Biological electron transport is classically thought to occur over nanometre distances, yet recent studies suggest that electrical currents can run along centimetre-long cable bacteria. The phenomenon remains elusive, however, as currents have not been directly measured, nor have the conductive structures been identified. Here we demonstrate that cable bacteria conduct electrons over centimetre distances via highly conductive fibres embedded in the cell envelope. Direct electrode measurements reveal nanoampere currents in intact filaments up to 10.1 mm long (>2000 adjacent cells). A network of parallel periplasmic fibres displays a high conductivity (up to 79 S cm−1), explaining currents measured through intact filaments. Conductance rapidly declines upon exposure to air, but remains stable under vacuum, demonstrating that charge transfer is electronic rather than ionic. Our finding of a biological structure that efficiently guides electrical currents over long distances greatly expands the paradigm of biological charge transport and could enable new bio-electronic applications.

Adaptive radiation of a lineage into a range of organisms with different niches underpins the evolution of life's diversity. Although the role of the environment in shaping adaptive radiation is well established, theory predicts that the evolvability and niche of the founding ancestor are also of importance. Direct demonstration of a causal link requires resolving the independent effects of these additional factors. Here, we accomplish this using experimental bacterial populations and demonstrate how the dynamics of adaptive radiation are constrained by the niche of the founder. We manipulated the propensity of the founder to undergo adaptive radiation and resolved the underlying causal changes in both its evolvability and niche. Evolvability did not change, but the propensity for adaptive radiation was altered by changes in the position and breadth of the niche of the founder. These observations provide direct empirical evidence for a link between the niche of organisms and their propensity for adaptive radiation. This general mechanism may have rendered the evolutionary dynamics of extant adaptive radiations dependent on chance events that determined their founding ancestors. niche evolution | ecological opportunity | biodiversity

For the following class of boundary value problems: where p > 0 and E are real parameters and I&( < E O , E O small enough, it can beshown that when f fulfills certain conditions, a unique 2~-time-periodic solution u(t, z ; c ) = u(t + 2*, 2 ; E ) exists. It is shown that this 2~p e r i o d i c solution u ( t , 2 ; E ) is analytic with respect to E for (61 < EO. This result will be used to justify a formal perturbation method for the construction of approximations to the time periodic solution. Integral expressions for the terms in the series representation d u i ( t , 2 ) for the time-periodic solution are derived with this perturbation method. As the time-periodic solution is now known to be analytic the series representation converges with anon zero radius of convergence. This series can be truncated to obtain approximations to the time periodic solution of O(cN+'). In a number of practical applications the integral expressions for the terms in the series representation for the time periodic solution can be evaluated by means of Fourier series. As the computation of the coefficients in these Fourier series is in general rather complicated these Fourier series are also truncated. In this way formal approximations can be obtained, formal in the sense that every u i ( t , z ) , i = 1,2, ..., N of the truncated series zz0 &ui(t, z ) is now represented by truncated Fourier-series. A Maple Computer Algebra program is given in the appendix to compute these formal approximations for the time-periodic solution of O(E**+'), where E' = E / E O when the first term uo has already been calculated or approximated. This program may be used to find an estimate for the radius of convergence for the series expansion in 6. As an illustration explicit examples are presented.

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