Faculty Opinions recommendation of Stochastic population growth in spatially heterogeneous environments.

2016 ◽  
Author(s):  
Shripad Tuljapurkar
Keyword(s):  
Population Growth ◽  
Heterogeneous Environments ◽  
Stochastic Population Growth

scholarly journals Stochastic population growth in spatially heterogeneous environments

2012 ◽  
Vol 66 (3) ◽  
pp. 423-476 ◽  
Author(s):  
Steven N. Evans ◽  
Peter L. Ralph ◽  
Sebastian J. Schreiber ◽  
Arnab Sen
Keyword(s):  
Population Growth ◽  
Heterogeneous Environments ◽  
Stochastic Population Growth

scholarly journals Fitness response variation within and among consumer species can be co-mediated by food quantity and biochemical quality

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Svenja Schälicke ◽  
Johannes Teubner ◽  
Dominik Martin-Creuzburg ◽  
Alexander Wacker
Keyword(s):  
Population Growth ◽  
Food Quality ◽  
Algal Species ◽  
Sensu Stricto ◽  
Heterogeneous Environments ◽  
Population Growth Rates ◽  
Food Quantity ◽  
Biochemical Quality ◽  
Response Variation ◽  
Species Specific

Abstract In natural heterogeneous environments, the fitness of animals is strongly influenced by the availability and composition of food. Food quantity and biochemical quality constraints may affect individual traits of consumers differently, mediating fitness response variation within and among species. Using a multifactorial experimental approach, we assessed population growth rate, fecundity, and survival of six strains of the two closely related freshwater rotifer species Brachionus calyciflorus sensu stricto and Brachionus fernandoi. Therefore, rotifers fed low and high concentrations of three algal species differing in their biochemical food quality. Additionally, we explored the potential of a single limiting biochemical nutrient to mediate variations in population growth response. Therefore, rotifers fed a sterol-free alga, which we supplemented with cholesterol-containing liposomes. Co-limitation by food quantity and biochemical food quality resulted in differences in population growth rates among strains, but not between species, although effects on fecundity and survival differed between species. The effect of cholesterol supplementation on population growth was strain-specific but not species-specific. We show that fitness response variations within and among species can be mediated by biochemical food quality. Dietary constraints thus may act as evolutionary drivers on physiological traits of consumers, which may have strong implications for various ecological interactions.

The Martin boundary for Polya's urn scheme, and an application to stochastic population growth

1964 ◽  
Vol 1 (2) ◽  
pp. 284-296 ◽  
Author(s):  
David Blackwell ◽  
David Kendall
Keyword(s):  
Markov Process ◽  
Population Growth ◽  
Transition Probability ◽  
Martin Boundary ◽  
Transition Probability Matrix ◽  
Stochastic Population Growth ◽  
Urn Scheme ◽  
Pólya’S Urn ◽  
Image Position ◽  
Positive Integers

1. In 1923 Eggenberger and Pólya introduced the following ‘urn scheme’ as a model for the development of a contagious phenomenon. A box contains b black and r red balls, and a ball is drawn from it at random with ‘double replacement’ (i.e. whatever ball is drawn, it is returned to the box together with a fresh ball of the same colour); the procedure is then continued indefinitely. A slightly more complicated version with m-fold replacement is sometimes discussed, but it will be sufficient for our purposes to keep m = 2 and it will be convenient further to simplify the scheme by taking b = r = 1 as the initial condition. We shall however generalise the scheme in another direction by allowing an arbitrary number k(≧2) of colours. Thus initially the box will contain k differently coloured balls and successive random drawings will be followed by double replacement as before. We write sn (a k-vector with jth component ) for the numerical composition of the box immediately after the nth replacement, so that and we observe that is a Markov process for which the state-space consists of all ordered k-ads of positive integers, the (constant) transition-probability matrix having elements determined by where Sn is the sum of the components of sn and (e(i))j = δij. We shall calculate the Martin boundary for this Markov process, and point out some applications to stochastic models for population growth.

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