A dragonfly spends most of its life underwater as a nymph. Grow the pond's population through six years of degree-days, reeds and fish, and see how many mosquito larvae the nymphs eat.
Each runs all six years headless for several values and reports the last year.
The science
Development by degree-days. Cold-blooded animals develop in proportion to accumulated heat above a threshold: dD/dt = max(0, Tw − T0) with T0 = 8 °C. Eggs hatch after 140 degree-days; a nymph passes 10 instars and is ready to emerge at about 1,500 degree-days. Pond temperature is Tw = Tm + warming + A cos(2π(d − 205)/365); its yearly degree-days have a closed form that the checks below compare with the daily sum.
Food and growth. A nymph eats mosquito larvae with a Holling type II functional response f = aM/(1 + a h M) (a grows with body size, handling time h = 1/6 day), and 80 % of its needs are met by other prey. Growth speed is scaled by the fraction of its daily need that is met.
Mortality. Per-day loss μ = μ0 + μfish/(1 + reeds/60) + μcan N/Kn: background, fish predation reduced by refuge among reed stems, and cannibalism (Kn rises with reeds). Mature nymphs climb reed stems to emerge between days 110 and 250 when the water is at least 11 °C; success is reeds/(reeds + 25) because no perch means no emergence.
Adults and eggs. Adults live about two weeks (daily survival 0.93), mature in 10 days and lay eggs in reed stems when the air is at least 15 °C: eggs scale with reeds/(reeds + 40). Mosquito larvae grow logistically, dM/dt = r(T) M (1 − M/K) + immigration − nymph feeding, K = 3,000 per m²; the dashed baseline shows the same pond without dragonflies.
Simplifications and honesty. One generic dragonfly species is modelled with parameters that are typical or tuned for a plausible pond (nymph densities of 10 to 100 per m²); the real values vary widely between species, many of which need two to five years. Cohorts are not individual animals, there is no wetland hydrology, drying, winter ice, pollution, birds or competing predators, mosquito adults are not modelled, and the strong effects of reeds and fish are partly built into the chosen coefficients. The numbers show how the mechanisms interact, not a forecast for any real pond. Animals are drawn about 10 times too large. Assets were modelled in Blender; the animals, flight and numbers are driven by the simulation on this page.