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Rodriguez R.A.,Fundacion Canaria Rafael Clavijo | Delgado J.D.,Pablo De Olavide University | Herrera A.M.,Fundacion Canaria Rafael Clavijo | Navarro R.M.,University of Cordoba, Spain | And 2 more authors.
Ecological Modelling | Year: 2013

Species coexistence has been a fundamental issue to understand ecosystem functioning since the beginnings of ecology as a science. The search of a reliable and all-encompassing explanation for this issue has become a complex goal with several apparently opposing trends. On the other side, seemingly unconnected with species coexistence, an ecological state equation based on the inverse correlation between an indicator of dispersal that fits gamma distribution and species diversity has been recently developed. This article explores two factors, whose effects are inconspicuous in such an equation at the first sight, that are used to develop an alternative general theoretical background in order to provide a better understanding of species coexistence. Our main outcomes are: (i) the fit of dispersal and diversity values to gamma distribution is an important factor that promotes species coexistence mainly due to the right-skewed character of gamma distribution; (ii) the opposite correlation between species diversity and dispersal implies that any increase of diversity is equivalent to a route of "ecological cooling" whose maximum limit should be constrained by the influence of the third law of thermodynamics; this is in agreement with the well-known asymptotic trend of diversity values in space and time; (iii) there are plausible empirical and theoretical ways to apply physical principles to explain important ecological processes; (iv) the gap between theoretical and empirical ecology in those cases where species diversity is paradoxically high could be narrowed by a wave model of species coexistence based on the concurrency of local equilibrium states. In such a model, competitive exclusion has a limited but indispensable role in harmonious coexistence with functional redundancy. We analyze several literature references as well as ecological and evolutionary examples that support our approach, reinforcing the meaning equivalence between important physical and ecological principles. © 2013 Elsevier B.V.

Rodriguez R.A.,Independent Researcher | Herrera A.M.,The Womans Group | Riera R.,Institute Pesquisas | Santander J.,Parque Nacional Sistema Arrecifal Veracruzano | And 10 more authors.
Ecological Modelling | Year: 2015

Despite the well-known thermodynamic traits of ecosystem functioning, their description by means of conventional physics should be regarded as incomplete, even if we take into account the most recent advancements in this field. The analytical difficulties in this field have been especially complex to get a reliable modeling of species diversity per plot (Hp) by endowing this indicator with a fully clear theoretical meaning. This article contributes to resolve such difficulties starting from (a) the previous proposal of an ecological state equation, and (b) the preceding empirical finding of an ecological equivalent of Planck's constant at the evolutionary scale. So, in the first instance, this article proposes an equation for density distributions of Hp values (EDH) based on a simple transformation of the Maxwell-Boltzmann distribution for molecular velocity values (M-BDv). Our results indicate that the above-mentioned equation allows an appropriate fit between expected and observed distributions. Besides, the transformation from M-BDv to EDH establishes connections between species diversity and other indicators that are consistent with well-known ecological principles. This article, in the second instance, uses EDHs from a wide spectrum of surveys as an analytical framework to explore the nature and meaning of stationary trophic information waves (STIWs) whose stationary nature depends on the biomass-dispersal trade-off in function of Hp values (B-DTO-H) that characterizes the most of the explored surveys. B-DTO-H makes these surveys behave as ecological cavity resonators (ECR) by trapping functional oscillations that bounce back and forth between the two opposite edges of the ECR: from r-strategy (at low biomass and diversity, and high dispersal) to K-strategy, and vice versa. STIWs were obtained by using the spline-adjusted values from the arithmetical difference between standardized values of species richness (S) and evenness (J') in function of Hp values (i.e., a 2D scalar space Hp, S-J'). Twice the distance on the abscissas (2δHp) between successive extreme values on the ordinates (whatever a maximum or a minimum) along the above-mentioned spline adjustment was taken as the value of ecological wavelength (λe). λe was assessed in order to obtain the value of the ecological equivalent of Planck's constant (heec) at the intra-survey scale that was calculated as: heec=λe×me×Ie; where me: individual biomass, and Ie: an ad-hoc indicator of dispersal activity. Our main result is that the observed value of heec's mantissa is statistically equivalent to the mantissa of the physical Planck's constant (h=6.62606957E-34Js) in all of the discontinuous (i.e., with interspersed categories in which n=0) statistical density distributions of Hp values per survey. This means that heec=6.62606957EϕJenat/individual, where ϕ=-xi, . ., -3, -2, -1, 0,+1, +2, +3, . .,+xi depending on the type of taxocenosis explored. That is to say, heec indicates the minimum amount of energy exchange allowed between two individuals. The exploration of the analytical meaning of this result in the final sections of the article explains why quantum mechanics (QM) is a useful tool in order to explain several key questions in evolutionary biology and ecology, as for example: the physical limit of adaptive radiation; the balance between competitive exclusion and functional redundancy to promote species coexistence by avoiding the negative effects of competitive exclusion; the apparent holes in the fossil record; the progression of body size along a wide spectrum of taxa as a general evolutionary trend; the non-continuous nature of net energy flow at the ecosystem level; the way in which the energy level is stabilized under stationary ecological conditions; the reasons of the higher sensitivity of high diversity ecosystems under environmental impact despite their higher stability under natural conditions; the tangible expression of complex concept as ecological inertia and elasticity; as well as the increased risk from pushing the biosphere until a rupture limit because of the potential discrete behavior of ecological resilience in the large scale due to the quantum nature of ecosystem functioning. © 2015 Elsevier B.V.

Rodriguez R.A.,Independent Researcher | Herrera A.M.,The Womans Group | Santander J.,Parque Nacional Sistema Arrecifal Veracruzano | Miranda J.V.,Parque Nacional Sistema Arrecifal Veracruzano | And 10 more authors.
Ecological Modelling | Year: 2015

There has been a categorically unresolved crucial question in ecology and evolutionary theory for many decades; perhaps from the times of Charles Darwin himself: Is it possible, under natural conditions, that two species can perform a commonly shared ecological niche? There are two extreme conventional responses that have kept divided the scientific community in this regard for almost forty years: (a) No; that is to say, the well-known competitive exclusion principle (CEP). (b) Yes; that is to say, the well-known hypothesis of full functional redundancy (HFR). Obviously, the reliability of both responses depends on an underlying and even more essential requisite: that the ecological niche of a given species can be assessed with such accuracy as we could want in order to detect the degree in which it is shared between coexisting species. This article is the seventh in a continuous series of interconnected recent publications that promotes an alternative understanding of ecology and evolutionary biology which is in favor of strong and mutually fruitful analytical links between biology and physics. This article analyzes the statistical behavior of ecological niches by taking into account two indicators that are essential to perform the ecological niche of all species: species diversity per plot (Hp) and eco-kinetic energy (Ee) as a proxy for trophic energy in a scalar field Hp, Ee in which an oscillating performance of ecological niches is deployed. According to our results, in the same measurement in which the accuracy of Hp assessments increases (reduction of Hp's standard deviation: σHp) the accuracy of Ee assessment decreases (increment of σEe), and vice versa, in agreement with a pattern that is completely equivalent to that of the Heisenberg's uncertainty principle in quantum mechanics (i.e.: σHpσEe1/2heec/2π where heec: ecological equivalent of Planck's constant found in previous publications). As a result, the ecological niche is, even in principle in addition to in practice, indeterminable with enough exactness to arrive to a categorical response to the above-stated question. This means that CEP and HFR are simultaneously true and false in the same measure, because the only feasible option to keep the functional stability of ecosystems is a wave-like combination of both options: when species are pushed to a high degree of coexistence (increase of partition of the gradient) in regard to Hp values (a trend in favor of HFR), their degree of coexistence in regard to Ee values diminishes (decrease of partition of the Ee gradient, a trend in favor of CEP), and vice versa. The final sections of the article highlight the eco-evolutionary, biogeographical and socio-economic meaning of this result, by offering plausible alternative explanations to a wide spectrum of phenomena that appear to be only partially understood so far, e.g.: the contradictory results about the relationship between body size, species diversity and macroevolutionary rates; the general environmental scenario in favor of macroevolutionary leaps with a low probability to leave footprints in the fossil record; the unnecessary, although stimulant, influence of geographic isolation to promote evolutionary changes; the island rule; and the general meaning of the interaction between nature and society. © 2015 Elsevier B.V.

Rodriguez R.A.,Apartment A | Herrera A.M.,Apartment A | Delgado J.D.,Pablo De Olavide University | Quiros T.,Parque Nacional Los Caimanes | And 9 more authors.
Ecological Modelling | Year: 2015

Conventional thermodynamics and statistical mechanics deal with the study of physical systems under equilibrium conditions (EC). Internal EC at a temperature that differs from the environment temperature are sustained, in general, by some type of artificial boundaries imposed with research aims or with quotidian utility goals in many kind of domestic appliances; the typical example of academic lab is a closed system immersed in a thermal bath which keeps the temperature constant. However, the ecosystem is a far-from-EC open system. Therefore, conventional thermodynamics and statistical mechanics tend to be orthodoxly regarded as limited to explain the ecosystem functioning since, at the first glance; there seem to be several essential functional differences between it and the previously-mentioned kind of physical systems. This viewpoint averse to conventional physics is paradoxical in regard to the current ecological paradigm given the fully thermodynamic foundation of ecosystem ecology. However, additional evidence in favor of the usefulness of conventional physics to describe the ecosystem functioning have recently been published, pointing out to the possibility that the analytical approach to ecology based on our undergraduate knowledge of physics, unfortunately, could have been hastily neglected before producing its most valuable results. This paper, fully based on the above-mentioned evidence, performs an unavoidable additional step in order to complete such a proposal by showing that the Boltzmann distribution of molecular energy values can be simply and successfully adapted to model the distribution of values of a proxy for trophic energy across an increasing gradient of energy levels, in a very similar fashion to that of a standard trophic pyramid. Starting from this result and by using a balanced combination between plausible theoretical considerations and abundant empirical data, we analyze why this approach is in agreement with well-known ecological principles, at the same time that we explore the general empirical advantages and aftermaths derived from this suggestion. Finally, the article explores the usefulness of the thermo-statistical modeling of eco-kinetic energy per plot to understand those essential physical factors that: promote biological evolution, facilitate species coexistence, can explain the holes in the fossil record, and enhance our current viewpoint about the ecological meaning of entropy. In summary, this article provides simply understandable additional information that indicates, despite its far-from-EC nature, any natural ecosystem is not far away from the most orthodox principles of conventional physics. © 2014 Elsevier B.V.

Rodriguez R.A.,Lucy Avenue | Herrera A.M.,The Womans Group | Santander J.,Parque Nacional Sistema Arrecifal Veracruzano | Miranda J.V.,Parque Nacional Sistema Arrecifal Veracruzano | And 4 more authors.
Ecological Modelling | Year: 2016

How complex systems are able to self-organize away from equilibrium and maintain their internal functional gradients over time, by adapting themselves and changing their own environment? This is one of the most interesting questions for contemporary ecology because of its potential usefulness to assess the ecological health of our natural environment by means of ecological monitoring. This article shows how a replacement and complementation of variables, that is very simple from the mathematical point of view, can be useful to transform the state equation previously developed to describe stationary ecological conditions into a state equation for non-stationary ecological conditions. The method applied was (a) empirically tested starting from field data collected from five surveys belonging to four different kinds of taxocenosis and (b) explained in a very brief and didactic way that can be easily understandable to everybody with a standard undergraduate training in ecological studies. The main result of this article is a simple mathematical equation that can be useful to perform an instantaneous assessment of the state and trend of ecosystem development in the short run starting from a single survey, that is to say, without the availability of long time series of data that allows the conventional studies of comparative ecology in order to assess the course of ecological succession. This proposal adds an innovative diagnostic tool empirically useful for ecological monitoring. © 2015 Elsevier B.V.

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