one more cat
The question, made mechanical
“How does someone end up with a hundred cats?” is usually asked as a question about a person. This playground asks it as a question about a system. A household is a small population with inflows (unsolicited arrivals the caregiver accepts, and births) and outflows (rehoming and permanent exits). Each month the caregiver faces one more accept-or-refuse decision, and the balance of those decisions, not any single choice, decides whether the count stays at one, settles at a pair, or drifts upward for years.
Why capacity, not count
The variable that governs welfare here is not the number of cats but the care-load ratio, the required care divided by the effective capacity to provide it.
Below one, there is slack. Above one, monitoring lapses, illness is caught late, and the extra work feeds back as still more load. This is why an organized sanctuary of eighty cats can sit in a stable regime while an overwhelmed home of fifteen is already in crisis. The number on its own tells you very little.
Three feedbacks that resist reversal
Growth is driven by loops, not by a bad decision. Cat solicitation raises the probability of accepting the next arrival. Unsterilized cats reproduce, and the model anchors that to a measured rate of roughly 1.4 litters a year with about three kittens each. A caregiver known to take cats in attracts more offers, so opportunities scale with the current population.
Reversal is harder than accumulation. Refusing an unknown cat is easy; surrendering a named, attached cat is not. That asymmetry is hysteresis: the population resists falling even once the caregiver wants it to, which is why late interventions in the intervention lab buy so much less than early ones.
What it is not
This is a transparent hypothesis generator, not a fitted predictor and not a diagnosis. A high cat count does not by itself indicate hoarding, and nothing here pathologizes multi-cat owners; the model deliberately routes organized high-count runs to a sanctuary regime rather than a crisis. The welfare and strain indices are visible proxies, not validated instruments. The calibration panel checks only that the engine reproduces the identities and the one literature rate it claims to encode, which is the honest limit of what a model like this can verify about itself.
Model changelog
- state: monthly population update n(t+1) = n + accepted arrivals + births - rehomed - deaths, with expected fractional flows or stochastic integer draws (Poisson / binomial) from a seeded PRNG.
- care system: rho = load / effective capacity, where load combines routinizable care with limited economies of scale, irreducible individual monitoring, and density / monitoring / disease multipliers that grow super-linearly past their thresholds.
- decision: P(accept) = logistic[2.7 * (benefit - perceived cost)]; benefit spans companionship, a second-cat bonus, rescue identity, solicitation, and reputation; perceived cost is discounted by habituation and raised by recognized overload and an intake-capacity gate.
- reproduction: literature-anchored 1.4 litters/yr and 3 kittens/litter, scaled by intensity, kitten survival, sterilized share, and current welfare.
- rehoming: attachment-based surrender aversion, crisis motivation, chaos penalty, and network factor, producing hysteresis between refusing and relinquishing.
- regimes: none / single / pair / stable multi-cat / rescue network / managed sanctuary / overload / accumulation crisis, with first-crossing threshold events at 1, 2, 5, 20, 50, 100, and 120 cats and at rho = 1.
- analysis surfaces: expected and stochastic timelines, a 200-run Monte-Carlo ensemble with quantile bands and overload / reach-120 probabilities, a 1-D threshold scanner with automatic cliff detection, a 2-D regime phase map, and an intervention lab (timed sterilization, rehoming, capacity, and intake boosts) with a no-intervention counterfactual.