END failed to simulate some random networks

[Xxiao-Li]

example:

The adj of a random network:

 0  0  0  0  1  0  0  1  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  1  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 1  1  0  0  1  0  0  0  1  0  0  0  0  0  0
 0  0  1  0  0  0  1  1  0  1  0  1  0  1  0
 0  1  0  0  0  0  0  0  1  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  1  1  1  0  0  0
 0  0  0  0  1  0  0  0  1  0  1  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  1  0  0  0  0  0  0  0  0  0  0  1  1  0
 0  0  1  0  1  0  0  1  0  0  0  0  0  0  0
 0  1  0  0  0  1  0  0  0  0  1  0  0  0  0
 0  0  0  0  0  0  0  0  0  1  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0

fw = Foodweb(adj)
params = default_model(
            fw,
            BodyMass(; Z = 100),
            ClassicResponse(; h = 2),
        )
B0 = rand(params.S) .+ 0.1

sol = simulate(
        params, B0, tmax;
        callback = CallbackSet(
            extinction_callback(params, 1e-6; verbose = false),  # extinction threshold
            TerminateSteadyState(1e-8, 1e-6, DiffEqCallbacks.allDerivPass; min_t = tmin),
        ),
        show_degenerated = false,
    )

it shows:

┌ Warning: Automatic dt set the starting dt as NaN, causing instability. Exiting.
└ @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/GMkz9/src/solve.jl:645
┌ Warning: NaN dt detected. Likely a NaN value in the state, parameters, or derivative value caused this outcome.
└ @ SciMLBase ~/.julia/packages/SciMLBase/R6qe7/src/integrator_interface.jl:618
retcode: DtNaN
Interpolation: 3rd order Hermite
t: 1-element Vector{Float64}:
 0.0
u: 1-element Vector{Vector{Float64}}:
 [0.33799431755994946, 0.9726350330830773, 0.9771703657739167, 0.9897313906566511, 0.5855513278526262, 0.720193374688015, 0.9330459139050444, 0.38000574182981206, 1.0712396001667956, 0.41164516484022906, 0.9524653571088514, 0.7202570690812273, 0.5095119945014907, 0.8785674805016142, 0.5898278369987708]

This is because species body mass:

julia> params.body_mass
15-element EcologicalNetworksDynamics.BodyMasses:
 Inf
 Inf
  1.0
 Inf
 Inf
 Inf
 Inf
 Inf
  1.0
 Inf
 Inf
 Inf
 Inf
 Inf
 Inf

julia> EcologicalNetworksDynamics.Internals.trophic_levels(params.A)
15-element Vector{Float64}:
 1.0573668690348124e16
 2.401919801264265e16
 1.0
 1.2172772905863732e16
 1.4098224920464162e16
 1.2009599006321326e16
 1.5142537877535582e16
 7.049112460232083e15
 1.0
 2.4019198012642644e16
 7.049112460232083e15
 1.4359303159732018e16
 2.401919801264265e16
 2.401919801264265e16
 2.401919801264265e16

[LalaBinks]

That's interesting.
I've not had any issues with my body mass ranges when I use the END before adding the invader.

[Xxiao-Li]

For niche, cascade, and random food webs, species body masses are given by their trophic levels. And their trophic levels are calculated based on the adjacency matrix.

In this specific random food web, the adj matrix results in extremely high trophic levels, this is (mainly?) because of the feeding cycles, for example, species 2, 10, 13, 14, and 15 form a closed feeding loop with no link to basal species (3 and 9). These closed cycles let trophic level goes to infinity?