2023 · Problem A — Dandelions: Friend? Foe? Both? Neither?
Spatial diffusion Population growth Multi-criteria indexThe problem in one paragraph
A single dandelion in puffball stage sits next to a 1-hectare empty plot. (1) Model the spread over 1, 2, 3, 6, 12 months in temperate / arid / tropical climates. (2) Build an "impact factor" model for invasive species that combines plant characteristics and harm. Apply it to dandelions and two other invasive plants of your choice (for specified regions).
How to frame the problem
Part 1: Spread
Two clean approaches:
- Diffusion + growth (PDE). $\partial P / \partial t = D \nabla^2 P + r P (1 - P/K)$, where $P(x,y,t)$ is density, $D$ is wind-driven dispersal coefficient, $r$ is growth rate, $K$ is carrying capacity. Solve on a 100×100 grid with a simple finite-difference scheme. Climate sets $D$, $r$, $K$.
- Agent-based / stochastic. Simulate individual dandelions, each producing seeds that disperse according to a wind-speed-dependent kernel (often log-normal in distance). Track count and footprint over time.
Climate parameter table to populate from literature:
| Climate | $r$ (growth) | $D$ (dispersal) | $K$ (carrying) |
|---|---|---|---|
| Temperate | high | high | high |
| Arid | low | medium | low |
| Tropical | medium (competes with native flora) | medium | medium |
Part 2: Impact factor
Construct an index combining:
- Reproductive rate / dispersal (how fast it spreads — from Part 1)
- Competitive displacement (% reduction in native plant biomass)
- Economic cost (e.g., agricultural loss, control budgets)
- Health impact (allergens, toxicity)
- Ecosystem disruption (pollinator network effects)
- Mitigating value (medicinal, edible, soil aeration — subtract this)
$I = w_1 R + w_2 D - w_3 V + w_4 C + w_5 H + w_6 E$
Where $V$ is the value/benefit term. Use AHP or EWM for weights. Validate by checking that known-severe invasives (e.g., kudzu, water hyacinth) score high and known-mild ones (e.g., dandelion itself in temperate regions) score moderate.
Other plants to try
- Kudzu (US Southeast) — high impact (large $R$, $D$, $C$, $E$).
- Water hyacinth (tropics, including Africa, India) — very high (clogs waterways).
- Japanese knotweed (UK, North America) — structural-damage cost is huge.
- Scotch broom (Pacific Northwest USA) — moderate, with allergenic profile.
Pitfalls
- Pure ODE growth without spatial dispersal won't show a "spread" pattern — judges expect spatial modeling.
- Climate dependence assumed without source / data.
- Index combines incommensurable units without normalization.
- No validation of the impact factor against known cases.