Laws in Darwinian Evolutionary Theory

P Ao

doi:10.1016/j.plrev.2005.03.002

Home/Archive/arXiv

arXiv · q-bio/0605020

Laws in Darwinian Evolutionary Theory

P Ao

View original source ↗Read source document ↗Export metadata ↓

Abstract

In the present article the recent works to formulate laws in Darwinian evolutionary dynamics are discussed. Although there is a strong consensus that general laws in biology may exist, opinions opposing such suggestion are abundant. Based on recent progress in both mathematics and biology, another attempt to address this issue is made in the present article. Specifically, three laws which form a mathematical framework for the evolutionary dynamics in biology are postulated. The second law is most quantitative and is explicitly expressed in the unique form of a stochastic differential equation. Salient features of Darwinian evolutionary dynamics are captured by this law: the probabilistic nature of evolution, ascendancy, and the adaptive landscape. Four dynamical elements are introduced in this formulation: the ascendant matrix, the transverse matrix, the Wright evolutionary potential, and the stochastic drive. The first law may be regarded as a special case of the second law. It gives the reference point to discuss the evolutionary dynamics. The third law describes the relationship between the focused level of description to its lower and higher ones, and defines the dichotomy of deterministic and stochastic drives. It is an acknowledgement of the hierarchical structure in biology. A new interpretation of Fisher's fundamental theorem of natural selection is provided in terms of the F-Theorem. The proposed laws are based on continuous representation in both time and population. Their generic nature is demonstrated through their equivalence to classical formulations. The present three laws appear to provide a coherent framework for the further development of the subject.

Explore related subjects

q-bio.PE cond-mat.stat-mech cs.NE math.OC nlin.AO physics.bio-ph q-bio.QM

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

P Ao. 2006-05-14. Laws in Darwinian Evolutionary Theory. https://doi.org/10.1016/j.plrev.2005.03.002

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

KEEP EXPLORING

Related papers

arXiv2026

Competition drives excessive recruitment in collective search

Groups that search collectively often exploit what they find by recruiting: one member directs others to a site it has found. Recruitment raises the number of members foraging at a known site, but the return per forager may fall as that number grows, so there is an intermediate optimal recruitment rate. In addition, a site may be used by more than one group. Here we analyze a model of two groups that forage from a single site whose return declines with the total number of foragers present. The two groups interact only through this shared return. The long-run outcome is either coexistence at the foraging site or monopoly by one group, and we analyze the boundary between these two outcomes. A group's best response to its rival is not monotone: it increases its own recruitment rate with the rival's recruitment rate in an attempt to preserve a monopoly, and then its recruitment rate drops discontinuously when it is no longer optimal to preserve a monopoly. We analyze how model parameters govern this shift: a group relinquishes monopoly when the site saturates at few foragers and when the rival group is small. When the two groups have comparable size there are multiple Nash equilibria, so either group may end up with the larger share. And when two equally matched groups compete, both recruit above the rate that maximizes their common return, so that each individual ends with less than it would in a single undivided group of the same total size.

q-bio.PE↗

arXiv2026

Selection Rules for Species Coexistence in a Hierarchical May-Leonard Model

One of the central challenges in evolutionary dynamics is understanding why some species combinations persist while others disappear. Although cyclic-interaction models have provided fundamental insights into biodiversity maintenance, much less is known about how hierarchical competitive interactions shape long-term community organization. Here, we investigate a hierarchical extension of the May-Leonard model, in which species interact through a directed predation chain while undergoing reproduction and mortality. Combining mean-field analysis with Monte Carlo simulations, we show that the fully coexisting state is generically unstable, causing the dynamics to evolve toward lower-dimensional coexistence states. The simulations further reveal stochastic extinctions dominating small populations with the dynamics progressively approaching the mean-field predictions as the system size increases. Rather than permitting arbitrary species combinations, the hierarchical-interaction structure dynamically constrains coexistence by selecting only specific subsets of species for long-term persistence. We show that these admissible coexistence states have a natural graph-theoretic interpretation as independent sets in the hierarchical interaction network, thereby providing general constraints on coexistence in hierarchical communities. Together, these results establish a theoretical framework linking hierarchical interactions, dynamical selection, graph topology, and biodiversity organization, extending the classical May-Leonard model beyond cyclic competition.

q-bio.PE↗

arXiv2026

Persistence of n-Species Lotka-Volterra Models with Periodic Pulses

Periodic impulsive interventions arise naturally in the management of biological populations, including chemotherapy, pesticide application, and infectious-disease treatment. We develop general conditions for permanence in n-species population models subject to periodic multiplicative pulse disturbances. Our main result provides a sufficient condition for permanence in terms of weighted long-term growth rates on a Morse decomposition of the extinction set, explicitly separating the contributions of continuous population dynamics from those of the periodic pulse. To establish this result, we transform the impulsive system into an associated autonomous continuous-time dynamical system and use this correspondence to extend classical permanence theory to periodically pulsed models. We further show that the same conditions imply robust permanence under sufficiently small perturbations to the continuous dynamics, pulse period, and pulse effects. We illustrate the framework with two Lotka-Volterra models motivated by biological control: competition between chemotherapy-sensitive and chemotherapy-resistant cancer cells, and integrated control of an agricultural pest using pesticides and parasitoids. These examples demonstrate how intervention frequency and intensity interact with underlying ecological interactions to determine whether populations coexist or are excluded. Our results provide a general framework for analyzing persistence in ecological systems subject to repeated discrete disturbances.

q-bio.PE↗