Scaling macroecological laws have captured the interest of both ecologists and physicists for two main reasons. First, the interest lies in their power of prediction: how many species will go extinct if the available habitat shrinks of a certain amount? How should reserves be designed to maximize biomass? Or total abundance? For the scope of predictions, it is crucial to know not only the analytical form of laws but also the values of scaling exponents. Secondly, scaling laws show how different types of ecosystems exhibit the same “macroscopic” behavior regardless of “microscopic” details, a property that in physics is called “universality”. This means that regardless of all the complex dynamics taking place inside the ecosystem (intra-species interaction, competition for resources, etc.) which could differ among different types of ecosystems or environmental conditions, in the end the system results to be described by only a small number of macroscopic variables (A, S,N,...) in a universal fashion, not depending on those microscopic details. In fact, it turns out that laws connecting these macroscopic variables are always power-law. This does not mean that the microscopic details are not important, but it does mean that there is something that characterizes all ecosystems, at a more fundamental level than microscopic details, which produces power-laws. It is instructive to take an example from physics: in a physical system at criticality all observables have power-law behavior. This is due to the fact that they all come from a free energy function that at criticality has a scaling form, and consequently all observable computable from it are power-laws the exponents of which are not all independent. What we argue here is that in the case of ecosystems the same role is played by the joint probability distribution P(n, m|A)dndm of finding a species of abundance n ∈ [n, n + dn] and typical mass m ∈ [m, m + dm] in an ecosystem of area A. In fact, all macroecological laws can be computed starting from this probability distribution, and in order for them to be power-laws it is required that this probability has a very specific form. We give an ansatz for P(n, m|A) (see Box 1) which allows to derive, by computing its marginals and moments, all the empirically observed scaling laws: i) Species-Area relationship S ∝ Az linking the number of species S to the area A of the ecosystem, ii) Damuth Law ${A}\propto m^{-\gamma}$, linking the density of a species of mass m to the mass m, iii) the community size-spectrum s(m|A)∝m−η, i.e. the probability of finding an individual of mass m regardless of species, iv) the scaling of total biomass M with area, v) the scaling of total abundance N with area, vi) the relative species abundance (RSA), i.e. the probability of finding a species with abundance m. In doing this, we must account for the fact that all the species in the ecosystem share the same (finite) amount of resources, and this gives a constraint on the total metabolism of the community (the sum of all individual metabolism). In particular, if we take the total amount of resources R to be proportional to the ecosystem area (e.g. for a forest the amount of light received is proportional to the forest area), then we argue that also the total metabolism B must be linearly proportional to A. In fact, a superlinear dependence would imply that in the limit of large A the metabolism per unit area would grow indefinitely, while the amount of resources per unit area stay finite. On the other hand, a sublinear dependence would mean that in the limit of large area the metabolism per unit area goes to zero, while the resources remain finite, which means that the available resources are not fully exploited. Thus, we take B ∝ A as a working assumption. Metabolism enters the picture through another well-established scaling law, _Kleiber Law_, linking the metabolism b of an individual to its mass m as b ∝ mα .This law has been widely verified in diverse types of ecosystems and in the following we will take it for given. The constrainton total metabolismis crucial to link consistently scaling laws among each other and get the relationships linking the scaling exponents. From the computation of macroecological scaling laws (see Box 2 for technical details) two linking relationships for scaling exponents emerge: \eta=\gamma+\Delta_2 z=\max\{0,\Phi_2(1+\gamma-\eta)\}-\max\{0,\Phi_2+\alpha-\eta)\} where Δ₂ is the scaling exponent for P(m|A) with m, Phi₂ that for the scaling of the biggest organism with A and η, γ, ζ were defined above. These relationships arise because when we compute the macroecological laws from P(m, n|A) and we look at how they scale in the limit of a large ecosystem area all the observable scaling exponents (γ, η, ζ,...) will be expressed in terms of the same five independent exponents (di supporto? com’è la parola giusta?) appearing in the definition of P(m, n|A) (see Box 1), plus the exponent of Kleiber Law, α. Consequently, the result is that they are not independent. The relationships that have received more attention in literature and that have been the object of more empirical validation are the Species-Area relationship, Damuth Law and the community size-spectrum. Let us then focus on what the two relationships tell us about their exponents ζ, γ and η in terms of compatibility with the set of values measured in the different kinds of ecosystems (we differentiate among forests, terrestrial ecosystems and aquatic ecosystems). We will then show what are the predictions of the framework for the scaling of M and N. First, let us make a point regarding energetic equivalence. It has often been assumed γ = α , a relationship that goes under the name of “energetic equivalence” because it implies that the total metabolism of a species of mass m, $B_m \propto ^S m^{-\gamma} m^\alpha$, does not scale with the mass, meaning that all species have the same total metabolism. A very simple calculation already tells us that if B ∝ A energetic equivalence is not compatible with a value z > 0 for the exponent of the Species-Area relationship, something that has been found by for forests, and for terrestrial ecosystems and , and for aquatic ecosystems: B=^S N(m) b(m) \propto A ^S m^{-\gamma}m^\alpha= A ^S 1= AS=A^{1+z} where we use Damuth Law to express the abundance of a species of mass m as N(m)∝Am−γ, Kleiber Law to express the metabolism of an individual of that species as b(m)∝malpha, then we exploit energetic equivalence, and finally in the last equivalence we use the Species-Area relationship. We then see that z must be zero if we want B ∝ A. We can reach the very same conclusion from relationship of our framework: if we substitute γ = α we get z = 0. Thus from we conclude that we must have γ > α in order to have z > 0. _Terrestrial ecosystems_ The values of exponents measured for terrestrial ecosystems are the following: z ⋍ 1/4 , γ ∈ [3/4, 1] , α ∈ [2/3, 3/4] , η ⋍ 1.4 . From this we get, using the relationships , that Δ₂ ∈ [0.4, 0.65] and Φ₂ = z/(γ − α). This is compatible with any value of α and γ in the intervals measured empirically, as long as γ ≠ α. The value of the exponent Φ₂ (scaling of the mass of the biggest organism) depends on these two values. Substituting these results in the equation for the scaling of total biomass (Box 2) we get a superlinear scaling with A: $M\propto A^{1+z {\gamma-\alpha}}$. This results could have interesting consequences for conservation ecology: it means to maximize the total biomass a small number of large reserves is better than a larger number of small reserves. The total number of organisms scales, instead, sublinearly with A: $N\propto A^{1-z {\gamma-\alpha}}$ _Forests_ The values of exponents measured for forests are the following: z ⋍ 1/4 , γ ⋍ 1 , α ∈ [3/4, 1] , η ⋍ 1.4 . We get then Δ₂ = 2/5, Φ₂ = 1. For M and N we get again the same results as for terrestrial ecosystems. _Aquatic ecosystems_ The values found empirically for z and η in this case differ substantially from the other two cases : the number of species S is reported to grow weakly with A, although z is statistically different from zero , while η ⋍ 2 according to . For the other two exponents, instead, the values are α ∈ [3/4, 1] and γ ∈ [3/4, 1] . By substituting these values in our linking relationships we have two possible cases: if γ < 1 then z = 0, which is not compatible with empirical findings; if γ = 1 then Δ₂ = η − γ = 1. The case Δ₂ = 1 is mathematically a special case which needs to be treated separately, so the results are not valid in that case. It turns out that this special case does describe well aquatic ecosystems: instead of what we have (see Box 2) is that the S grows logarithmically with A, something which may rationalize the the observations of very low values of z reported in the literature. At the place of we get \eta=1+\gamma telling us γ = η − 1 = 1 for the aquatic case. The total biomass is weakly superlinear, and the total number of organisms linear. In conclusion, from the introduced framework we derived relationships linking the scaling exponents which are compatible with values measured in diverse types of ecosystems. This gives us an insight on how the different ecological pattern influence each other. An interesting example of this is the following: for aquatic ecosystems, where there are no barriers to limit dispersion, z is smaller than in terrestrial ecosystems because all species are everywhere . This difference in one exponent generates, through the linking, differences in all the set of exponents, explaining why also η is different for the two cases. The framework also makes predictions on scaling relationships that haven’t been measured yet, e.g that of P(m|A) and that of the total biomass, which results to scale superlinearly with the area of the ecosystem.