Size-structured models

Author(s):  
Louis W. Botsford ◽  
J. Wilson White ◽  
Alan Hastings

This chapter begins by revisiting the M’Kendrick/von Foerster model, but using size instead of age as the state variable. It then uses the lessons from that model to describe how individual growth and mortality rates determine both stand distributions (a population of mixed ages) and cohort distributions (all one age). In particular, incorporating variability in growth trajectories is shown to be important in obtaining realistic results—though it is not without pitfalls. Ultimately, the numerical calculations required to model size-structured populations for future projections are more challenging than those needed for age structure, so the chapter closes by discussing some mathematical tools that have been developed to accomplish this. These include the integral projection model, a recent approach that is very useful because, while more complex, it has a lot in common with the age-structured models examined in Chapters 3 and 4.

2021 ◽  
pp. 341-350
Author(s):  
Maria Paniw ◽  
Gabriele Cozzi ◽  
Stefan Sommer ◽  
Arpat Ozgul

In socially structured animal populations, vital rates such as survival and reproduction, are affected by complex interactions among individuals of different social ranks and among social groups. Due to this complexity, mechanistic approaches to model vital rates may be preferred over commonly used structured population models. However, mechanistic approaches come at a cost of increased modelling complexity, computational requirements, and reliance on simulated metrics, while structured population models are analytically tractable. This chapter compares different approaches to modelling population dynamics of socially structured populations. It first simulates individual-based data based on the life cycle of a hypothetical cooperative breeder and then projects population dynamics using a matrix population model (MPM), an integral projection model (IPM), and an individual-based model (IBM). The authors demonstrate that, when projecting population size or structure, the relatively simpler MPM can outperform both the IPM and IBM. However, mechanistic details parametrised in the more complex IBM are required to accurately project interactions within social groups. The R scripts in this chapter provide a roadmap to both simulate data that best describe a socially structured system and assess the level of model complexity needed to capture the dynamics of the system.


2010 ◽  
Vol 78 (4) ◽  
pp. 239-249 ◽  
Author(s):  
Lee Worden ◽  
Louis W. Botsford ◽  
Alan Hastings ◽  
Matthew D. Holland

2001 ◽  
Vol 77 (2) ◽  
pp. 153-166 ◽  
Author(s):  
BRIAN CHARLESWORTH

Formulae for the effective population sizes of autosomal, X-linked, Y-linked and maternally transmitted loci in age-structured populations are developed. The approximations used here predict both asymptotic rates of increase in probabilities of identity, and equilibrium levels of neutral nucleotide site diversity under the infinite-sites model. The applications of the results to the interpretation of data on DNA sequence variation in Drosophila, plant, and human populations are discussed. It is concluded that sex differences in demographic parameters such as adult mortality rates generally have small effects on the relative effective population sizes of loci with different modes of inheritance, whereas differences between the sexes in variance in reproductive success can have major effects, either increasing or reducing the effective population size for X-linked loci relative to autosomal or Y-linked loci. These effects need to be accounted for when trying to understand data on patterns of sequence variation for genes with different transmission modes.


1995 ◽  
Vol 83 (3) ◽  
pp. 548
Author(s):  
Tom J. de Jong ◽  
B. Charlesworth

2010 ◽  
Vol 42 (2) ◽  
pp. 103 ◽  
Author(s):  
Zulfaidah Penata Gama ◽  
Pablo Morlacchi ◽  
Giuseppe Carlo Lozzia ◽  
Johann Baumgärtner ◽  
Anna Giorgi

The spatial distribution of Aphis spiraecola Patch was studied in two commercial yarrow fields located in the Swiss and Italian Alps and represented by Taylor’s (1961) power law. The respective parameters indicate a highly aggregated distribution and lead to a high optimum sample size of 400-500 plants in the design of a sampling program. Opportunities for reducing the sampling efforts are discussed. The infestation patterns were studied on the basis of Vansickle’s (1977) time varying distributed delay adequate for modelling the dynamics of age-structured populations. Published literature data were used to parametrize the functions representing the temperature-dependent duration and survival of the nymphal and adult stage. Likewise, literature data were available to obtain reliable estimates for the parameters of the fecundity function comprising the reproductive profile and the number of nymphs produced at different temperatures. The field data were used to parametrize the functions for wing formation and a compound mortality compromising the effects of plant senescence, stem cutting and natural enemies. The model satisfactorily represented the observed infestation patterns. However, there are opportunities for improving parameter estimation and validation. Moreover, the separation of the compound mortality into host plant and natural enemy effects would improve the mechanistic basis of the model and lead towards a tool that could be used to study bottom-up and top-down effects in the yarrow-aphid-natural enemy system.


Author(s):  
Anna Clara Balbina Silva ◽  
Afonso Pelli

Compreender os mecanismos que regulam a dinâmica das populações espacialmente estruturadas é um desafio crítico para os ecólogos e gestores de conservação. A dinâmica de populações é um ramo da ecologia que estuda as populações como sistema em atividades, relacionando as influências ambientais com a distribuição e abundância dos indivíduos e suas interações com o ambiente. O presente artigo é uma revisão bibliográfica, com o objetivo de identificar produções científicas relevantes sobre dinâmica populacional. Para isso, foram utilizados periódicos revisados por pares, na base de Periódicos Capes. A pesquisa foi realizada em junho de 2019, utilizando-se as palavras-chave para título contendo: "population dynamics" e no assunto “ecology”, a partir de 2014, quando o texto completo estava disponível. Foram considerados como critérios de exclusão os artigos publicados antes de 2014. Após a leitura dos títulos dos artigos, foram selecionados 34 artigos que foram lidos na íntegra. Em livros disponíveis no acervo da biblioteca da Universidade Federal do Triângulo Mineiro, foram selecionados quatro livros no tema dinâmica populacional. O referencial teórico aborda os aspectos da dinâmica de populações, tabela de vida, formas de crescimento e interações populacionais. Ressalta-se a necessidade de novos estudos que ainda possuem lacunas, que venha complementar e contribuir para o conhecimento de organismos que faltam ou ainda não possuem registros de estudos. Palavras-chave: Taxas de Natalidade e Mortalidade. Atributos Populacionais. Dispersão. AbstractUnderstanding the mechanisms that regulate the dynamics of spatially structured populations is a critical challenge for ecologists and conservation managers. Population dynamics is a branch of ecology that studies populations as a system in activities, relating environmental influences to the individuals’ distribution and abundance and their interactions with the environment. This article is a bibliographic review, aiming to identify relevant scientific productions about population dynamics. Thus. peer-reviewed journals were used in the Capes Periodicals base, the research was conducted in June 2019, using the keywords for title containing "population dynamics" and in the subject "ecology", from 2014, when the full text was available. Exclusion criteria were: articles published before 2014, after reading the article titles, 34 articles were selected that met the initially proposed criteria and were read in full. In books available in the library collection of the Federal University of Triângulo Mineiro, with a search for the dynamic population theme, 4 books were used. The theoretical framework addresses the aspects of population dynamics, life table, forms of growth and population interactions. It is emphasized  the need for further studies that still have gaps, which will complement and contribute to the knowledge of organisms that are missing or do not have study records. Keywords: Birth and Mortality Rates. Population Attributes. Dispersion.


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