  In this work we study a non-local version of the Fisher-KPP equation,
\begin{equation*} \begin{cases} \frac{\partial u}{\partial
t}=\tfrac{1}{2}\Delta u +u (1- \phi \ast u), \quad t>0, \quad x\in \mathbb{R},
u(0,x)=u_0(x), \quad x\in \mathbb{R} \end{cases} \end{equation*} and its
relation to $\textit{branching Brownian motion with decay of mass}$ as
introduced by Addario-Berry and Penington (2017), i.e. a particle system
consisting of a standard branching Brownian motion (BBM) with a competitive
interaction between nearby particles. Particles in the BBM with decay of mass
have a position in $\mathbb{R}$ and a mass, branch at rate 1 into two daughter
particles of the same mass and position, and move independently as Brownian
motions. Particles lose mass at a rate proportional to the mass in a
neighbourhood around them (as measured by the function $\phi$).
  We obtain two types of results. First, we study the behaviour of solutions to
the partial differential equation above. We show that, under suitable
conditions on $\phi$ and $u_0$, the solutions converge to 1 behind the front
and are globally bounded, improving recent results of Hamel and Ryzhik
(arxiv:arXiv:1307.3001). Second, we show that the hydrodynamic limit of the BBM
with decay of mass is the solution of the non-local Fisher-KPP equation. We
then harness this to obtain several new results concerning the behaviour of the
particle system.
