richness is not proportional to area. it is a power of it.
the arrhenius relation: species = c × area raised to z. c is the richness of the first hectare. z is the rate at which new species appear as area grows.
for trees i take c = 150 and z = 0.232. those two values carry one rich hectare to roughly sixteen thousand tree species at the scale of the whole amazon basin, the estimate of ter steege and colleagues, 2013.
richness is also bounded above by the stem count. on small areas that bound is the active one.
ground_ha = market cap / 10,000 trees = floor(565 × ground_ha × maturity) kinds = min(trees, 16,000, floor(150 × ground_ha ^ 0.232)) group = floor(c × ground_ha ^ z × maturity)
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one mark per tree species resolved, first 600.
| taxon | c | z | stratum | species |
|---|---|---|---|---|
| trees | 150 | 0.232 | floor | |
| anurans | 14 | 0.20 | floor | |
| formicidae | 90 | 0.22 | floor | |
| fungi | 300 | 0.25 | floor | |
| birds | 45 | 0.19 | understory | |
| epiphytes | 60 | 0.21 | canopy |
c and z for trees are fitted to published figures. the remaining taxa use constants fixed by me. they are parameters, not measurements.
| scalar | area | canopy | stems | tree species | anurans | formicidae | fungi | birds | epiphytes |
|---|---|---|---|---|---|---|---|---|---|
| $1,000 | 1,000 m² | 0.0 m | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| $10,000 | 10,000 m² | 12.0 m | 188 | 150 | 4 | 30 | 100 | 15 | 0 |
| $100,000 | 100,000 m² | 24.0 m | 3,766 | 255 | 14 | 99 | 355 | 46 | 64 |
| $1,000,000 | 1,000,000 m² | 36.0 m | 56,500 | 436 | 35 | 247 | 948 | 107 | 157 |
| $10,000,000 | 10,000,000 m² | 48.0 m | 565,000 | 744 | 55 | 411 | 1,687 | 167 | 255 |
| $100,000,000 | 100,000,000 m² | 60.0 m | 5,650,000 | 1,270 | 88 | 682 | 3,000 | 258 | 415 |
| now |
under contraction, area shrinks and the canopy drops. taxa are lost in reverse order of arrival. epiphytes first, then birds. formicidae and fungi persist longest and return first.
nothing is removed. the derivation is evaluated again on a smaller scalar and fewer species satisfy it.
| scalar × | tree species | species lost |
|---|---|---|