Roots of diversity relations

Statistical Physics of Evolving Systems

Evolution is customarily perceived as a biological process. However, when formulated in terms of physics, evolution is understood to entail everything. Based on the axiom of everything comprising quanta of actions (e.g., quanta of light), statistical physics describes any system evolving toward thermodynamic balance with its surroundings systems. Fluxes of quanta naturally select those processes leveling out differences in energy as soon as possible. This least-time maxim results in ubiquitous patterns (i.e., power laws, approximating sigmoidal cumulative curves of skewed distributions, oscillations, and even the regularity of chaos). While the equation of evolution can be written exactly, it cannot be solved exactly. Variables are inseparable since motions consume driving forces that affect motions (and so on). Thus, evolution is inherently a non-deterministic process. Yet, the future is not all arbitrary but teleological, the final cause being the least-time free energy consumption itself. Eventually, trajectories are computable when the system has evolved into a state of balance where free energy is used up altogether.

Epidemic as a natural process

Mathematical epidemiology is a well-recognized discipline to model infectious diseases. It also provides guidance for public health officials to limit outbreaks. Nevertheless, epidemics take societies by surprise every now and then, for example, when the Ebola virus epidemic raged seemingly unrestrained in Western Africa. We provide insight to this capricious character of nature by describing the epidemic as a natural process, i.e., a phenomenon governed by thermodynamics. Our account, based on statistical mechanics of open systems, clarifies that it is impossible to predict accurately epidemic courses because everything depends on everything else. Nonetheless, the thermodynamic theory yields a comprehensive and analytical view of the epidemic. The tenet subsumes various processes in a scale-free manner from the molecular to the societal levels. The holistic view accentuates overarching procedures in arresting and eradicating epidemics.

A generalized approach to the modeling of the species-area relationship

This paper proposes a statistical generalized species-area model (GSAM) to represent various patterns of species-area relationship (SAR), which is one of the fundamental patterns in ecology. The approach enables the generalization of many preliminary models, as power-curve model, which is commonly used to mathematically describe the SAR. The GSAM is applied to simulated data set of species diversity in areas of different sizes and a real-world data of insects of Hymenoptera order has been modeled. We show that the GSAM enables the identification of the best statistical model and estimates the number of species according to the area.

Estimation of species extinction: what are the consequences when total species number is unknown?

The species-area relationship (SAR) is known to overestimate species extinction but the underlying mechanisms remain unclear to a great extent. Here, I show that when total species number in an area is unknown, the SAR model exaggerates the estimation of species extinction. It is proposed that to accurately estimate species extinction caused by habitat destruction, one of the principal prerequisites is to accurately total the species numbers presented in the whole study area. One can better evaluate and compare alternative theoretical SAR models on the accurate estimation of species loss only when the exact total species number for the whole area is clear. This presents an opportunity for ecologists to simulate more research on accurately estimating Whittaker's gamma diversity for the purpose of better predicting species loss.

The significance of sex

Sexual and asexual modes of proliferation are associated with advantages and disadvantages, yet a profound percept that would account for both ways of reproduction is missing. On the basis of the 2nd law of thermodynamics we find that both sexual and asexual reproduction can be regarded as a means to consume free energy in least time. Parthenogenesis is a fast way to consume a rich repository of free energy, e.g., an ample stock of food with a large number of individuals, whereas sexual reproduction is a fast way to consume diverse and dispersed resources with a large variety of individuals. Most organisms have adapted to their surroundings accordingly and some organisms switch from one mode of reproduction to the other depending on the amount and dispersion of free-energy sources. We conclude that the least-time free energy consumption in respective surroundings, as the general criterion of natural selection, determines also sexual and asexual modes of reproduction.

Ecological succession as an energy dispersal process

Ecological succession is described by the 2nd law of thermodynamics. According to the universal law of the maximal energy dispersal, an ecosystem evolves toward a stationary state in its surroundings by consuming free energy via diverse mechanisms. Species are the mechanisms that conduct energy down along gradients between repositories of energy which consist of populations at various thermodynamic levels. The salient characteristics of succession, growing biomass production, increasing species richness and shifting distributions of species are found as consequences of the universal quest to diminish energy density differences in least time. The analysis reveals that during succession the ecosystem's energy transduction network, i.e., the food web organizes increasingly more effective in the free energy reduction by acquiring new, more effective and abandoning old, less effective species of energy transduction. The number of species does not necessarily peak at the climax state that corresponds to the maximum-entropy partition of species maximizing consumption of free energy. According to the theory of evolution by natural selection founded on statistical physics of open systems, ecological succession is one among many other evolutionary processes.

In the light of time

The concept of time is examined using the second law of thermodynamics that was recently formulated as an equation of motion. According to the statistical notion of increasing entropy, flows of energy diminish differences between energy densities that form space. The flow of energy is identified with the flow of time. The non-Euclidean energy landscape, i.e. the curved space–time, is in evolution when energy is flowing down along gradients and levelling the density differences. The flows along the steepest descents, i.e. geodesics are obtained from the principle of least action for mechanics, electrodynamics and quantum mechanics. The arrow of time, associated with the expansion of the Universe, identifies with grand dispersal of energy when high-energy densities transform by various mechanisms to lower densities in energy and eventually to ever-diluting electromagnetic radiation. Likewise, time in a quantum system takes an increment forwards in the detection-associated dissipative transformation when the stationary-state system begins to evolve pictured as the wave function collapse. The energy dispersal is understood to underlie causality so that an energy gradient is a cause and the resulting energy flow is an effect. The account on causality by the concepts of physics does not imply determinism; on the contrary, evolution of space–time as a causal chain of events is non-deterministic.

Natural hierarchy emerges from energy dispersal

Hierarchical organization of 'systems within systems' is an apparent characteristic of nature. For many biotic and abiotic systems it is known how the nested structural and functional order builds up, yet the general principle why matter evolves to hierarchies has remained unfamiliar to many. We clarify that increasingly larger integrated systems result from the quest to decrease free energy according to the 2nd law of thermodynamics. The argumentation is based on the recently derived equation of motion for natural processes. Hierarchically organized energy transduction machinery emerges naturally when it provides increased rates of energy dispersal. Likewise, a hierarchical system will dismantle into its constituents when they as independent systems will provide higher rates of entropy increase. Since energy flows via interactions, decreasing strengths of interactions over increasingly larges lengths scales mark natural boundaries for nested integrated systems.