Dynamics of Populations of Consumers

1995 ◽  
pp. 87-105
Author(s):  
Ivan Valiela
Genetics ◽  
2000 ◽  
Vol 154 (4) ◽  
pp. 1893-1906 ◽  
Author(s):  
Jian Li ◽  
Hong-Wen Deng

Abstract The Deng-Lynch method was developed to estimate the rate and effects of deleterious genomic mutations (DGM) in natural populations under the assumption that populations are either completely outcrossing or completely selfing and that populations are at mutation-selection (M-S) balance. However, in many plant and animal populations, selfing or outcrossing is often incomplete in that a proportion of populations undergo inbreeding while the rest are outcrossing. In addition, the degrees of deviation of populations from M-S balance are often not known. Through computer simulations, we investigated the robustness and the applicability of the Deng-Lynch method under different degrees of partial selfing or partial outcrossing and for nonequilibrium populations approaching M-S balance at different stages. The investigation was implemented under constant, variable, and epistatic mutation effects. We found that, generally, the estimation by the Deng-Lynch method is fairly robust if the selfing rate (S) is <0.10 in outcrossing populations and if S > 0.8 in selfing populations. The estimation may be unbiased under partial selfing with variable and epistatic mutation effects in predominantly outcrossing populations. The estimation is fairly robust in nonequilibrium populations at different stages approaching M-S balance. The dynamics of populations approaching M-S balance under various parameters are also studied. Under mutation and selection, populations approach balance at a rapid pace. Generally, it takes 400–2000 generations to reach M-S balance even when starting from homogeneous individuals free of DGM. Our investigation here provides a basis for characterizing DGM in partial selfing or outcrossing populations and for nonequilibrium populations.


2021 ◽  
Vol 53 (1) ◽  
pp. 251-278
Author(s):  
Adrián González Casanova ◽  
Juan Carlos Pardo ◽  
José Luis Pérez

AbstractIn this paper, we introduce a family of processes with values on the nonnegative integers that describes the dynamics of populations where individuals are allowed to have different types of interactions. The types of interactions that we consider include pairwise interactions, such as competition, annihilation, and cooperation; and interactions among several individuals that can be viewed as catastrophes. We call such families of processes branching processes with interactions. Our aim is to study their long-term behaviour under a specific regime of the pairwise interaction parameters that we introduce as the subcritical cooperative regime. Under such a regime, we prove that a process in this class comes down from infinity and has a moment dual which turns out to be a jump-diffusion that can be thought as the evolution of the frequency of a trait or phenotype, and whose parameters have a classical interpretation in terms of population genetics. The moment dual is an important tool for characterizing the stationary distribution of branching processes with interactions whenever such a distribution exists; it is also an interesting object in its own right.


Science ◽  
1931 ◽  
Vol 73 (1904) ◽  
pp. 700-702
Author(s):  
W. H. Longley

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