Analyse the Simulated Dynamics

Once the dynamics of the community have been simulated, we can analyse the results to better understand the behaviour of the community. To do so, we provide a few functions to compute various properties of the community dynamics.

Let's first simulate the dynamics of a species-rich community with the niche model:

using EcologicalNetworksDynamics, Plots

S = 20 # Number of species.
C = 0.1 # Connectance.
foodweb = Foodweb(:niche; S, C)
m = default_model(foodweb)
B0 = rand(S) # Vector of initial biomasses.
t = 100 # Simulation time.
sol = simulate(m, B0, t)

retcode: Success
Interpolation: 3rd order Hermite
t: 36-element Vector{Float64}:
   0.0
   0.06386844727462122
   0.14627165536579728
   0.22883174565162434
   0.3172277066398547
   0.437358837681323
   0.5777264842673768
   0.7770620279364578
   1.0202435533210048
   1.3650101440007452
   ⋮
  44.7789145976874
  48.81834107298829
  52.6458811276706
  59.83729272583517
  66.19851380161774
  74.13308881400377
  81.97536401939114
  91.64467801320588
 100.0
u: 36-element Vector{Vector{Float64}}:
 [0.7562704523721434, 0.7775119939252512, 0.4934712560266089, 0.15272995134848244, 0.8230440276144474, 0.24966857561705436, 0.49182090062124795, 0.8678731681961157, 0.29337440850120045, 0.36694042792262394, 0.904783966404354, 0.7282271304794009, 0.8563243773667578, 0.38898354159389137, 0.5163047180070125, 0.39414388642250386, 0.012660628010274344, 0.14279289241183168, 0.31588418466450296, 0.8276395298003312]
 [0.7912686591172828, 0.7879079009923095, 0.4975812156396402, 0.15697530825632725, 0.8288528272673289, 0.2593884223416226, 0.4972152527352207, 0.8619073377356102, 0.30578820312807903, 0.3756651593752839, 0.9258450194377033, 0.7412605320634633, 0.8349146247216992, 0.39778178036592304, 0.5210495436831054, 0.39481693137523427, 0.013237628164211356, 0.14866386404480486, 0.25011888937669496, 0.5090158141965344]
 [0.8137185189929851, 0.8016900370408259, 0.5029983792019891, 0.16254547223770216, 0.8359662697774156, 0.26425668802446695, 0.4958178084511365, 0.8458437763698899, 0.32253586240741244, 0.3870103252633543, 0.9241850542297907, 0.7386228336878488, 0.809906742384554, 0.40869503253295775, 0.5265602915097131, 0.39199667751739214, 0.013599041514764824, 0.1559089140448133, 0.19281104107533095, 0.28468042793946796]
 [0.8183778098418905, 0.8158522791304397, 0.5084996299538272, 0.16818767966705625, 0.8422140858518621, 0.26325260432651043, 0.4903487472925322, 0.8239704932228227, 0.3398590895848868, 0.3983022525995576, 0.9013750349647032, 0.7240406280934689, 0.7870996626586325, 0.41901707071837785, 0.5312805808349914, 0.38665669954632487, 0.01366145567714041, 0.16299368283755777, 0.1566519759597893, 0.18608223032243013]
 [0.8149432351003132, 0.8313700942523103, 0.5144232019956166, 0.1742520114457628, 0.8476348073998293, 0.2594919087307624, 0.4830185046785365, 0.7970040119731369, 0.3587656303829598, 0.41016751837544696, 0.8679687314739543, 0.7034199206665586, 0.7646732409344034, 0.4292989891723141, 0.5354035928612563, 0.3794349347876384, 0.013587269568426916, 0.17049838953948027, 0.13179279075938924, 0.1357909452790837]
 [0.8049019907605592, 0.8530117842982382, 0.5224616046331049, 0.18245478556753572, 0.8526934567540065, 0.2527967654356643, 0.47234095889894573, 0.7573636840896636, 0.38473410898613036, 0.42573978281625163, 0.8183801100356931, 0.6727316622332324, 0.7369701449456065, 0.4419121001380982, 0.5395143110183057, 0.36838844270926707, 0.013397207954681014, 0.18059699619005376, 0.11061971369058814, 0.10166768073186036]
 [0.790160274415936, 0.8790646851004753, 0.5317323649455624, 0.19184968968859653, 0.8551489045081464, 0.24425734886785397, 0.4597598406557148, 0.7092956094855558, 0.41501841472708284, 0.44288478614966614, 0.7603906400162227, 0.6363993372949991, 0.7080732311091696, 0.4546238739909057, 0.5423410435394771, 0.35475486126306804, 0.013126175579770265, 0.19221445810407242, 0.09569102831138758, 0.08132306579641542]
 [0.7673496384661407, 0.9173862238955074, 0.5444209810604891, 0.2045076651323329, 0.8523880747111766, 0.2319900835375098, 0.4424172394998848, 0.6411794375123483, 0.45693273169081755, 0.46481357742632856, 0.6826727970792711, 0.5868425180168357, 0.6725362911960115, 0.4690532127394976, 0.5433344106894926, 0.33525461256352124, 0.012712736239731452, 0.2082326364917451, 0.08364444892765106, 0.06655347248542762]
 [0.7388893279183215, 0.9660321008245155, 0.5586287909203169, 0.21819316694710522, 0.8399003624373137, 0.21749633193051235, 0.4224869195308487, 0.5621305131141522, 0.5046891969130665, 0.487058878617678, 0.5980461727220172, 0.5315411953627632, 0.6366447630393238, 0.4815717454649488, 0.541129664874759, 0.31231162035700155, 0.012202315315973038, 0.22675368127275605, 0.07622295099107562, 0.05772904987258389]
 [0.699250264256208, 1.0379460039939856, 0.57507764890615, 0.23280183935487214, 0.8080433427353629, 0.19828222272364884, 0.3966332702738916, 0.46292913254316254, 0.5632979554947977, 0.5094817127316819, 0.49809927903807344, 0.4637969242487661, 0.5975328273954029, 0.49216256730394814, 0.5347739465401715, 0.2824614510564566, 0.011498700679254304, 0.2507052328330623, 0.07238722887929064, 0.052320699599023926]
 ⋮
 [0.25573069666685383, 1.5560289110121046, 0.040504835460067196, 0.0025159637619173755, 0.3723843167386513, 0.019625071757510305, 0.19630236435726417, 0.08262751761093516, 0.688832050858957, 0.5464572541674971, 0.025277404145423427, 0.09162533617377343, 0.5917856166865703, 0.5913796995984547, 0.5915668255389346, 0.14469367079532985, 0.003762779860593314, 0.4784102668445551, 0.22018121916251465, 0.19105131394518776]
 [0.2592721901748465, 1.5574014240878304, 0.03903249660843011, 0.0018239364113985899, 0.3725991603105944, 0.018790273188513715, 0.19615443397293325, 0.0832085261564297, 0.6882747873038554, 0.5464318550032157, 0.02380494045020151, 0.09003084801617686, 0.592169858145832, 0.5909337858013967, 0.5915534656971488, 0.144878020903248, 0.0037813209833161684, 0.47801489706086814, 0.22024013199231413, 0.1908481380703142]
 [0.26231337280129957, 1.55850322890013, 0.03782742623675526, 0.0013483876864972093, 0.37268674906757765, 0.018047942885426334, 0.19603074397986398, 0.08372156007963315, 0.6880757156598382, 0.5463570940370349, 0.022545556034258247, 0.08866983202976624, 0.592761205244325, 0.5902891076144149, 0.5918018344640124, 0.14502204696537235, 0.0037936451614537185, 0.4778126841582875, 0.22031333318624957, 0.19070892911904455]
 [0.267350849123346, 1.5601178083549314, 0.03595133094069996, 0.0007625412944829235, 0.3728104086087963, 0.016773708754427866, 0.19588972014148254, 0.08456778652775629, 0.6879352762113279, 0.546145752606593, 0.02047926746906156, 0.08646294226985428, 0.5917735789992853, 0.5922751508661425, 0.5919730443978889, 0.14525363610909084, 0.0038057031198773963, 0.47719528189449684, 0.2204030906931301, 0.1904667312471503]
 [0.2711824128466479, 1.5612471498687024, 0.034624865698659434, 0.00046339199084182694, 0.37302259010455174, 0.015766093502391002, 0.19567107431215752, 0.08518904739500062, 0.6878382502422521, 0.5461044587705722, 0.0189225275869276, 0.08484257468097567, 0.5919180138732174, 0.591817825508189, 0.5918783404263399, 0.14544167142113998, 0.0038064394410060303, 0.47739737299545154, 0.22041543478442557, 0.19023720237148664]
 [0.2752601566772351, 1.5623890204446755, 0.03329760921555121, 0.00024905490716866914, 0.37320031043161506, 0.014644306163958593, 0.19547529156803073, 0.0858026248969031, 0.6877209487125207, 0.5459977921724977, 0.017260576799165366, 0.08316269084052942, 0.5918338765153833, 0.5918546052744884, 0.591842093834322, 0.14564202938239068, 0.0037967124322977235, 0.47743853821821014, 0.22045672879117187, 0.1900278339436279]
 [0.2786777964187318, 1.56329058063884, 0.03225589933780135, 0.00013530145934132458, 0.3733490923085627, 0.01366445904056742, 0.19532300873182176, 0.0862697158951426, 0.6876205665345622, 0.54593632727748, 0.015864266214472088, 0.08181293021444853, 0.5918063897895905, 0.5918021019679568, 0.5918046903888844, 0.14582527752685254, 0.0037782611762427975, 0.47749497276508224, 0.22049074394961204, 0.18986208460767218]
 [0.2822237742733296, 1.5641766247995488, 0.03124520167639319, 6.353713688254111e-5, 0.3734895893338572, 0.012605652381398965, 0.19517839964151326, 0.08669818191106952, 0.6875301215740698, 0.5458724196909229, 0.014407768353726697, 0.08048296826854924, 0.591769381061175, 0.5917702585552373, 0.5917697288593176, 0.14602998824281174, 0.0037465339154981736, 0.477541259582201, 0.2205290896625908, 0.1897036808862585]
 [0.28481049843205225, 1.5647876519967168, 0.03055660717125213, 3.3269226623737364e-5, 0.37358617262117255, 0.011803374785560677, 0.19508165104783115, 0.08697036196673992, 0.6874664253402204, 0.5458320989972734, 0.013337610478294824, 0.0795708695966052, 0.5917460744804744, 0.5917458927633371, 0.5917460024567938, 0.14618930062903987, 0.003713236422996831, 0.477573236788737, 0.22055728700562563, 0.18959718135243928]

When running the dynamics of a rich initial pool of species, we generally observe the extinction of some species. You can access the number of surviving species at the end of the simulation with:

richness(sol[end]) # Number of surviving species at the end of the simulation.

20

You can also get the trajectory of the species richness through time with:

richness(sol) # Richness at each time step.

36-element Vector{Int64}:
 20
 20
 20
 20
 20
 20
 20
 20
 20
 20
  ⋮
 20
 20
 20
 20
 20
 20
 20
 20
 20

Similarly, you can compute the persistence, that is the proportion of species that are present at each time step:

persistence(sol) # Equivalent to: richness(sol) ./ S

36-element Vector{Float64}:
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 ⋮
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0
 1.0

Or the total biomass of the community:

total_biomass(sol)

36-element Vector{Float64}:
 10.360450017306036
 10.099254914018081
  9.879349194203812
  9.737723693084803
  9.622939729377178
  9.492677291887485
  9.358109633550077
  9.18422278936172
  8.989658748427034
  8.739482250587212
  ⋮
  6.690743115143095
  6.689244490338865
  6.6886303953112405
  6.6883936096298235
  6.687786737820936
  6.687352801221742
  6.687064466243665
  6.686834159806351
  6.686704803559787

Or the shannon diversity index:

shannon_diversity(sol)

36-element Vector{Float64}:
 17.003042156473537
 17.018914051101156
 16.84269041479207
 16.701708835026928
 16.625121833698028
 16.58966794899239
 16.58876088284237
 16.599438744026422
 16.58530224704094
 16.486348020264284
  ⋮
 12.00211083287161
 11.974457671599753
 11.95153868213353
 11.915219824138523
 11.888954620182508
 11.861608176052352
 11.839144418648377
 11.816029237426255
 11.799208783606419

For example, you can plot how a few of these properties evolve through time:

time = sol.t
plot(
    time,
    total_biomass(sol);
    xlabel = "Time",
    ylabel = "Observable",
    label = "Total biomass",
)
plot!(time, richness(sol); label = "Richness")
plot!(time, shannon_diversity(sol); label = "Shannon diversity")