The 3D version of this simulation runs a discrete 10×10 grid of individual trees and spreads mass-attacks between named neighbors with a stochastic per-tree infection roll. This 2D version is a genuinely different computation: the same three biological mechanisms drive a continuous reaction-diffusion field u(x,y)∈[0,1] (local infestation intensity) evolved with real finite differences on a grid, exactly the Fisher–KPP equation used to model real invasion fronts (genes, epidemics, insect outbreaks):
∂u/∂t = D·∇²u + r·u·(1 − u/K)
Overwinter survival (applied once per year, same
cold-hardening curve as the 3D model):
S(Tmin) = 1 / (1 + e^-k(Tmin − T50)), T50=-34°C, k=0.28
Annual growth rate: r = G·ln(R0_eff), R0_eff = R0·(1 − 0.6·pred)
Carrying cap: K = 1 − 0.6·vigor
Diffusion: D = D0·(1 − 0.4·vigor)
Fisher-KPP traveling-wave speed (analytic result):
c = 2·√(D·r) [cells / simulated year]
Every year the field is culled uniformly by S(Tmin) (winter), then relaxes under logistic growth-with-diffusion for the rest of the year (growing season). Because r and D above are exactly the same three sliders as the 3D model (winter cold, summer voltinism, tree defense, natural-enemy pressure), you can watch the *same* climate mechanism produce a *mathematically predictable* invasion speed instead of a hand-tuned stochastic spread — the "measured vs predicted" stat box tracks the outbreak ring's real radius each year and compares it to the closed-form c=2√(Dr), which is the textbook derivation for how fast a favorable mutation, disease, or (here) an insect population front advances into unoccupied territory.
- Winter minimum temp — colder winters push S(Tmin) toward 0, culling the field before spring; the strongest brake on outbreaks, and the one climate warming is removing.
- Summer temperature — crossing ≈21°C flips generations/year (G) from 1 to 2, squaring the per-year growth exponent and roughly doubling r.
- Tree defense — raises the local carrying capacity ceiling's resistance (lower K) and slows neighbor-to-neighbor spread (lower D) — both must be overcome for the front to advance.
- Natural-enemy pressure — woodpeckers, clerid beetles and parasitoids trim the effective reproductive rate that feeds r.