Guinea pig herd planner

Inputs

A is a sow's age at her first litter, a_j her age at litter j, R the age she stops breeding, and c the expected surviving daughters per later litter (L litter size, s pup survival, f female share).

Adjustments per litter

Sow survival combines background mortality with an extra hazard h_b while breeding (from age M until she stops):

Background survival ℓ(a) is either flat, (1−m)^a/365, or the table below, with a constant daily hazard inside each half-year band k:

Source and caveats. This is not an official mortality table. It comes from one study (Mata, PeerJ 2025): Kaplan–Meier on the ages at death of 675 pet guinea pigs that died under UK vet care in 2019 (Royal Veterinary College VetCompass records), in half-year intervals with no censoring.

• It is the age-at-death distribution of one year's deaths, not a cohort followed from birth. Treating it as death probabilities by age assumes the pet population was stable over time, which is untested.
• Only animals that reached a vet are included. Pups that die at breeders or before sale (~6–8 weeks) are mostly missing, so early-age deaths are likely understated. Pup losses are modelled separately through s.
• These are pets, not breeding sows. Sows that breed repeatedly likely die faster at the same age; d and h_b cover that, but h_b is an assumption with no data behind it.
• The tail rests on very few animals: the 7.5–8 yr value (0.27) is smoothed to 0.46, and values past 8.5 years are extrapolated.

ρ₁ ≈ 0.8: first litters averaged 3.2–3.5 pups vs 3.6–4.7 for later ones in a breeding colony (Rowlands, J. Hygiene, 1949). φ: pups of sows over 900 days survived 0.43 vs 0.71 in a lab colony (ratio 0.61).

Daughters per sow (R₀) and growth rate (Euler–Lotka)

This counts litters by number (j), which is exact for an uncrowded herd with a boar present. The simulation tracks, for each age group, the share of sows that haven't had a litter yet, so a sow that misses a cycle (crowding, no boar) still gets the smaller first litter when she finally breeds.

The herd grows if and only if R₀ > 1; the right side falls as r rises, so there is exactly one root. T̄ is the generation time (average age of mothers). This r is the growth rate of an uncrowded, non-inbred herd; crowding and inbreeding only slow it.

Boar availability

The chance a fertile boar was alive at conception: all n_b starting boars dead, and no young fertile male (Poisson approximation, M_b = expected males born on day b). β → 1 as the herd grows.

Crowding (no selling or neutering)

A sow conceives with probability δ at conception time; a sow that doesn't waits for her next cycle. With no culling, births fall to zero as the herd fills its space, so it levels off near K. A fast-growing herd can overshoot K for a while (by ~15% with no deaths and back-to-back litters) because pregnancies already underway still deliver. If N > K, the herd never reaches N. This logistic form is an assumption: guinea pigs breed less when crowded, but the exact curve isn't measured.

Inbreeding

N_f = sows of breeding age, N_m = fertile boars, θ = average relatedness (coancestry) of the breeders, F = inbreeding of pups born now. Starting pigs are assumed unrelated. 2B is the number of lethal equivalents: about 3.1 is the median for juvenile survival across 40 zoo mammal populations (Ralls, Ballou & Templeton, Conservation Biology 1988; the exact figure couldn't be checked against the paper). At F = 0.25 (full-sib parents) that cuts pup survival by about 32%. This uses effective population size, not a full pedigree; the Monte Carlo uses the same approximation with actual counts. In the average model N_e comes from average herd sizes, which runs that died out pull down, so for very small starting herds (under ~10) it overstates inbreeding and runs a few percent to ~15% pessimistic; the Monte Carlo is the better guide there.

Whole-litter stillbirths

Same average, more variable outcomes; it only matters in the Monte Carlo.

Costs and space

Upkeep is summed over pig-days until the herd reaches N. Default prices are pet-owner prices; a breeder buying in bulk would pay less per pig.

Special case: Fibonacci-like

With no mortality, no retirement, ρ₁ = 1, and a first litter exactly two intervals after birth (A = 2I), set x = e^rI: