AlderIPM-Sim Web

Alnus-beetle-parasitoid-bird ecoepidemic model — runs entirely in your browser

Pick a black alder forest

Click any pin below to load a parameter calibration built from the literature metadatabase and adjusted for that site’s climate. Grey pins are seed sites (no reviewed literature values yet); amber pins have partial coverage; green pins have full coverage. Confidence intervals and citation counts appear beside every slider in the Parameters tab after selection.

Tree / Foliage

Beetle

Parasitoid

Bird

Uses Newton-Raphson iteration on the annual map to find (A*, F*, K*, D*)

1-D Bifurcation Diagram

2-D RP Boundary Contour

Parameter Fitting to Field Data

Upload a multi-year time series (CSV with a header row; any subset of columns year, A, F, K, D is accepted) and estimate a chosen subset of model parameters by Nelder-Mead least squares. After fitting, the forecast regime is classified (stable coexistence, parasitoid-free, outbreak cycles, or canopy collapse).

1. Data

2. Parameters to fit

Select up to six parameters. Others stay at their current Parameters-tab values.

3. Initial conditions & run

Data Source

Settings

(0 = auto: 50% of series length)

Sensitivity Analysis (LHS-PRCC)

Latin Hypercube Sampling with Partial Rank Correlation Coefficients identifies which parameters most strongly influence the dominant eigenvalue ρ* and regime shift probability. This is computationally intensive — please be patient.

Simulation Settings

Cost Weights

10
1
5
5
5
2

Custom Strategy

0.10 0.00 0.00

Scenario Comparison

Save parameter sets as named scenarios, compare them side-by-side, and explore parameter sensitivity with 1-D sweeps.

Save Current Parameters

No scenarios saved.

Compare Scenarios

Save at least 2 scenarios to compare.

1-D Parameter Sweep

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About AlderIPM-Sim

AlderIPM-Sim is a browser-based decision-support tool for managing Agelastica alni (alder leaf beetle) outbreaks in European alder (Alnus) forests. It implements a coupled ecoepidemiological model that integrates:

  • Within-season continuous dynamics — a 4-state ODE system (susceptible larvae S, parasitised larvae I, adult parasitoid flies F, cumulative defoliation D) solved with 4th-order Runge-Kutta integration over a ~50-day larval vulnerability window.
  • Annual discrete map — between-year transitions for beetle reproduction (Beverton-Holt), parasitoid overwinter survival, and foliage recovery/decline.
  • Biological control — parasitism by Meigenia mutabilis (Holling Type II functional response) and generalist avian predation by passerine birds.

How to Use

  1. Parameters tab: Adjust model parameters using the sliders. Each parameter has ecologically meaningful bounds. Click the info icon next to any parameter for its ecological description. Use "Share Configuration" to encode your settings in a shareable URL.
  2. Simulation tab: Set initial conditions (A0, F0, D0) and control inputs (uC, uP), then click "Run Simulation" to see multi-year dynamics across 4 subplots. Use the within-season viewer to inspect daily dynamics for any year. Export results as CSV or JSON.
  3. Equilibrium tab: Click "Compute Fixed Points" to find equilibria of the annual map using Newton-Raphson iteration. The table shows stability (eigenvalue analysis of the Jacobian), plus resistance (R1) and resilience (R2) metrics. Phase portraits show trajectory shape in A-F and A-D planes.
  4. Early Warnings tab: Detect critical slowing down signals that precede regime shifts. Use simulated data or upload a CSV with time-series observations. The PRCC horizontal bar chart shows which parameters most influence system stability.
  5. Control Comparison tab: Compare 3 management strategies by running parallel simulations. The Pareto scatter shows the cost-defoliation trade-off for each strategy.

Parameter Glossary

Model Equations

Within-season ODE (daily, τ ∈ [0, T])

dS/dτ = -β·S·F/(1+h·S) - c_B·B·(S+I)/(1+a_B·(S+I)) - (μ_S + u_C)·S
dI/dτ =  β·S·F/(1+h·S) - c_B·B·(S+I)/(1+a_B·(S+I)) - (μ_I + δ + u_C)·I
dF/dτ =  η·δ·I - μ_F·F + u_P
dD/dτ =  κ·(S + I)

Annual map (between years)

A(t+1) = R_B · σ_A · S(T) / (1 + σ_A · S(T) / K(t))
F(t+1) = σ_F · F(T)
K(t+1) = K_0 · exp(-φ · D(T))
D(t+1) = D(T)

Early Warning Signals

As the system approaches a bifurcation (tipping point), critical slowing down causes three measurable changes in state-variable time series:

  • Increasing variance — perturbations decay more slowly, widening the distribution.
  • Increasing lag-1 autocorrelation — successive observations become more correlated as "memory" of perturbations grows.
  • Spectral reddening — the power spectrum shifts toward lower frequencies.

Each indicator is tested for a monotonic increasing trend using Kendall's τ rank correlation. The traffic-light alert system is: GREEN (no significant trends), AMBER (one indicator significant), RED (both variance and autocorrelation increasing).

References

  • Scheffer, M. et al. (2009). Early-warning signals for critical transitions. Nature, 461, 53–59.
  • Dakos, V. et al. (2012). Methods for detecting early warnings of critical transitions in time series. PLoS ONE, 7(7), e41010.

Technical Notes

This application runs entirely in the browser with no server-side computation. The ODE system is integrated using 4th-order Runge-Kutta (dt = 0.1 days). Equilibria are found via Newton-Raphson with numerical Jacobian computation. All charts are rendered with Plotly.js using the Okabe-Ito colorblind-safe palette. Dark mode and all settings are saved to localStorage.

Source code is available in the alder-ipm-sim-web/ directory alongside companion R and Python packages.