scholarly journals The formal demography of kinship II: Multistate models, parity, and sibship

2020 ◽  
Author(s):  
Hal Caswell
Keyword(s):  
Unsolved Problem ◽  
Stage Structure ◽  
Multistate Models ◽  
Matrix Formulation ◽  
High Parity ◽  
Structured Population ◽  
Parity Distribution ◽  
Focal Individual ◽  
Dramatic Shift ◽  
Projection Matrices

AbstractBackgroundRecent kinship models focus on the age structures of kin as a function of the age of the focal individual. However, variables in addition to age have important impacts. Generalizing age-specific models to multistate models including other variables is an important and hitherto unsolved problem.ObjectivesOur aim is to develop a multistate kinship model, classifying individuals jointly by age and other criteria (generically, “stages”).MethodsWe use the vec-permutation method to create multistate projection matrices including age- and stage-dependent survival, fertility, and transitions. These matrices operate on block-structured population vectors that describe the age×stage structure of each kind of kin, at each age of a focal individual.ResultsThe new matrix formulation is directly comparable to, and greatly extends, the recent age-classified kinship model of Caswell (2019a). As an application, we derive a model that includes age and parity. We obtain, for all types of kin, the joint age×parity structure, the marginal age and parity structures, and the (normalized) parity distributions, at every age of the focal individual. We show how to use the age×parity distributions to calculate the distributions of sibship sizes of kin.As an example, we apply the model to Slovakia (1960–2014). The results include a dramatic shift in the parity distribution as the frequency of low-parity kin increased and that of high-parity kin decreased.ContributionThe new model extends the formal demographic analysis of kinship to age×stage-classified models. In addition to parity, other stage classifications, including marital status, maternal age effects, and sex are now open to analysis.

Demographic methods in epidemiology

2021 ◽  
pp. 351-362
Author(s):  
Petra Klepac ◽  
C. Jessica E. Metcalf
Keyword(s):  
Infectious Disease ◽  
Life Stage ◽  
Stage Structure ◽  
Population Modelling ◽  
Disease Epidemiology ◽  
Infectious Disease Epidemiology ◽  
Structured Population ◽  
The Face ◽  
Demographic Methods ◽  
Host Mortality

Demography is both shaped by and shapes infectious disease dynamics. Infectious pathogens can increase host mortality. Host birth rates introduce new susceptible individuals into the population, which allows infections to persist in the face of the depletion of susceptible individuals that can result from mortality or immunity that can follow infection. Many important processes in infectious disease epidemiology, from transmission to vaccination, vary as a function of age or life stage. Epidemiology thus requires demographic methods. This chapter introduces broad expectations for patterns emerging from the intersection between demography and epidemiology and presents a set of structured population modelling tools that can be used to dissect important processes, including next generation methods, and estimation of R0 in the context of stage structure and with important differences in time-scale between host demography and pathogen life cycle.

scholarly journals Persistence for a Two-Stage Reaction-Diffusion System

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 396 ◽  
Author(s):  
Robert Stephen Cantrell ◽  
Chris Cosner ◽  
Salomé Martínez
Keyword(s):  
Asymptotic Behavior ◽  
Reaction Diffusion ◽  
Stage Structure ◽  
Positive Equilibrium ◽  
Small Diffusion ◽  
Structured Population ◽  
Reaction Diffusion Model ◽  
Linearized System ◽  
Diffusion Rates ◽  
Reproductive Rates

In this article, we study how the rates of diffusion in a reaction-diffusion model for a stage structured population in a heterogeneous environment affect the model’s predictions of persistence or extinction for the population. In the case of a population without stage structure, faster diffusion is typically detrimental. In contrast to that, we find that, in a stage structured population, it can be either detrimental or helpful. If the regions where adults can reproduce are the same as those where juveniles can mature, typically slower diffusion will be favored, but if those regions are separated, then faster diffusion may be favored. Our analysis consists primarily of estimates of principal eigenvalues of the linearized system around ( 0 , 0 ) and results on their asymptotic behavior for large or small diffusion rates. The model we study is not in general a cooperative system, but if adults only compete with other adults and juveniles with other juveniles, then it is. In that case, the general theory of cooperative systems implies that, when the model predicts persistence, it has a unique positive equilibrium. We derive some results on the asymptotic behavior of the positive equilibrium for small diffusion and for large adult reproductive rates in that case.

On a Model Representing Stage-Structured Population Growth with State-Dependent Time Delay

1997 ◽  
Vol 05 (04) ◽  
pp. 469-488 ◽  
Author(s):  
Ashraf Fathallah ◽  
Ovide Arino
Keyword(s):  
Total Population ◽  
Stage Structure ◽  
Single Species ◽  
Maturation Period ◽  
New Model ◽  
Structured Population ◽  
Global Properties ◽  
State Dependent ◽  
Age Of Maturity ◽  
Positivity And Boundedness

A new model for the growth of a single-species with a two-stage structure is developed employing a state-dependent age of maturity. The paper discusses some remarks in a previous model where the time to maturity is state dependent. Then, we present a new model which is mainly based on making the maturation period of juveniles depend on the total population size not at the present time t but at an earlier time stage, namely, the time when they were born. The paper considers both biological and mathematical aspects. Emphasis is given to the basic theory of the solutions, such as local and global properties of existence, uniqueness, positivity and boundedness.

“Preparation of Single Crystalline Gold Films for ED Studies”

1972 ◽  
Vol 30 ◽  
pp. 634-635
Author(s):  
Joseph D. C. Peng
Keyword(s):  
Crystal Morphology ◽  
Diffraction Theory ◽  
Scattering Matrix ◽  
Vacuum Evaporation ◽  
Gold Films ◽  
Matrix Formulation ◽  
Silver Films ◽  
Single Crystalline ◽  
Grating Pattern ◽  
Stacking Disorder

The relative intensities of the ED spots in a cross-grating pattern can be calculated using N-beam electron diffraction theory. The scattering matrix formulation of N-beam ED theory has been previously applied to imperfect microcrystals of gold containing stacking disorder (coherent twinning) in the (111) crystal plane. In the present experiment an effort has been made to grow single-crystalline, defect-free (111) gold films of a uniform and accurately know thickness using vacuum evaporation techniques. These represent stringent conditions to be met experimentally; however, if a meaningful comparison is to be made between theory and experiment, these factors must be carefully controlled. It is well-known that crystal morphology, perfection, and orientation each have pronounced effects on relative intensities in single crystals.The double evaporation method first suggested by Pashley was employed with some modifications. Oriented silver films of a thickness of about 1500Å were first grown by vacuum evaporation on freshly cleaved mica, with the substrate temperature at 285° C during evaporation with the deposition rate at 500-800Å/sec.

High Parity Poses the Greatest Risk for SIDS

2005 ◽  
Vol 39 (8) ◽  
pp. 40
Author(s):  
KERRI WACHTER
Keyword(s):  
High Parity

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

2005 ◽  
Vol 10 (4) ◽  
pp. 365-381 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Population Model ◽  
Local Stability ◽  
Deterministic Model ◽  
Random Mating ◽  
Spatial Diffusion ◽  
Neumann Problems ◽  
Structured Population ◽  
Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi
Keyword(s):  
Convex Polytopes ◽  
Polynomial Systems ◽  
Matrix Formulation ◽  
Bivariate Polynomials ◽  
Homogeneous Coordinates ◽  
The Matrix ◽  
Projective Vector ◽  
Coordinate Rings ◽  
Resultant Matrix ◽  
The Given

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

Less is more: Simple stimuli provoke more variable search strategies.

2020 ◽  
Author(s):  
Anna Nowakowska ◽  
Alasdair D F Clarke ◽  
Jessica Christie ◽  
Josephine Reuther ◽  
Amelia R. Hunt
Keyword(s):  
Line Segment ◽  
Search Strategies ◽  
Complex Objects ◽  
Search Behaviour ◽  
Line Segments ◽  
Surface Level ◽  
Efficient Search ◽  
Less Is More ◽  
Dramatic Shift

We measured the efficiency of 30 participants as they searched through simple line segment stimuli and through a set of complex icons. We observed a dramatic shift from highly variable, and mostly inefficient, strategies with the line segments, to uniformly efficient search behaviour with the icons. These results demonstrate that changing what may initially appear to be irrelevant, surface-level details of the task can lead to large changes in measured behaviour, and that visual primitives are not always representative of more complex objects.

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