Self-thinning: slope of log (biomass) vs log (density) is -1/2 whereas slope of log (weight) vs log (density) is -3/2, why?
Biomass here refers to the total mass of all the organisms in the population (in a unit of area), added together.

Weight here refers to the average weight or mass of an individual.

If biomass decreases, that could be because the individuals got lighter, or it could be because there are fewer of them, or both.



Added

I think I see what's happening.

Let $W$ be the average mass of an individual, $N$ be the number of individuals, and $B$ be their total biomass. Then of course,

$B=WN$

Let's start with:


$W$ is proportional to $N^{-\frac{3}{2}}$
$N$ is proportional to $N$ (duh). Let's rewrite that though, as:
$N$ is proportional to $N^1$


But that means:

$B=WN$ is proportional to $N^{-\frac{3}{2}} \cdot N^{1} =N^{-\frac{3}{2}+1} = N^{-\frac{1}{2}}$

Density increases with density (N). Weight per individual  decreases with the -3/2rd power (W). So their product, biomass decreases with the -3/2 + 1 = -1/2nd power  (B=WN).