Froese, R. | Search bioRxiv

bioRxiv2026

Evidence for the 1/e-law predicting optimal timing of reproduction across taxa

The timing of peak reproductive effort is a central problem in life-history theory, yet a simple first-principles target for that timing relative to lifespan has been missing. We propose that generation time is an optimal stopping time. Under the 1/e-law of best choice, the unique strategy that guarantees the highest minimum probability of selecting a superior option is to wait until a cumulative fraction 1/e of opportunities has passed. When reproductive opportunities arrive in an approximately time-homogeneous way over adult life, that threshold is 1/e (about 37%) of maximum lifespan. This fraction is confirmed by standard population dynamics for indeterminate growers, combining von Bertalanffy growth with constant mortality. A compilation of published reproductive schedules in plants, animals, and humans illustrates the predicted alignment across taxa and absolute timescales. The 1/e-law thus supplies an organizing quantitative account of a core life-history schedule.

evolutionary biology↗

bioRxiv2022

The thermodynamics of reproduction constrain species ranking dynamics and diversity

Iniguez, Pineda, Gershenson, and Barabasi proposed that complex systems can be simplified and analyzed in terms of the dynamics of ordered lists. For social, economic, and infrastructural systems, they succeeded in modeling the dynamics of ranking with two mechanisms, namely displacement (i.e., shuffling of ranks among existing elements) and replacement of elements by new elements. A general pattern is that, for open systems with influx and outflux of elements, e.g., a list with a subset of elements, only the top of the list is stable; for closed systems, top and bottom are stable. This model was fitted to empirical data, resulting in a universal curve in which displacement and replacement parameters are inversely related, which implies that a single parameter could regulate both. Our aim is twofold: First, we demonstrate that the pattern generalizes to ranking of biological species, based on FishBase records of fish taxonomy and life history traits. Second, we propose a candidate for a unified mechanism, based on a recent model of the thermodynamics of self-replication.

evolutionary biology↗

bioRxiv2019

Mechanical constraints influence microtubule orientation in plant cells

In growing plant cells, parallel ordering of microtubules (MTs) along the inner surface of the cell membrane influences the direction of cell expansion and thereby plant morphology. For correct expansion of organs that primarily grow by elongating, such as roots and stems, MTs must bend in the high-curvature direction along the cylindrically shaped cell membrane in order to form the required circumferential arrays. Previous studies, which have recapitulated the self-organization of these arrays, ignored MT mechanics and assumed MTs follow geodesics of the cell surface. Here, we show, through analysis of a derived Euler-Lagrange equation, that an elastic MT constrained to a cylindrical surface will deflect away from geodesics and toward low curvature directions to minimize bending energy. This occurs when the curvature of the cell surface is relatively high for a given anchor density. In the limit of infinite anchor density, MTs always follow geodesics. We compare our analytical predictions to measured curvatures and anchor densities and find that the regime in which cells are forming these cortical arrays straddles the region of parameter space in which arrays must form under the antagonistic influence of this mechanically induced deflection. Although this introduces a potential obstacle to forming circumferentially orientated arrays that needs to be accounted for in the models, it also raises the question of whether plants use this mechanical phenomenon to regulate array orientation. The model also constitutes an elegant generalization of the classical Euler-bucking instability along with an intrinsic unfolding of the associated pitchfork bifurcation.\n\nSIGNIFICANCE STATEMENTThe cortical microtubule array in plant cells is a dynamic structure whose organization influences cell function, growth, and plant morphology. During cell growth, the array must be highly ordered and perpendicular to the axis of expansion. In other instances, it can be disordered or axially oriented. Experimental and modelling studies have outlined the importance of various microtubule-microtubule interactions in the ordering and orienting process. We explore the influence of cell shape on the bending of microtubules that has been largely ignored to date. We find that cell shape can induce microtubule bending that steers them away from high-curvature directions. This bending force can act as an obstacle to proposed mechanisms for array organization and also as a mechanism for regulating reorientation of the array.

cell biology↗