Deforestation and world population sustainability: a quantitative analysis

Abstract

In this paper we afford a quantitative analysis of the sustainability of current world population growth in relation to the parallel deforestation process adopting a statistical point of view. We consider a simplified model based on a stochastic growth process driven by a continuous time random walk, which depicts the technological evolution of human kind, in conjunction with a deterministic generalised logistic model for humans-forest interaction and we evaluate the probability of avoiding the self-destruction of our civilisation. Based on the current resource consumption rates and best estimate of technological rate growth our study shows that we have very low probability, less than 10% in most optimistic estimate, to survive without facing a catastrophic collapse.

Figure 1

On the left: plot of the solution of Eq. (1) with the initial condition N₀ = 6 × 10⁹ at initial time t = 2000 A.C. On the right: plot of the solution of Eq. (2) with the initial condition R₀ = 4 × 10⁷. Here β = 700 and a₀ = 10⁻¹².

Figure 2

On the left: plot of the solution of Eq. (1) with the initial condition N₀ = 6 × 10⁹ at initial time t = 2000 A.C. On the right: plot of the solution of Eq. (2) with the initial condition R₀ = 4 × 10⁷. Here β = 170 and a₀ = 10⁻¹².

Figure 3

(Left) Comparison between theoretical prediction of Eq. (15) (black curve) and numerical simulation of Eq. (3) (cyan curve) for γ = 4 (arbitrary units). (Right) Comparison between theoretical prediction of Eq. (15) (red curve) and numerical simulation of Eq. (3) (black curve) for γ = 1/4 (arbitrary units).

Figure 4

(Left panel) Probability p_suc of reaching Dyson value before reaching “no-return” point as function of α and a for β = 170. Parameter a is expressed in Km² ys⁻¹. (Right panel) 2D plot of p_suc for a = 1.5 × 10⁻⁴ Km² ys⁻¹ as a function of α. Red line is p_suc for β = 170. Black continuous lines (indistinguishable) are p_suc for β = 300 and 700 respectively (see also Fig. 6). Green dashed line indicates the value of α corresponding to Moore’s law.

Figure 5

Average time τ (in years) to reach Dyson value before hitting “no-return” point (success, left) and without meeting Dyson value (failure, right) as function of α and a for β = 170. Plateau region (left panel) where τ ≥ 50 corresponds to diverging τ, i.e. Dyson value not being reached before hitting “no-return” point and therefore failure. Plateau region at τ = 0 (right panel), corresponds to failure not occurring, i.e. success. Parameter a is expressed in Km² ys⁻¹.

Figure 6

Probabilityp_suc of reaching Dyson value before hitting “no-return” point as function of α and a for β = 300 (left) and 700 (right). Parameter a is expressed in Km² ys⁻¹.

Figure 7

Probability of reaching Dyson value p_suc before reaching “no-return” point as function of β and α for a = 1.5 × 10⁻⁴ Km² ys⁻¹.