Range expansions lead to distinctive patterns of genetic variation in populations, even in the absence of selection. These patterns and their genetic consequences have been well studied for populations advancing through successive short-ranged migration events. However, most populations harbor some degree of long-range dispersal, experiencing rare yet consequential migration events over arbitrarily long distances. Although dispersal is known to strongly affect spatial genetic structure during range expansions, the resulting patterns and their impact on neutral diversity remain poorly understood. Here, we systematically study the consequences of long-range dispersal on patterns of neutral variation during range expansion in a class of dispersal models which spans the extremes of local (effectively short-ranged) and global (effectively well-mixed) migration. We find that sufficiently long-ranged dispersal leaves behind a mosaic of monoallelic patches, whose number and size are highly sensitive to the distribution of dispersal distances. We develop a coarse-grained model which connects statistical features of these spatial patterns to the evolution of neutral diversity during the range expansion. We show that growth mechanisms that appear qualitatively similar can engender vastly different outcomes for diversity: Depending on the tail of the dispersal distance distribution, diversity can be either preserved (i.e., many variants survive) or lost (i.e., one variant dominates) at long times. Our results highlight the impact of spatial and migratory structure on genetic variation during processes as varied as range expansions, species invasions, epidemics, and the spread of beneficial mutations in established populations.

Up to 80% of the cost of vaccination programmes is due to the cold chain problem (that is, keeping vaccines cold). Inexpensive, biocompatible additives to slow down the degradation of virus particles would address the problem. Here we propose and characterize additives that, already at very low concentrations, improve the storage time of adenovirus type 5. Anionic gold nanoparticles (10^-8-10^-6 M) or polyethylene glycol (PEG, molecular weight ∼8,000 Da, 10^-7-10^-4 M) increase the half-life of a green fluorescent protein expressing adenovirus from ∼48 h to 21 days at 37 °C (from 7 to >30 days at room temperature). They replicate the known stabilizing effect of sucrose, but at several orders of magnitude lower concentrations. PEG and sucrose maintained immunogenicity in vivo for viruses stored for 10 days at 37 °C. To achieve rational design of viral-vaccine stabilizers, our approach is aided by simplified quantitative models based on a single rate-limiting step.