Entities in biology and economics grow convexly then slow as they saturate; growth may be unbounded but remains sub-logarithmic.

The claim is hedged. True if the biology and economics literature (e.g. allometric or logistic/Gompertz growth, firm-growth studies) supports a typical pattern in which growth is first convex and then slows as it saturates, with size that may be unbounded but grows more slowly than the logarithm of time. Mostly true if the convex-then-saturating pattern is well supported but the specific 'sub-logarithmic' rate is only partly supported or is a mathematical characterization rather than an empirically established one. Mixed if the convex-saturating pattern holds in one domain only, or the asymptotic claim conflicts with common models (e.g. logistic growth being bounded) and is offered without support. Mostly false if the pattern is shown to be an exception rather than the rule. False if entities typically grow without slowing (e.g. sustained exponential growth).

Set before the research began.

1. E1 Exponential, logistic, and Gompertz growth Chebfun (numerical software project examples page) · 15 June 2015

   “In this model, the per capita growth rate decreases linearly to zero as the population $P$ approaches a fixed value, known as the carrying capacity.”

2. E2 Exponential, logistic, and Gompertz growth Chebfun (numerical software project examples page) · 15 June 2015

   “The result is unbounded growth, which is not biologically realistic.”

3. E3 Exponential, logistic, and Gompertz growth Chebfun (numerical software project examples page) · 15 June 2015

   “The Gompertz model has been recognized for some time as a reasonable model for some tumors [1-2]. However, it too is considered inadequate for many realistic uses.”

4. E4 When is Gibrat’s law a law? - Small Business Economics Springer (Small Business Economics) · 18 November 2011

   “The results reject Gibrat’s law on an aggregate level, since small firms grow faster than large firms. However, Gibrat’s law is confirmed about as often as it is rejected when industry-specific regressions are estimated.”

E1 and E2 support the convex-then-saturating pattern in biology: standard logistic models slow to zero growth at a carrying capacity, and unbounded growth is called biologically unrealistic. E3, however, notes that saturating models such as Gompertz are considered inadequate for many realistic uses. In economics, E4 finds that small firms grow faster than large firms in aggregate, but Gibrat's law of size-independent growth holds about as often as it is rejected at industry level. So the pattern is only partly supported there. No evidence addresses the specific 'unbounded but sub-logarithmic' rate, and the common models cited are bounded. The claim is therefore supported in one domain and only partly in the other.