Effect of decreasing population growth-rate on deforestation and population sustainability Gerardo Aquino and Mauro Bologna Goldsmiths, University of London; aquigerardo@gmail.com Departamento de Ingenier´ ıa El´ ectrica-Electr´ onica, Universidad de Tarapac´a, Arica, Chile; mauroh69@gmail.com Abstract We consider the effect of non-constant parameters on the human-forest interaction logistic model coupled with human technological growth introduced in [1]. In recent years in fact, a decrease in human popula- tion growth rate has emerged which can be measured to about 1.7% drop per year since 1960 value which coincides with latest UN projections for next decades up to year 2100 [2]. We therefore consider here the effect of decreasing human population growth-rate on the aforementioned model and we evaluate its effect on the probability of survival of human civilisation without going through a catastrophic collapse in pop- ulation. We find that for realistic values of the human population carrying capacity of the earth (measured by parameter β) this decrease would not affect previ- ous results leading to a low probability of avoiding a catastrophic collapse. For larger more optimistic val- ues of β instead, a decrease in growth-rate would tilt the probability in favour of a positive outcome, i.e. from 10-20% up to even 95% likelihood of avoiding collapse. Introduction The problem of the survival of humanity, for long time the subject of science fiction and catastrophist movies, has recently become central in both scientific and social debate, due to various factors, among them climate changes, intensive exploitation of resources and more generally a deterioration of the planetary ecosystem. Recently, the authors of Ref.[1] pointed out the serious repercussions on the life of the planet of uncontrolled deforestation. The model examined in [1] considered the strong connection between the use of the resources (i.e. the forests) and the techno- logical development [3, 1] governed by the following equations d dt N (t) = rN (t)  1 − N (t) βR(t)  , (1) d dt R(t) = r ′ R(t)  1 − R(t) R c  − a 0 N (t)R(t) (2) for the the world population N and the forest-covered surface R. The parameters involved in Eqs. (1) and (2) are: β, a positive constant related to the human population carrying capacity of the earth, r the growing rate for humans (estimated as r ∼ 0.01years −1 ) [4], a 0 which may be identified as the technological parameter representing the ability of exploiting the resources, r ′ the renewability parame- ter characterising how quickly the resources are able to regenerate and finally R c , the resource carrying capacity of the earth that in our case may be identi- fied with the initial 60 million square Kilometers of forest. 1 R dR dt ≈−a 0 N (3) The actual population of the earth is N ∼ 7.5 × 10 9 inhabitants with a maximum carrying capacity es- 1 arXiv:2111.08763v1 [q-bio.PE] 16 Nov 2021