540719177445, 0.5847632500571833, 0.6121718215563, 0.5320994567203565, 0.48664395676303857], nothing, nothing, [2.1841340473649624, 2.194134047364962, 2.204134047364962, 2.2141340473649618, 2.2241340473649616, 2.2341340473649614, 2.244134047364961, 2.254134047364961, 2.2641340473649607, 2.2741340473649605  …  2.7341340473649507, 2.7441340473649505, 2.7541340473649503, 2.76413404736495, 2.77413404736495, 2.7841340473649496, 2.7941340473649494, 2.804134047364949, 2.814134047364949, 2.8189606917370034], NoiseProcess{Float64, 1, Float64, Float64, Nothing, Nothing, typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST), typeof(DiffEqNoiseProcess.WHITE_NOISE_BRIDGE), Nothing, false, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, RSWM{Float64}, Nothing, Xoshiro}(DiffEqNoiseProcess.WHITE_NOISE_DIST, 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4.862050260829891, 4.872050260829891  …  4.91205026082989, 4.92205026082989, 4.9320502608298895, 4.942050260829889, 4.952050260829889, 4.962050260829889, 4.972050260829889, 4.982050260829888, 4.992050260829888, 5.0], NoiseProcess{Float64, 1, Float64, Float64, Nothing, Nothing, typeof(DiffEqNoiseProcess.WHITE_NOISE_DIST), typeof(DiffEqNoiseProcess.WHITE_NOISE_BRIDGE), Nothing, false, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}, RSWM{Float64}, Nothing, Xoshiro}(DiffEqNoiseProcess.WHITE_NOISE_DIST, DiffEqNoiseProcess.WHITE_NOISE_BRIDGE, [4.782050260829893, 5.0], [0.0, 0.3767351556081006], [0.0, 0.3767351556081006], nothing, 5.0, 0.3767351556081006, nothing, 0.00794973917011177, -0.08058462314464514, nothing, -0.08058462314464514, nothing, 0.0, nothing, nothing, ResettableStacks.ResettableStack{Tuple{Float64, Float64, Nothing}, false}(Tuple{Float64, Float64, Nothing}[], 0, 0), 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Xoshiro(0x295f77fdacefe713, 0x6462109a61c73453, 0x49a95ba60225ed86, 0x4d9a5f8378cdb2eb, 0xe1f3fd405fa3ff25), true, true, true, nothing), nothing, SDEProblem{Float64, Tuple{Float64, Float64}, false, SciMLBase.NullParameters, Nothing, SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}, typeof(Main.g), Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, Nothing}(SDEFunction{false, SciMLBase.FullSpecialize, typeof(Main.f), typeof(Main.g), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing}(Main.f, Main.g, LinearAlgebra.UniformScaling{Bool}(true), nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, 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The number of particles alive at the end of the sampled trajectory is:

using AbstractTrees
num_alive = treebreadth(sol)

43

The longest lineage in the tree is:

max_lineage_length = treeheight(sol)

10

Note that the actual tree structure implementing the AbstractTrees interface is the field sol.tree of type BranchingProcessNode. When tree operations like the ones above are called on a BranchingProcessSolution, they are delegated to the tree field. Hence we can call the same operations on any instance of aBranchingProcessNode, for instance

num_alive_sub = treebreadth(sol.tree.children[1])

33

Values at the tips of a branching process

We are often interested in the values at the tips of a branching process, that is, the values at the final time $T$ of a branching experiment of the particles alive at that time. To obtain these values, we use an iterator over the leaves of the tree and use the array interface for SciMLSolutions:

tip_vals = [node.sol[end] for node in Leaves(sol)]

43-element Vector{Float64}:
  4.005312258084205
  2.340082119480956
  2.1441698260104203
  1.493088085132137
  1.5016037383560283
  1.3330855211177224
  0.28256151221563397
  0.21123995836772086
  0.3380003505614073
  1.4431235683201626
  ⋮
 -0.5452018193650859
  0.37491570255622797
 -0.6814784286112359
 -1.5888066026399699
  2.114989637188242
  0.8326850775669992
  0.850303721949143
  1.3448512018539989
  1.139756560463017

Again the call Leaves(sol) is delegated to its tree field, that is, it is equivalent to Leaves(sol.tree).

Because it is common to need the final value of a particle, this has been implemented as the value associated with a node:

tip_vals == [nodevalue(node) for node in Leaves(sol)]

true

An even shorter short-cut is to call the function tip_values:

tip_vals = tip_values(sol)