Analytic solution of Hubbell's model of local community dynamics

Alan McKane; David Alonso; Ricard Sole

Home/Archive/arXiv

arXiv · physics/0305022

Analytic solution of Hubbell's model of local community dynamics

Alan McKane·David Alonso·Ricard Sole

View original source ↗Read source document ↗Export metadata ↓

Abstract

Recent theoretical approaches to community structure and dynamics reveal that many large-scale features of community structure (such as species-rank distributions and species-area relations) can be explained by a so-called neutral model. Using this approach, species are taken to be equivalent and trophic relations are not taken into account explicitly. Here we provide a general analytic solution to the local community model of Hubbell's neutral theory of biodiversity by recasting it as an urn model i.e.a Markovian description of states and their transitions. Both stationary and time-dependent distributions are analysed. The stationary distribution -- also called the zero-sum multinomial -- is given in closed form. An approximate form for the time-dependence is obtained by using an expansion of the master equation. The temporal evolution of the approximate distribution is shown to be a good representation for the true temporal evolution for a large range of parameter values.

Explore related subjects

physics.bio-ph cond-mat.stat-mech q-bio.PE

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Alan McKane, David Alonso, Ricard Sole. 2003-05-07. Analytic solution of Hubbell's model of local community dynamics. https://arxiv.org/abs/physics/0305022

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Spontaneous polarization for protrusion-driven cell crawling

We propose a minimal one-dimensional continuum model for the spontaneous initiation of protrusion-driven cell crawling on a rigid substrate. The cell cytoskeleton is represented as a viscous actin meshwork that turns over in the bulk and polymerizes at two moving cell edges. Symmetry breaking arises from the feedback between cell motion, an external chemical regulator of actin nucleation, and actin polymerization at the cell fronts. When the cell moves, the regulator becomes polarized around the moving boundaries, thereby imposing different actin nucleation densities at the two edges. This generates unequal protrusive rates, which in turn reinforce motion and sustain the chemical polarization. Above a critical protrusive activity, the static symmetric state loses stability and the system undergoes a bifurcation toward a motile polarized state. Depending on how the external cue controls actin nucleation, the transition can be either supercritical or subcritical, leading in the latter case to coexistence between static and motile states. Using parameter values appropriate for keratocyte cells, the model predicts crawling speeds of the correct order of magnitude and actin-density profiles that are qualitatively similar to experimental observations, including asymmetric edge-localized density peaks. These results identify a generic mechanism by which external biochemical regulation of actin nucleation can trigger spontaneous motility along a one-dimensional track without requiring molecular motors, specific adhesion dynamics, deformable substrates, or pre-existing polarity.

physics.bio-ph↗

arXiv2026

A Transient-Network Model of Condensate Aging and Morphology Transition in Phase Separation

Biomolecular condensates can undergo striking changes, such as transitioning from a liquid-like to a gel- or a solid-like aggregate due to changes in molecular interactions in response to changes in the biochemical environment. The question of how modified molecular interactions lead to such a transition in the material properties and spatial organization of condensates has not yet been elucidated. To address this question, we represent the biochemical environment as a triphasic mixture comprising a liquid-like protein-rich phase, a network-like protein-rich phase, and solvent. Owing to a change in the biochemical environment, protein molecules can reversibly switch between two conformational states. In a switched conformational state, the cross-linking domains of molecules are exposed which promote transient network formation in phase separated states. We develop a transient-network model and a continuum framework that couples phase separation, molecular switching, and dynamic cross-linking to predict condensate morphology and mechanics. The transient-network model predicts that a non-aging network behaves like a Maxwell fluid. When a network slowly ages via stabilization of cross-links, it shows Maxwell-like behavior and waiting time-dependent relaxation. However, a strongly aged network shows elastic recoil like characteristic of a Kelvin-Voigt solid. Our coupled continuum model demonstrates that the interplay of molecular switching and dynamic cross-linking in network formation shapes the spatial organization of condensate phases. In summary, this work demonstrates a mechanistic route explaining how conformational switching and molecular cross-linking regulate material properties and morphology of condensates.

physics.bio-ph↗

arXiv2026

Unraveling Primary Energy Conversion Dynamics in Intact Cells of Gemmatimonas groenlandica

Photosynthetic bacteria have evolved specialized light-harvesting structures to efficiently capture sunlight. Here, we investigate the ultrafast dynamics in intact cells of Gemmatimonas groenlandica, featuring unique double-ring LHh-LH1 photosynthetic complexes containing bacteriochlorophyll a. Two-dimensional electronic spectroscopy with lock-in detection allows us to directly observe primary energy-conversion processes, from excitation-energy transfer within the antenna system to the formation of a charge-separated state in the reaction center, taking place on 50 ps time scale. Through comparison with Rhodospirillum rubrum, which lacks the outer antenna ring, we use a combination of global analysis and nodal/center line slope analyses to resolve LHh-LH1 excitation energy transfer which occurs on a ~1-2 ps timescale in Gemmatimonas groenlandica.

physics.bio-ph↗