From growth equations for a single species to Lotka–Volterra equations for two interacting species

2020 ◽  
Author(s):  
Hugo Fort
Keyword(s):  
Single Species ◽  
Volterra Equations ◽  
Interacting Species ◽  
Growth Equations

scholarly journals Whose trait is it anyways? Coevolution of joint phenotypes and genetic architecture in mutualisms

2021 ◽  
Vol 288 (1942) ◽  
pp. 20202483
Author(s):  
Anna M. O’Brien ◽  
Chandra N. Jack ◽  
Maren L. Friesen ◽  
Megan E. Frederickson
Keyword(s):  
Association Studies ◽  
Single Species ◽  
Genome Wide Association Studies ◽  
Interacting Species ◽  
Fitness Effects ◽  
Evolutionary Conflict ◽  
Fitness Consequences ◽  
Genome Wide ◽  
Fitness Benefits ◽  
Multiple Genomes

Evolutionary biologists typically envision a trait’s genetic basis and fitness effects occurring within a single species. However, traits can be determined by and have fitness consequences for interacting species, thus evolving in multiple genomes. This is especially likely in mutualisms, where species exchange fitness benefits and can associate over long periods of time. Partners may experience evolutionary conflict over the value of a multi-genomic trait, but such conflicts may be ameliorated by mutualism’s positive fitness feedbacks. Here, we develop a simulation model of a host–microbe mutualism to explore the evolution of a multi-genomic trait. Coevolutionary outcomes depend on whether hosts and microbes have similar or different optimal trait values, strengths of selection and fitness feedbacks. We show that genome-wide association studies can map joint traits to loci in multiple genomes and describe how fitness conflict and fitness feedback generate different multi-genomic architectures with distinct signals around segregating loci. Partner fitnesses can be positively correlated even when partners are in conflict over the value of a multi-genomic trait, and conflict can generate strong mutualistic dependency. While fitness alignment facilitates rapid adaptation to a new optimum, conflict maintains genetic variation and evolvability, with implications for applied microbiome science.

scholarly journals GEO2RNAseq: An easy-to-use R pipeline for complete pre-processing of RNA-seq data

2019 ◽  
Author(s):  
Bastian Seelbinder ◽  
Thomas Wolf ◽  
Steffen Priebe ◽  
Sylvie McNamara ◽  
Silvia Gerber ◽  
...  
Keyword(s):  
Gene Expression ◽  
Single Species ◽  
Gene Expression Omnibus ◽  
Rna Seq ◽  
Sequencing Data ◽  
Interacting Species ◽  
Link Type ◽  
Fastq Format ◽  
Standard Tool ◽  
Processing Steps

ABSTRACTIn transcriptomics, the study of the total set of RNAs transcribed by the cell, RNA sequencing (RNA-seq) has become the standard tool for analysing gene expression. The primary goal is the detection of genes whose expression changes significantly between two or more conditions, either for a single species or for two or more interacting species at the same time (dual RNA-seq, triple RNA-seq and so forth). The analysis of RNA-seq can be simplified as many steps of the data pre-processing can be standardised in a pipeline.In this publication we present the “GEO2RNAseq” pipeline for complete, quick and concurrent pre-processing of single, dual, and triple RNA-seq data. It covers all pre-processing steps starting from raw sequencing data to the analysis of differentially expressed genes, including various tables and figures to report intermediate and final results. Raw data may be provided in FASTQ format or can be downloaded automatically from the Gene Expression Omnibus repository. GEO2RNAseq strongly incorporates experimental as well as computational metadata. GEO2RNAseq is implemented in R, lightweight, easy to install via Conda and easy to use, but still very flexible through using modular programming and offering many extensions and alternative workflows.GEO2RNAseq is publicly available at https://anaconda.org/xentrics/r-geo2rnaseq and https://bitbucket.org/thomas_wolf/geo2rnaseq/overview, including source code, installation instruction, and comprehensive package documentation.

A Framework for the Role of Time in Ecology

2019 ◽  
pp. 1-6
Author(s):  
Eric Post
Keyword(s):  
Single Species ◽  
Interacting Species ◽  
Way Of Thinking ◽  
Measuring Stick

This introductory chapter provides an overview of the role of time in ecology. Generally speaking, time is considered as a conceptual axis, much like space, along which one can measure ecological events and their durations. In ecology, time also allows one to describe, ascribe rates to, and quantify differences in, for example, changes in abundance within and among populations of single species and interacting species. In such a framework, time is a measuring stick and half of the stage—the complementary half of which is space—upon which ecology plays out. Over the ensuing chapters, an argument will be constructed for the development of a framework for a novel way of thinking about time in ecology, using the study of phenology as an exemplar for doing so.

scholarly journals Predicting ecosystem shifts requires new approaches that integrate the effects of climate change across entire systems

2011 ◽  
Vol 8 (2) ◽  
pp. 164-166 ◽  
Author(s):  
Bayden D. Russell ◽  
Christopher D. G. Harley ◽  
Thomas Wernberg ◽  
Nova Mieszkowska ◽  
Stephen Widdicombe ◽  
...  
Keyword(s):  
Climate Change ◽  
Life Stage ◽  
Experimental Studies ◽  
Single Species ◽  
Ecosystem Change ◽  
Energy Budgets ◽  
Ecological Change ◽  
Ecological Processes ◽  
Interacting Species ◽  
Climatic Impacts

Most studies that forecast the ecological consequences of climate change target a single species and a single life stage. Depending on climatic impacts on other life stages and on interacting species, however, the results from simple experiments may not translate into accurate predictions of future ecological change. Research needs to move beyond simple experimental studies and environmental envelope projections for single species towards identifying where ecosystem change is likely to occur and the drivers for this change. For this to happen, we advocate research directions that (i) identify the critical species within the target ecosystem, and the life stage(s) most susceptible to changing conditions and (ii) the key interactions between these species and components of their broader ecosystem. A combined approach using macroecology, experimentally derived data and modelling that incorporates energy budgets in life cycle models may identify critical abiotic conditions that disproportionately alter important ecological processes under forecasted climates.

scholarly journals Reining in the Red Queen: the dynamics of adaptation and extinction reexamined

Paleobiology ◽  
10.1666/13009 ◽  
2013 ◽  
Vol 39 (4) ◽  
pp. 560-575 ◽  
Author(s):  
Geerat J. Vermeij ◽  
Peter D. Roopnarine
Keyword(s):  
Evolutionary Game ◽  
Single Species ◽  
Ecosystem Productivity ◽  
Red Queen ◽  
Interacting Species ◽  
Living Things ◽  
Zero Sum ◽  
Selective Regime ◽  
The Red Queen

One of the most enduring evolutionary metaphors is Van Valen's (1973) Red Queen. According to this metaphor, as one species in a community adapts by becoming better able to acquire and defend resources, species with which it interacts are adversely affected. If those other species do not continuously adapt to compensate for this biotically caused deterioration, they will be driven to extinction. Continuous adaptation of all species in a community prevents any single species from gaining a long-term advantage; this amounts to the Red Queen running in place. We have critically examined the assumptions on which the Red Queen metaphor was founded. We argue that the Red Queen embodies three demonstrably false assumptions: (1) evolutionary adaptation is continuous; (2) organisms are important agents of extinction; and (3) evolution is a zero-sum process in which living things divide up an unchanging quantity of resources. Changes in the selective regime need not always elicit adaptation, because most organisms function adequately under many “suboptimal” conditions and often compensate by demonstrating adaptive flexibility. Likewise, ecosystems are organized in such a way that they tend to be robust and capable of absorbing invasions and extinctions, at least up to a point. With a simple evolutionary game involving three species, we show that Red Queen dynamics (continuous adaptation by all interacting species) apply in only a very small minority of possible outcomes. Importantly, cooperation and facilitation among species enable competitors to increase ecosystem productivity and therefore to enlarge the pool and turnover of resources. The Red Queen reigns only under a few unusual circumstances.

scholarly journals NONMONOTONIC PATTERN FORMATION IN THREE SPECIES LOTKA–VOLTERRA SYSTEM WITH COLORED NOISE

2005 ◽  
Vol 05 (02) ◽  
pp. L305-L311 ◽  
Author(s):  
A. FIASCONARO ◽  
D. VALENTI ◽  
B. SPAGNOLO
Keyword(s):  
Pattern Formation ◽  
Noise Intensity ◽  
Colored Noise ◽  
Multiplicative Noise ◽  
Volterra Equations ◽  
Volterra System ◽  
Spatiotemporal Evolution ◽  
Species Concentration ◽  
Interacting Species ◽  
Nonmonotonic Behavior

A coupled map lattice of generalized Lotka–Volterra equations in the presence of colored multiplicative noise is used to analyze the spatiotemporal evolution of three interacting species: one predator and two preys symmetrically competing each other. The correlation of the species concentration over the grid as a function of time and of the noise intensity is investigated. The presence of noise induces pattern formation, whose dimensions show a nonmonotonic behavior as a function of the noise intensity. The colored noise induces a greater dimension of the patterns with respect to the white noise case and a shift of the maximum of its area towards higher values of the noise intensity.

scholarly journals Stochastic dynamics and mean field approach in a system of three interacting species

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Davide Valenti ◽  
Bernardo Spagnolo
Keyword(s):  
Stochastic Dynamics ◽  
Temporal Dynamics ◽  
Mean Field ◽  
Spatial Domain ◽  
Volterra Equations ◽  
Time Behaviour ◽  
Time Step ◽  
Field Approach ◽  
Interacting Species ◽  
Cml Model

AbstractThe spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied, by using Lotka-Volterra equations. A correlated dichotomous noise acts on the interaction parameter between the two preys, and a multiplicative white noise affects directly the dynamics of the three species. After analyzing the time behaviour of the three species in a single site, we consider a two-dimensional spatial domain, applying a mean field approach and obtaining the time behaviour of the first and second order moments for different multiplicative noise intensities. We find noise-induced oscillations of the three species with an anticorrelated behaviour of the two preys. Finally, we compare our results with those obtained by using a coupled map lattice (CML) model, finding a good qualitative agreement. However, some quantitative discrepancies appear, that can be explained as follows: i) different stationary values occur in the two approaches; ii) in the mean field formalism the interaction between sites is extended to the whole spatial domain, conversely in the CML model the species interaction is restricted to the nearest neighbors; iii) the dynamics of the CML model is faster since an unitary time step is considered.

scholarly journals Species competition: coexistence, exclusion and clustering

2009 ◽  
Vol 367 (1901) ◽  
pp. 3183-3195 ◽  
Author(s):  
Emilio Hernández-García ◽  
Cristóbal López ◽  
Simone Pigolotti ◽  
Ken H. Andersen
Keyword(s):  
Analytical Solution ◽  
Carrying Capacity ◽  
Volterra Equations ◽  
Stability Conditions ◽  
Species Competition ◽  
Ecological Interactions ◽  
Niche Space ◽  
Interacting Species ◽  
Species Trait ◽  
Different Types

We present properties of Lotka–Volterra equations describing ecological competition among a large number of interacting species. First we extend previous stability conditions to the case of a non-homogeneous niche space, i.e. that of a carrying capacity depending on the species trait. Second, we discuss mechanisms leading to species clustering and obtain an analytical solution for a state with a lumped species distribution for a specific instance of the system. We also discuss how realistic ecological interactions may result in different types of competition coefficients.

scholarly journals Modifying and reacting to the environmental pH drives bacterial interactions

2017 ◽  
Author(s):  
Christoph Ratzke ◽  
Jeff Gore
Keyword(s):  
Feedback Loop ◽  
Bacterial Population ◽  
Single Species ◽  
Pairwise Interaction ◽  
Environmental Parameter ◽  
Bacterial Populations ◽  
Bacterial Interactions ◽  
Interacting Species ◽  
Species Change ◽  
Microbial Systems

AbstractMicrobes usually exist in communities consisting of myriad different but interacting species. These interactions are typically mediated through environmental modifications; microbes change the environment by taking up resources and excreting metabolites, which affects the growth of both themselves and also other microbes. A very common environmental modification is a change of the environmental pH. Here we show that changing and reacting to the pH leads to a feedback loop that can determine the fate of bacterial populations. We find experimentally that these pH changes can decide the fate of bacterial populations; they can either facilitate or inhibit growth, and in extreme cases will cause extinction of the bacterial population. Moreover, modifying the pH can determine the interactions between different species. Understanding how single species change the pH and react to it allowed us to estimate their pairwise interaction outcomes. Those interactions lead to a set of generic interaction motifs—bistability, succession, murder suicide, and mutualism—that may be independent of which environmental parameter is modified and thus reoccur in different microbial systems.

scholarly journals Exact Reduction of the Generalized Lotka–Volterra Equations via Integral and Algebraic Substitutions

Computation ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 49
Author(s):  
Rebecca E. Morrison
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Chemical Reactions ◽  
Reduction Process ◽  
Approximate Model ◽  
Reduced Model ◽  
Volterra Equations ◽  
Coupled Dynamics ◽  
Interacting Species ◽  
Promising Type

Systems of interacting species, such as biological environments or chemical reactions, are often described mathematically by sets of coupled ordinary differential equations. While a large number β of species may be involved in the coupled dynamics, often only α<β species are of interest or of consequence. In this paper, we explored how to construct models that include only those given α species, but still recreate the dynamics of the original β-species model. Under some conditions detailed here, this reduction can be completed exactly, such that the information in the reduced model is exactly the same as the original one, but over fewer equations. Moreover, this reduction process suggests a promising type of approximate model—no longer exact, but computationally quite simple.

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