scholarly journals Does deterministic coexistence theory matter in a finite world?

2018 ◽  
Author(s):  
Sebastian J. Schreiber ◽  
Jonathan M. Levine ◽  
Oscar Godoy ◽  
Nathan J.B. Kraft ◽  
Simon P. Hart
Keyword(s):  
Growth Rates ◽  
Species Coexistence ◽  
Deterministic Model ◽  
Empirical Studies ◽  
Finite Size ◽  
Niche Overlap ◽  
Demographic Stochasticity ◽  
Deterministic Models ◽  
Deterministic Theory ◽  
Population Sizes

AbstractContemporary studies of species coexistence are underpinned by deterministic models that assume that competing species have continuous (i.e. non-integer) densities, live in infinitely large landscapes, and coexist over infinite time horizons. By contrast, in nature species are composed of discrete individuals subject to demographic stochasticity, and occur in habitats of finite size where extinctions occur in finite time. One important consequence of these discrepancies is that metrics of species coexistence derived from deterministic theory may be unreliable predictors of the duration of species coexistence in nature. These coexistence metrics include invasion growth rates and niche and competitive differences, which are now commonly applied in theoretical and empirical studies of species coexistence. Here we test the efficacy of deterministic coexistence metrics on the duration of species coexistence in a finite world. We introduce new theoretical and computational methods to estimate coexistence times in a stochastic counterpart of a classic deterministic model of competition. Importantly, we parameterized this model using experimental field data for 90 pairwise combinations of 18 species of annual plants, allowing us to derive biologically-informed estimates of coexistence times for a natural system. Strikingly, we find that for species expected to deterministically coexist, habitat sizes containing only tens of individuals have predicted coexistence times of greater than 1, 000 years. We also find that invasion growth rates explain 60% of the variation in intrinsic coexistence times, reinforcing their general usefulness in studies of coexistence. However, only by integrating information on both invasion growth rates and species’ equilibrium population sizes could most (> 99%) of the variation in species coexistence times be explained. Moreover, because of a complex relationship between niche overlap/competitive differences and equilibrium population sizes, increasing niche overlap and increasing competitive differences did not always result in decreasing coexistence times as deterministic theory would predict. Nevertheless, our results tend to support the informed use of deterministic theory for understanding the duration of species coexistence, while highlighting the need to incorporate information on species’ equilibrium population sizes in addition to invasion growth rates.

scholarly journals Stochastic competitive exclusion leads to a cascade of species extinctions

2016 ◽  
Author(s):  
José A Capitán ◽  
Sara Cuenda ◽  
David Alonso
Keyword(s):  
Community Ecology ◽  
Competitive Exclusion ◽  
Deterministic Model ◽  
Niche Partitioning ◽  
Environmental Stochasticity ◽  
Exclusion Principle ◽  
Limiting Similarity ◽  
Demographic Stochasticity ◽  
Deterministic Models ◽  
Analytical Approximations

AbstractCommunity ecology has traditionally relied on the competitive exclusion principle, a piece of common wisdom in conceptual frameworks developed to describe species assemblages. Key concepts in community ecology, such as limiting similarity and niche partitioning, are based on competitive exclusion. However, this classical paradigm in ecology relies on implications derived from simple, deterministic models. Here we show how the predictions of a symmetric, deterministic model about the way extinctions proceed can be utterly different from the results derived from the same model when ecological drift (demographic stochasticity) is explicitly considered. Using analytical approximations to the steady-state conditional probabilities for assemblages with two and three species, we demonstrate that stochastic competitive exclusion leads to a cascade of extinctions, whereas the symmetric, deterministic model predicts a multiple collapse of species. To test the robustness of our results, we have studied the effect of environmental stochasticity and relaxed the species symmetry assumption. Our conclusions highlight the crucial role of stochasticity when deriving reliable theoretical predictions for species community assembly.

Dietary overlap and food resource partitioning among fish species of a tropical estuary in Northeastern Brazil

Gaia Scientia ◽  
2016 ◽  
Vol 10 (4) ◽  
pp. 86-95 ◽  
Author(s):  
Adna Ferreira da Silva Garcia ◽  
Ana Lúcia Vendel
Keyword(s):  
Resource Partitioning ◽  
Species Coexistence ◽  
Food Resource ◽  
River Estuary ◽  
Niche Overlap ◽  
Northeastern Brazil ◽  
Dietary Overlap ◽  
Feeding Niche ◽  
Tropical Environments ◽  
Food Resource Partitioning

The current work investigates dietary overlap and food partitioning among nine abundant carnivorous fishes caught in the shallow waters of the Paraíba do Norte river estuary, Paraíba State, Brazil. Fishes were sampled with a beach seine net between January and December 2008 and a total of 958 specimens had their stomach content analyzed. Crustacea was the dominant food resource for Lutjanus alexandrei, L. jocu and Bathygobius soporator, whereas Telostei were consumed mainly by Centropomus undecimalis and C. parallelus. In contrast, Polychaeta were preyed upon mainly by Diapterus rhombeus, Eucinostomus argenteus, Sciades herzbergii and S. parkeri. Although most species consumed similar food items, they did that in varying proportions and amounts. Overall, the niche overlap among species was low (< 0.60), but there were several cases where pair of species had their feeding niche highly overlapped (between 0.72 and 0.97). These findings corroborate the hypothesis that food resource partitioning determines species coexistence in estuarine tropical environments.

scholarly journals Determinism

2021 ◽  
Vol 20 (5) ◽  
pp. 1-34
Author(s):  
Edward A. Lee
Keyword(s):  
Quantum Physics ◽  
Deterministic Model ◽  
Physical World ◽  
Deterministic Models ◽  
Newtonian Physics ◽  
Physical Systems ◽  
Newton’S Laws ◽  
And Behavior

This article is about deterministic models, what they are, why they are useful, and what their limitations are. First, the article emphasizes that determinism is a property of models, not of physical systems. Whether a model is deterministic or not depends on how one defines the inputs and behavior of the model. To define behavior, one has to define an observer. The article compares and contrasts two classes of ways to define an observer, one based on the notion of “state” and another that more flexibly defines the observables. The notion of “state” is shown to be problematic and lead to nondeterminism that is avoided when the observables are defined differently. The article examines determinism in models of the physical world. In what may surprise many readers, it shows that Newtonian physics admits nondeterminism and that quantum physics may be interpreted as a deterministic model. Moreover, it shows that both relativity and quantum physics undermine the notion of “state” and therefore require more flexible ways of defining observables. Finally, the article reviews results showing that sufficiently rich sets of deterministic models are incomplete. Specifically, nondeterminism is inescapable in any system of models rich enough to encompass Newton’s laws.

scholarly journals Polygenic local adaptation in metapopulations: a stochastic eco-evolutionary model

2020 ◽  
Author(s):  
Enikő Szép ◽  
Himani Sachdeva ◽  
Nick Barton
Keyword(s):  
Population Size ◽  
Local Adaptation ◽  
Genetic Drift ◽  
Diffusion Approximation ◽  
Joint Distribution ◽  
Evolutionary Model ◽  
Ecological Niches ◽  
Demographic Stochasticity ◽  
Linkage Disequilibria ◽  
Population Sizes

AbstractThis paper analyses the conditions for local adaptation in a metapopulation with infinitely many islands under a model of hard selection, where population size depends on local fitness. Each island belongs to one of two distinct ecological niches or habitats. Fitness is influenced by an additive trait which is under habitat-dependent directional selection. Our analysis is based on the diffusion approximation and accounts for both genetic drift and demographic stochasticity. By neglecting linkage disequilibria, it yields the joint distribution of allele frequencies and population size on each island. We find that under hard selection, the conditions for local adaptation in a rare habitat are more restrictive for more polygenic traits: even moderate migration load per locus at very many loci is sufficient for population sizes to decline. This further reduces the efficacy of selection at individual loci due to increased drift and because smaller populations are more prone to swamping due to migration, causing a positive feedback between increasing maladaptation and declining population sizes. Our analysis also highlights the importance of demographic stochasticity, which exacerbates the decline in numbers of maladapted populations, leading to population collapse in the rare habitat at significantly lower migration than predicted by deterministic arguments.

scholarly journals Resource partitioning and ecomorphological variation in two syntopic species of Lebiasinidae (Characiformes) in an Amazonian stream

2016 ◽  
Vol 46 (1) ◽  
pp. 25-36 ◽  
Author(s):  
Nathália Carina dos Santos SILVA ◽  
Aluízio José Lopes da COSTA ◽  
José LOUVISE ◽  
Bruno Eleres SOARES ◽  
Vanessa Cristine e Souza REIS ◽  
...  
Keyword(s):  
Resource Partitioning ◽  
Trophic Ecology ◽  
Species Coexistence ◽  
Stomach Contents ◽  
Relative Length ◽  
Niche Overlap ◽  
The Body ◽  
Feeding Strategies ◽  
Relative Depth ◽  
Feeding Niche

ABSTRACTResource partitioning is important for species coexistence. Species with similar ecomorphology are potential competitors, especially when phylogenetically close, due to niche conservatism. The aim of this study was to investigate the resource partitioning among populations of two species of lebiasinids (Copella nigrofasciata and Pyrrhulina aff. brevis) that co-occur in a first-order Amazonian stream, analyzing the trophic ecology, feeding strategies and ecomorphological attributes related to the use of food and space by these species. Fish were captured in May and September 2010. The stomach contents of 60 individuals were analyzed and quantified volumetrically to characterize the feeding ecology of both species. Eleven morphological attributes were measured in 20 specimens and combined in nine ecomorphological indices. Both species had an omnivorous-invertivorous diet and consumed predominantly allochthonous items. Both showed a tendency to a generalist diet, but intrapopulational variation in resource use was also detected. Overall feeding niche overlap was high, but differed between seasons: low during the rainy season and high in the dry season. In the latter, the food niche overlap was asymmetric because C. nigrofasciata consumed several prey of P. aff. brevis, which reduced its food spectrum. The ecomorphological analysis suggests that C. nigrofasciatahas greater swimming capacity (greater relative length of caudal peduncle) than P. aff. brevis, which has greater maneuverability and tendency to inhabit lentic environments (greater relative depth of the body). Our results demonstrate that these species have similar trophic ecology and suggest a spatial segregation, given by morphological differences related to locomotion and occupation of habitat, favoring their coexistence.

Asymptotic behavior of a generalization of Bailey's simple epidemic

1971 ◽  
Vol 3 (02) ◽  
pp. 220-221
Author(s):  
George H. Weiss ◽  
Menachem Dishon
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Rate Constants ◽  
Deterministic Model ◽  
Stochastic Theory ◽  
Expected Number ◽  
Deterministic Theory ◽  
Mean Values ◽  
Image Position ◽  
Fixed Population

It has been shown that for many epidemic models, the stochastic theory leads to essentially the same results as the deterministic theory provided that one identifies mean values with the functions calculated from the deterministic differential equations (cf. [1]). If one considers a generalization of Bailey's simple epidemic for a fixed population of size N, represented schematically by where I refers to an infected, S refers to a susceptible, and α and β are appropriate rate constants, then it is evident that at time t = ∞, the expected number of infected individuals must be zero provided that β &gt; 0. If x(t) denotes the number of infected at time t, then the deterministic model is summarized by

Influence of substrate composition and flow rate on growth ofAzospirillum brasilenseCd in a co-culture with 3 sorghum rhizobacteria

2004 ◽  
Vol 50 (10) ◽  
pp. 861-867 ◽  
Author(s):  
Daniela Lippi ◽  
Maria Rita De Paolis ◽  
Elena Di Mattia ◽  
Tito Pietrosanti ◽  
Isabella Cacciari
Keyword(s):  
Flow Rate ◽  
Growth Rates ◽  
Azospirillum Brasilense ◽  
High Growth ◽  
Niche Overlap ◽  
Competitive Behavior ◽  
Bacterial Strains ◽  
Biolog System ◽  
Influence Of Substrate ◽  
Disodium Succinate

The ability of Azospirillum brasilense Cd to colonize the niche occupied by 3 bacterial strains previously isolated from sorghum rhizosphere was studied by means of the Biolog system. The isolates were identified by different methods as strains belonging to Pseudomonas putida, Stenotrophomonas maltophilia, and Klebsiella terrigena species. Several C sources, also chosen among the constituents of sorghum root exudates, were used to evaluate the metabolic profiles of Azospirillum and the sorghum rhizobacteria. Azospirillum brasilense Cd exploited the same class of C compounds as the sorghum rhizobacteria and overlapped in their niche requirements. Since structure and functioning of a microbial community are largely affected by the flow rate of nutrient supply, the competitive behavior of A. brasilense Cd was studied in a chemostat mixed culture under C-limited conditions using disodium succinate as C source. Only at high growth rates, i.e., when the C source was highly supplied, A. brasilense Cd appeared to be a good competitor and it became the dominant species, whereas at low growth rates, it was outnumbered by the other species. However, the coexistence of all the strains was always maintained, thus suggesting that interactions other than competition or a potential cross-feeding might occur within the mixed culture.Key words: Azospirillum brasilense, competition, metabolic profile, niche overlap, sorghum rhizobacteria.

Effect of protozoan predation on relative abundance of fast- and slow-growing bacteria

1989 ◽  
Vol 35 (5) ◽  
pp. 578-582 ◽  
Author(s):  
James L. Sinclair ◽  
Martin Alexander
Keyword(s):  
Growth Rate ◽  
Bacterial Community ◽  
Relative Abundance ◽  
Growth Rates ◽  
Bacterial Species ◽  
Test Species ◽  
Fast Growing ◽  
Population Sizes ◽  
Slow Growing ◽  
Fast Growing Species

The survival of six bacterial species that had different growth rates was tested in raw sewage and sewage that was rendered free of protozoa. When test bacteria were added to protozoa-free sewage at densities of approximately 105 to 106 cells/mL, five of the six species did not decline below 105 cells/mL. If protozoa were present, the population sizes of all test species were markedly reduced, but bacterial species able to grow faster in artificial media had the larger number of survivors. When the same bacteria were inoculated into protozoa-free sewage at densities of less than 103 cells/mL, only the three species able to grow quickly in artificial media increased in abundance. When the six species were inoculated at the same densities into sewage containing protozoa, the three slow-growing species were rapidly eliminated, and two of the three fast-growing species survived in detectable numbers. We suggest that in environments with intense protozoan predation, protozoa may alter the composition of the bacterial community by eliminating slow-growing bacteria.Key words: growth rate, predation, protozoa, sewage.

scholarly journals Insights into the deterministic skill of air quality ensembles from the analysis of AQMEII data

2016 ◽  
Vol 16 (24) ◽  
pp. 15629-15652 ◽  
Author(s):  
Ioannis Kioutsioukis ◽  
Ulas Im ◽  
Efisio Solazzo ◽  
Roberto Bianconi ◽  
Alba Badia ◽  
...  
Keyword(s):  
Air Quality ◽  
Deterministic Model ◽  
Ensemble Methods ◽  
Ground Level ◽  
Chemical Mechanism ◽  
Second Phase ◽  
Air Quality Model ◽  
Quality Model ◽  
Deterministic Models ◽  
Ensemble Mean

Abstract. Simulations from chemical weather models are subject to uncertainties in the input data (e.g. emission inventory, initial and boundary conditions) as well as those intrinsic to the model (e.g. physical parameterization, chemical mechanism). Multi-model ensembles can improve the forecast skill, provided that certain mathematical conditions are fulfilled. In this work, four ensemble methods were applied to two different datasets, and their performance was compared for ozone (O3), nitrogen dioxide (NO2) and particulate matter (PM10). Apart from the unconditional ensemble average, the approach behind the other three methods relies on adding optimum weights to members or constraining the ensemble to those members that meet certain conditions in time or frequency domain. The two different datasets were created for the first and second phase of the Air Quality Model Evaluation International Initiative (AQMEII). The methods are evaluated against ground level observations collected from the EMEP (European Monitoring and Evaluation Programme) and AirBase databases. The goal of the study is to quantify to what extent we can extract predictable signals from an ensemble with superior skill over the single models and the ensemble mean. Verification statistics show that the deterministic models simulate better O3 than NO2 and PM10, linked to different levels of complexity in the represented processes. The unconditional ensemble mean achieves higher skill compared to each station's best deterministic model at no more than 60 % of the sites, indicating a combination of members with unbalanced skill difference and error dependence for the rest. The promotion of the right amount of accuracy and diversity within the ensemble results in an average additional skill of up to 31 % compared to using the full ensemble in an unconditional way. The skill improvements were higher for O3 and lower for PM10, associated with the extent of potential changes in the joint distribution of accuracy and diversity in the ensembles. The skill enhancement was superior using the weighting scheme, but the training period required to acquire representative weights was longer compared to the sub-selecting schemes. Further development of the method is discussed in the conclusion.

scholarly journals Global Stability of Multigroup SIRS Epidemic Model with Varying Population Sizes and Stochastic Perturbation around Equilibrium

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaoming Fan
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Stochastic Perturbation ◽  
Endemic Equilibrium ◽  
Random Perturbations ◽  
Sirs Epidemic Model ◽  
Population Sizes ◽  
Time Average ◽  
The Difference ◽  
Varying Population

We discuss multigroup SIRS (susceptible, infectious, and recovered) epidemic models with random perturbations. We carry out a detailed analysis on the asymptotic behavior of the stochastic model; when reproduction numberℛ0>1, we deduce the globally asymptotic stability of the endemic equilibrium by measuring the difference between the solution and the endemic equilibrium of the deterministic model in time average. Numerical methods are employed to illustrate the dynamic behavior of the model and simulate the system of equations developed. The effect of the rate of immunity loss on susceptible and recovered individuals is also analyzed in the deterministic model.

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