We ask the question "when will natural selection on a gene in a spatially structured population cause a detectable trace in the patterns of genetic variation observed in the contemporary population?". We focus on the situation in which 'neighbourhood size', that is the effective local population density, is small. The genealogy relating individuals in a sample from the population is embedded in a spatial version of the ancestral selection graph and through applying a diffusive scaling to this object we show that whereas in dimensions at least three, selection is barely impeded by the spatial structure, in the most relevant dimension, d = 2, selection must be stronger (by a factor of log(1/µ) where µ is the neutral mutation rate) if we are to have a chance of detecting it. The case d = 1 was handled in Etheridge et al. (2015).The mathematical interest is that although the system of branching and coalescing lineages that forms the ancestral selection graph converges to a branching Brownian motion, this reflects a delicate balance of a branching rate that grows to infinity and the instant annullation of almost all branches through coalescence caused by the strong local competition in the population.

We obtain the Brownian net of Sun and Swart (2008) as the scaling limit of the paths traced out by a system of continuous (one-dimensional) space and time branching and coalescing random walks. This demonstrates a certain universality of the net, which we have not seen explored elsewhere. The walks themselves arise in a natural way as the ancestral lineages relating individuals in a sample from a biological population evolving according to the spatial Lambda-Fleming-Viot process. Our scaling reveals the effect, in dimension one, of spatial structure on the spread of a selectively advantageous gene through such a population.A construction of an appropriate state space for x → w t (x) can be found in Véber and Wakolbinger (2013). Using the identificationthis state space is in one-to-one correspondence with the space M λ of measures on R×{a, A} with 'spatial marginal' Lebesgue measure, which we endow with the topology of vague convergence. By a slight abuse of notation, we also denote the state space of the process (w t ) t∈R by M λ .Definition 2.1 (One-dimensional SΛFV with selection (SΛFVS)) Fix R ∈ (0, ∞) and υ ∈ (0, 1] and let µ be a finite measure on (0, R]. Further, let Π be a Poisson point process on R × R × (0, ∞) with intensity measure dx ⊗ dt ⊗ µ(dr).(2.1)The one-dimensional spatial Λ-Fleming-Viot process with selection (SΛFVS) driven by (2.1) is the M λ -valued process (w t ) t∈R with dynamics given as follows.If (x, t, r) ∈ Π, a reproduction event occurs at time t within the closed interval [x − r, x + r]. With probability 1 − s the event (x, t, r) is neutral, in which case:

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Knowledge of the spatial organization of economic activity within a city is a key to policy concerns. However, in developing cities with high levels of informality, this information is often unavailable. Recent progress in machine learning together with the availability of street imagery offers an affordable and easily automated solution. Here, we propose an algorithm that can detect what we call visible establishments using street view imagery. By using Medellín, Colombia as a case study, we illustrate how this approach can be used to uncover previously unseen economic activity. By applying spatial analysis to our dataset, we detect a polycentric structure with five distinct clusters located in both the established centre and peripheral areas. Comparing the density of visible establishments with that of registered firms, we infer that informal activity concentrates in poor but densely populated areas. Our findings highlight the large gap between what is captured in official data and the reality on the ground.