Information Flow in Spatially Structured Populations Open Access

Smith, Tyler (Summer 2021)

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Spatial structure has a strong effect on biological systems at many scales, with information flow being limited by the rate at which individual constituents of the system move through space.

At the population scale, limited dispersal of individuals and the accumulation of mutations results in isolation by distance, in which individuals found further apart tend to be less related, as measured by the proportion of their genomes shared identical-by-descent. Classic models assume dispersal distances are drawn from a thin-tailed distribution and predict that relatedness should decrease exponentially as the separation between pairs becomes large. We study the effect of heavy-tailed dispersal on patterns of isolation by distance and find that a power-law dispersal kernel leads to power-law decay of relatedness at large distances and either power-law or logarithmic decay at short distances depending on the exact form of the kernel. The model is then used to solve the inverse problem of inferring dispersal from empirical isolation by distance curves.

At the cellular level, limited exchange and degradation of messenger molecules between cells bound the precision of gradient sensing. Precision increases with the length of a cell collective in the gradient direction up to this bound and then saturates. Intuition from studies of concentration sensing suggests that precision should also increase with detector length in the direction transverse to the gradient, since then spatial averaging should reduce the noise. However, here we show that, unlike for concentration sensing, the precision of gradient sensing decreases with transverse length for the simplest gradient sensing model, local excitation–global inhibition. The reason is that gradient sensing ultimately relies on a subtraction of measured concentration values. While spatial averaging indeed reduces the noise in these measurements, it also reduces the covariance between the measurements, which results in the net decrease in precision. We demonstrate how a recently introduced gradient sensing mechanism, regional excitation–global inhibition, overcomes this effect and recovers the benefit of transverse averaging.

Work on an unrelated problem in quantum mechanics is also presented, and a self-contained introduction is given in the relevant chapter.

Table of Contents

Introduction 1

Role of Spatial Averaging in Multicellular Gradient Sensing 9

Isolation by Distance in Population with Power-law Dispersal 29

Inferring Power-law Dispersal from Patterns of Isolation by Distance 71

Quantum Geometry and Semiclassical Electron Dynamics 106

Summary 118

Alternative Derivations of the Probability of Identity by Descent 120

Perturbative Corrections and Geometric Calculations 123

Bibliography 129

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