scholarly journals Invasion fitness, inclusive fitness, and reproductive numbers in heterogeneous populations

2016 ◽  
Author(s):  
Laurent Lehmann ◽  
Charles Mullon ◽  
Erol Akcay ◽  
Jeremy Van Cleve
Keyword(s):  
Growth Rate ◽  
Mutant Allele ◽  
Inclusive Fitness ◽  
Weighted Average ◽  
Structured Populations ◽  
Basic Reproductive Number ◽  
Reproductive Value ◽  
Reproductive Number ◽  
Invasion Fitness ◽  
Fitness Measures

How should fitness be measured to determine which phenotype or "strategy" is uninvadable when evolution occurs in subdivided populations subject to local demographic and environmental heterogeneity? Several invasion fitness measures, such as basic reproductive number, lifetime dispersal success of a local lineage, or inclusive fitness have been proposed to address this question, but the relationships between them and their generality remains unclear. Here, we ascertain uninvadability (all mutant strategies always go extinct) in terms of the growth rate of a mutant allele arising as a single copy in a population. We show from this growth rate that uninvadability is equivalently characterized by at least three conceptually distinct invasion fitness measures: (i) lineage fitness, giving the average personal fitness of a randomly sampled mutant lineage member; (ii) inclusive fitness, giving a reproductive value weighted average of the direct fitness cost and relatedness weighted indirect fitness benefits accruing to a randomly sampled mutant lineage member; and (iii) three types of reproductive numbers, giving lifetime success of a local lineage. Our analysis connects approaches that have been deemed different, generalizes the exact version of inclusive fitness to class-structured populations, and provides a biological interpretation of selection on a mutant allele under arbitrary strength of selection.

What Is Fitness?

2015 ◽  
Author(s):  
James A.R. Marshall
Keyword(s):  
Reproductive Success ◽  
Inclusive Fitness ◽  
Structured Populations ◽  
Reproductive Value ◽  
Costs And Benefits ◽  
Risk Of Death ◽  
Fitness Effects ◽  
Inclusive Fitness Theory ◽  
Definition Of ◽  
Evolutionary Fitness

This chapter considers the problem of correctly defining fitness costs and benefits in inclusive fitness theory, when competition occurs between offspring who are relatives. It reviews the definition of evolutionary fitness and shows how its misinterpretation explains many previous misunderstandings as to whether inclusive fitness theory always makes accurate predictions. The chapter begins with a discussion of Haldane's dilemma, which can be formalized with fitness equations that show that the risk of death can make fitness effects all-or-nothing. It then examines how inclusive fitness models can be constructed to deal with reproductive value and class-structured populations. It also shows how costs and benefits can be expressed as payoffs that are proportional to reproductive success, as changes in production of offspring, or as changes in evolutionary fitness. Finally, it presents examples that illustrate when fitness, payoffs, and fecundity are different, and how inclusive fitness analyses can be performed properly in such situations.

scholarly journals The Sensitivity of the Epidemic Growth Rate to Weather Variables, with an Application to Yellow Rust on Wheat

2007 ◽  
Vol 97 (2) ◽  
pp. 202-210 ◽  
Author(s):  
Konstantina Papastamati ◽  
Frank van den Bosch
Keyword(s):  
Growth Rate ◽  
Life Cycle ◽  
Latent Period ◽  
Puccinia Striiformis ◽  
Yellow Rust ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
General View ◽  
Weather Variable ◽  
Weather Variables

We first show how to estimate the exponential epidemic growth rate, r, for different combinations of three weather variables. Then we derive a method to quantify the sensitivity of r to a weather variable as a function of the pathogen life cycle variables of latent period, basic reproductive number, and the mean and standard deviation of the sporulation curve. The method can be used to identify the most important weather variable and pathogen life cycle component in terms of epidemic progress. The method is applied to yellow rust, caused by Puccinia striiformis, on winter wheat. We conclude that the most important weather variable for the progress of yellow rust is temperature, followed by dew period and light quantity. By far, the most important pathogen life cycle component is the basic reproductive number, especially at low and high temperatures. This disagrees with the general view that latent period is the most important variable at low temperatures. We discuss explanations of this.

scholarly journals When do individuals maximize their inclusive fitness?

2019 ◽  
Author(s):  
Laurent Lehmann ◽  
François Rousset
Keyword(s):  
Behavioral Ecology ◽  
Mutant Allele ◽  
Inclusive Fitness ◽  
Order Approximation ◽  
Structured Populations ◽  
Weak Selection ◽  
Individual Control ◽  
First Order ◽  
Best Response ◽  
First Order Approximation

AbstractAdaptation is often described in behavioral ecology as individuals maximizing their inclusive fitness. Under what conditions does this hold and how does this relate to the gene-centered perspective of adaptation? We unify and extend the literature on these questions to class-structured populations. We demonstrate that the maximization (in the best-response sense) of class-specific inclusive fitness obtains in uninvadable population states (meaning that all deviating mutant go extinct). This defines a genuine actor-centered perspective on adaptation. But this inclusive fitness is assigned to all bearers of a mutant allele in a given class and depends on distributions of demographic and genetic contexts. These distributions, in turn, usually depend on events in previous generations and are thus not under individual control. This prevents, in general, from envisioning individuals themselves as autonomous fitness-maximizers, each with its own inclusive fitness. For weak selection, however, the dependence on earlier events can be neglected. We then show that each individual in each class appears to maximize its own inclusive fitness when all other individuals exhibit fitness-maximizing behavior. This defines a genuine individual-centered perspective of adaptation and justifies formally, as a first-order approximation, the long-heralded view of individuals appearing to maximize their own inclusive fitness.

Structured Populations and Games over Generations

2020 ◽  
pp. 231-260
Author(s):  
John M. McNamara ◽  
Olof Leimar
Keyword(s):  
Tail Length ◽  
The State ◽  
Structured Populations ◽  
Reproductive Value ◽  
Lifetime Reproductive Success ◽  
Value Maximization ◽  
Invasion Fitness ◽  
Current State ◽  
Mean Lifetime ◽  
New Criterion

The actions and state of an individual in one generation can affect the state of offspring in the next generation, and hence the ability of these offspring to leave offspring themselves. This chapter deals with games in this multigenerational setting. Projection matrices are used to keep track of the state and number of descendants in successive years and generations. Invasion fitness is then defined in terms of the leading eigenvalue of the projection matrix. Simple examples illustrate these concepts and show how to apply them. Reproductive value is a function that measures how the ability to leave descendants in future generations depends on the current state. The Nash equilibrium condition is reformulated in terms of reproductive value maximization. This new criterion is used to justify the fitness proxy used in the analysis of sex allocation earlier in the book. The analysis is extended to the case where offspring may inherit aspects of their mother’s quality, with a focus on the question of whether high-quality mothers should produce sons or daughters. As a second application of reproductive value maximization, the co-evolution of female preference for a particular male trait and the trait itself is analysed, with the evolution of tail length in the widowbird as an illustrative application. Mean lifetime reproductive success is used as a fitness proxy in much of the book. Its use is finally justified in this chapter, where the fitness proxy is used to analyse the evolutionarily stable age of first reproduction in a population.

scholarly journals Epidemic Landscape and Forecasting of SARS-CoV-2 in India

2020 ◽  
Author(s):  
Aravind Lathika Rajendrakumar ◽  
Anand Thakarakkattil Narayanan Nair ◽  
Charvi Nangia ◽  
Prabhal Kumar Chourasia ◽  
Mehul Kumar Chourasia ◽  
...  
Keyword(s):  
Growth Rate ◽  
Doubling Time ◽  
Time Series Data ◽  
Epidemiologic Studies ◽  
Basic Reproductive Number ◽  
Series Data ◽  
Reproductive Number ◽  
Peak Time ◽  
Local Cluster ◽  
The Mean

BACKGROUNDIndia was one of the countries to institute strict measures for SARS-CoV-2 control in early phase. Since, then, the epidemic growth trajectory was slow before registering an explosion of cases due to local cluster transmissions.METHODSWe estimated growth rate and doubling time of SARS-CoV-2 for India and high burden states using crowd sourced time series data. Further, we also estimated Basic Reproductive Number (R0) and time dependent reproductive number (Rt) using serial intervals from the data. We compared the R0 estimated from five different methods and R0 from SB was further used in analysis. We modified standard SIR models to SIRD model to accommodate deaths using R0 with the Sequential Bayesian method (SBM) for simulation in SIRD models.RESULTSOn an average, 2.8 individuals were infected by an index case. The mean serial interval was 3.9 days. The R0 estimated from different methods ranged from 1.43 to 1.85. The mean time to recovery was 14 ± 5.3 days. Daily epidemic growth rate of India was 0.16 [95%CI; 0.14, 0.17] with a doubling time of 4.30 days [95%CI; 3.96, 4.70]. From the SIRD model, it can be deduced that the peak of SARS-CoV-2 in India will be around mid-July to early August 2020 with around 12.5% of population likely to be infected at the peak time.CONCLUSIONSThe pattern of spread of SARS-CoV-2 in India is suggestive of community transmission. There is a need to increase fund for infectious disease research and epidemiologic studies. All the current gains may be reversed rapidly if air travel and social mixing resumes rapidly. For the time being, these must be resumed only in a phased manner, and should be back to normal levels only after we are prepared to deal with the disease with efficient tools like vaccine or a medicine.

scholarly journals Hamilton's inclusive fitness in finite-structured populations

2014 ◽  
Vol 369 (1642) ◽  
pp. 20130360 ◽  
Author(s):  
Peter D. Taylor ◽  
Wes Maciejewski
Keyword(s):  
Inclusive Fitness ◽  
Structured Populations ◽  
Reproductive Value ◽  
Frequency Change ◽  
Fitness Effect ◽  
The Past ◽  
Heterogeneous Structures ◽  
Evolutionary Trajectories ◽  
Precise Measure ◽  
Homogeneous Environment

Hamilton's formulation of inclusive fitness has been with us for 50 years. During the first 20 of those years attention was largely focused on the evolutionary trajectories of different behaviours, but over the past 20 years interest has been growing in the effect of population structure on the evolution of behaviour and that is our focus here. We discuss the evolutionary journey of the inclusive-fitness effect over this epoch, nurtured as it was in an essentially homogeneous environment (that of ‘transitive’ structures) having to adapt in different ways to meet the expectations of heterogeneous structures. We pay particular attention to the way in which the theory has managed to adapt the original constructs of relatedness and reproductive value to provide a formulation of inclusive fitness that captures a precise measure of allele-frequency change in finite-structured populations.

scholarly journals Utility of R 0 as a predictor of disease invasion in structured populations

2006 ◽  
Vol 4 (13) ◽  
pp. 315-324 ◽  
Author(s):  
Paul C Cross ◽  
Philip L.F Johnson ◽  
James O Lloyd-Smith ◽  
Wayne M Getz
Keyword(s):  
Group Structure ◽  
Classification Tree ◽  
Theoretical Work ◽  
Structured Populations ◽  
Basic Reproductive Number ◽  
Infectious Period ◽  
Reproductive Number ◽  
Factors Affecting ◽  
Hierarchical Nature ◽  
Local Transmission

Early theoretical work on disease invasion typically assumed large and well-mixed host populations. Many human and wildlife systems, however, have small groups with limited movement among groups. In these situations, the basic reproductive number, R 0 , is likely to be a poor predictor of a disease pandemic because it typically does not account for group structure and movement of individuals among groups. We extend recent work by combining the movement of hosts, transmission within groups, recovery from infection and the recruitment of new susceptibles into a stochastic model of disease in a host metapopulation. We focus on how recruitment of susceptibles affects disease invasion and how population structure can affect the frequency of superspreading events (SSEs). We show that the frequency of SSEs may decrease with the reduced movement and the group sizes due to the limited number of susceptible individuals available. Classification tree analysis of the model results illustrates the hierarchical nature of disease invasion in host metapopulations. First, the pathogen must effectively transmit within a group ( R 0 >1), and then the pathogen must persist within a group long enough to allow for movement among the groups. Therefore, the factors affecting disease persistence—such as infectious period, group size and recruitment of new susceptibles—are as important as the local transmission rates in predicting the spread of pathogens across a metapopulation.

scholarly journals Dynamics analysis of an online gambling spreading model on scale-free networks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yu Kong ◽  
Tao Li ◽  
Yuanmei Wang ◽  
Xinming Cheng ◽  
He Wang ◽  
...  
Keyword(s):  
Network Topology ◽  
Negative Impact ◽  
Online Gambling ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Scale Free ◽  
Spreading Model ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
Gambling Policy

AbstractNowadays, online gambling has a great negative impact on the society. In order to study the effect of people’s psychological factors, anti-gambling policy, and social network topology on online gambling dynamics, a new SHGD (susceptible–hesitator–gambler–disclaimer) online gambling spreading model is proposed on scale-free networks. The spreading dynamics of online gambling is studied. The basic reproductive number $R_{0}$ R 0 is got and analyzed. The basic reproductive number $R_{0}$ R 0 is related to anti-gambling policy and the network topology. Then, gambling-free equilibrium $E_{0}$ E 0 and gambling-prevailing equilibrium $E_{ +} $ E + are obtained. The global stability of $E_{0}$ E 0 is analyzed. The global attractivity of $E_{ +} $ E + and the persistence of online gambling phenomenon are studied. Finally, the theoretical results are verified by some simulations.

scholarly journals Effects of social distancing on the spreading of COVID-19 inferred from mobile phone data

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hamid Khataee ◽  
Istvan Scheuring ◽  
Andras Czirok ◽  
Zoltan Neufeld
Keyword(s):  
Mobile Phone ◽  
Basic Reproductive Number ◽  
Mobile Phone Data ◽  
Reproductive Number ◽  
Expansion Phase ◽  
Social Distancing ◽  
Exponential Expansion ◽  
Total Death ◽  
Mobility Reduction ◽  
Epidemiological Parameters

AbstractA better understanding of how the COVID-19 pandemic responds to social distancing efforts is required for the control of future outbreaks and to calibrate partial lock-downs. We present quantitative relationships between key parameters characterizing the COVID-19 epidemiology and social distancing efforts of nine selected European countries. Epidemiological parameters were extracted from the number of daily deaths data, while mitigation efforts are estimated from mobile phone tracking data. The decrease of the basic reproductive number ($$R_0$$ R 0 ) as well as the duration of the initial exponential expansion phase of the epidemic strongly correlates with the magnitude of mobility reduction. Utilizing these relationships we decipher the relative impact of the timing and the extent of social distancing on the total death burden of the pandemic.

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