Matt Miller: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=239
en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 26 Feb 2021 13:09:11 GMTFri, 26 Feb 2021 13:09:11 GMTNew applications published by Matt Millerhttps://www.maplesoft.com/images/Application_center_hp.jpgMatt Miller: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=239
Density dependent natural selection
https://www.maplesoft.com/applications/view.aspx?SID=3895&ref=Feed
This worksheet is explores the paper Jonathan Roughgarden, 1971, Density dependent natural selection , Ecology 52 : 453-468, in which Roughgarden merges population genetics with population ecology.<img src="https://www.maplesoft.com/view.aspx?si=3895//applications/images/app_image_blank_lg.jpg" alt="Density dependent natural selection" style="max-width: 25%;" align="left"/>This worksheet is explores the paper Jonathan Roughgarden, 1971, Density dependent natural selection , Ecology 52 : 453-468, in which Roughgarden merges population genetics with population ecology.https://www.maplesoft.com/applications/view.aspx?SID=3895&ref=FeedWed, 20 Jun 2001 00:00:00 ZMatt MillerMatt MillerGraphical analysis of the chemostat equations
https://www.maplesoft.com/applications/view.aspx?SID=3850&ref=Feed
Graphical analysis of the chemostat equations for modeling population biology<img src="https://www.maplesoft.com/view.aspx?si=3850/450.jpg" alt="Graphical analysis of the chemostat equations" style="max-width: 25%;" align="left"/>Graphical analysis of the chemostat equations for modeling population biologyhttps://www.maplesoft.com/applications/view.aspx?SID=3850&ref=FeedWed, 20 Jun 2001 00:00:00 ZMatt MillerMatt MillerDemography of the vegetable ivory palm Pytelephas seemanii in Colombia, and the impact of seed harvesting
https://www.maplesoft.com/applications/view.aspx?SID=3626&ref=Feed
This paper is an analysis of a stage-based model of the dynamics of a palm tree species, using, a modification of the Leslie model. In this case, the assumption is that the stage of an organism (size class) is a better indicator of reproductive performance and survival than age is. This assumption works well for many plants, and any organism in which size is correlated with survival and fecundity. <img src="https://www.maplesoft.com/view.aspx?si=3626//applications/images/app_image_blank_lg.jpg" alt="Demography of the vegetable ivory palm Pytelephas seemanii in Colombia, and the impact of seed harvesting " style="max-width: 25%;" align="left"/>This paper is an analysis of a stage-based model of the dynamics of a palm tree species, using, a modification of the Leslie model. In this case, the assumption is that the stage of an organism (size class) is a better indicator of reproductive performance and survival than age is. This assumption works well for many plants, and any organism in which size is correlated with survival and fecundity. https://www.maplesoft.com/applications/view.aspx?SID=3626&ref=FeedMon, 18 Jun 2001 00:00:00 ZMatt MillerMatt MillerPod-specific demography of killer-whales
https://www.maplesoft.com/applications/view.aspx?SID=3625&ref=Feed
This paper is an analysis of a stage-based model of the dynamics of killer whales, a modification of the Leslie model. In this case, the assumption is that the stage of an organism (yearling, juvenile, mature female, post-reproductive female) is a better indicator of reproductive performance and survival than age is. This assumption works well for many plants, and any organism in which size is correlated with survival and fecundity<img src="https://www.maplesoft.com/view.aspx?si=3625//applications/images/app_image_blank_lg.jpg" alt="Pod-specific demography of killer-whales" style="max-width: 25%;" align="left"/>This paper is an analysis of a stage-based model of the dynamics of killer whales, a modification of the Leslie model. In this case, the assumption is that the stage of an organism (yearling, juvenile, mature female, post-reproductive female) is a better indicator of reproductive performance and survival than age is. This assumption works well for many plants, and any organism in which size is correlated with survival and fecundityhttps://www.maplesoft.com/applications/view.aspx?SID=3625&ref=FeedMon, 18 Jun 2001 00:00:00 ZMatt MillerMatt MillerEvolutionarily stable strategies
https://www.maplesoft.com/applications/view.aspx?SID=3610&ref=Feed
Consider a population in which there are conflicts. Each individual has fitness w prior to the conflict, and its fitness changes after the conflict. The average fitness of an individual is its baseline fitness plus the fitness change resulting from an encounter with another individual, weighted by the probability of such an encounter. For a population with 2 types of individuals, H and D, in proportion p and (1-p) in the population, the fitness wh of type H individuals is dependent upon the fitness change ehh associated with encountering another H individual ( the probability of such an encounter is p), and the fitness change ehd associated with encountering a D individual (the probability of such an encounter is 1-p):
<img src="https://www.maplesoft.com/view.aspx?si=3610//applications/images/app_image_blank_lg.jpg" alt="Evolutionarily stable strategies" style="max-width: 25%;" align="left"/>Consider a population in which there are conflicts. Each individual has fitness w prior to the conflict, and its fitness changes after the conflict. The average fitness of an individual is its baseline fitness plus the fitness change resulting from an encounter with another individual, weighted by the probability of such an encounter. For a population with 2 types of individuals, H and D, in proportion p and (1-p) in the population, the fitness wh of type H individuals is dependent upon the fitness change ehh associated with encountering another H individual ( the probability of such an encounter is p), and the fitness change ehd associated with encountering a D individual (the probability of such an encounter is 1-p):
https://www.maplesoft.com/applications/view.aspx?SID=3610&ref=FeedMon, 18 Jun 2001 00:00:00 ZMatt MillerMatt MillerPopulation growth and the earth's human carrying capacity
https://www.maplesoft.com/applications/view.aspx?SID=3550&ref=Feed
Population growth and the earth's human carrying capacity is the focus of this application. The annual rate of increase of the earth's population was 0.04% per year from AD 1 to 1650, rose to a peak of 2.1% per year around 1965-1970, and is now 1.6%. What are the consequences of these differences in rates? <img src="https://www.maplesoft.com/view.aspx?si=3550//applications/images/app_image_blank_lg.jpg" alt="Population growth and the earth's human carrying capacity " style="max-width: 25%;" align="left"/>Population growth and the earth's human carrying capacity is the focus of this application. The annual rate of increase of the earth's population was 0.04% per year from AD 1 to 1650, rose to a peak of 2.1% per year around 1965-1970, and is now 1.6%. What are the consequences of these differences in rates? https://www.maplesoft.com/applications/view.aspx?SID=3550&ref=FeedMon, 18 Jun 2001 00:00:00 ZMatt MillerMatt MillerCompetition models
https://www.maplesoft.com/applications/view.aspx?SID=3549&ref=Feed
The basic theory of competition is discussed in this application where the 'effective carrying capacity' of the environment in this case is reduced by the presence of competitors for resources.
<img src="https://www.maplesoft.com/view.aspx?si=3549//applications/images/app_image_blank_lg.jpg" alt="Competition models " style="max-width: 25%;" align="left"/>The basic theory of competition is discussed in this application where the 'effective carrying capacity' of the environment in this case is reduced by the presence of competitors for resources.
https://www.maplesoft.com/applications/view.aspx?SID=3549&ref=FeedMon, 18 Jun 2001 00:00:00 ZMatt MillerMatt MillerImplementation of Euler's Method in Population Growth Models
https://www.maplesoft.com/applications/view.aspx?SID=3548&ref=Feed
Manually implements Euler's method for solving differential equations numerically, using population growth as a working example. We look at two simple models of population growth for a bunch of (pseudo-)rabbits. To distinguish them, we use R and S to denote the respective rabbit populations. Both begin with size 10, and both have intrinsic (per capita) rate of increase r = 0.1.
<img src="https://www.maplesoft.com/view.aspx?si=3548//applications/images/app_image_blank_lg.jpg" alt="Implementation of Euler's Method in Population Growth Models" style="max-width: 25%;" align="left"/>Manually implements Euler's method for solving differential equations numerically, using population growth as a working example. We look at two simple models of population growth for a bunch of (pseudo-)rabbits. To distinguish them, we use R and S to denote the respective rabbit populations. Both begin with size 10, and both have intrinsic (per capita) rate of increase r = 0.1.
https://www.maplesoft.com/applications/view.aspx?SID=3548&ref=FeedMon, 18 Jun 2001 00:00:00 ZMatt MillerMatt MillerMathematical treatment of competition theory
https://www.maplesoft.com/applications/view.aspx?SID=3546&ref=Feed
This application describes Volterra's proposal of two logistically growing species having rates of increase that were determined by their own as well as their competitors' abundance<img src="https://www.maplesoft.com/view.aspx?si=3546//applications/images/app_image_blank_lg.jpg" alt="Mathematical treatment of competition theory" style="max-width: 25%;" align="left"/>This application describes Volterra's proposal of two logistically growing species having rates of increase that were determined by their own as well as their competitors' abundancehttps://www.maplesoft.com/applications/view.aspx?SID=3546&ref=FeedMon, 18 Jun 2001 00:00:00 ZMatt MillerMatt MillerHopf bifurcation in a predator-prey model
https://www.maplesoft.com/applications/view.aspx?SID=3502&ref=Feed
The behavior of the solutions of a Dynamic System is often strongly dependent upon its parameters. As one varies a parameter continuously, equilibrium points can come and go, spawning limit cycles which then may survive or fade away. An example is Hopf Bifurcation in a predator-prey model. Using animation, we examine the bifurcation as a parameter changes, first with a single trajectory and then with multiple trajectories. Finally, a two-variable animation is created which shows how another parameter in the system affects the bifurcation.<img src="https://www.maplesoft.com/view.aspx?si=3502//applications/images/app_image_blank_lg.jpg" alt="Hopf bifurcation in a predator-prey model" style="max-width: 25%;" align="left"/>The behavior of the solutions of a Dynamic System is often strongly dependent upon its parameters. As one varies a parameter continuously, equilibrium points can come and go, spawning limit cycles which then may survive or fade away. An example is Hopf Bifurcation in a predator-prey model. Using animation, we examine the bifurcation as a parameter changes, first with a single trajectory and then with multiple trajectories. Finally, a two-variable animation is created which shows how another parameter in the system affects the bifurcation.https://www.maplesoft.com/applications/view.aspx?SID=3502&ref=FeedMon, 18 Jun 2001 00:00:00 ZMatt MillerMatt MillerDynamics of arthropod predator-prey systems
https://www.maplesoft.com/applications/view.aspx?SID=3501&ref=Feed
This application describes the dynamics of arthropod predator-prey systems where the first part explores the standard density independent and dependent models. The second part is concerned with a more general (algebraic) eigenvalue analysis of both the original and the density dependent models. The last part investigates the stability analysis from a graphical point of view, giving an idication why the jacobian matrix is used. <img src="https://www.maplesoft.com/view.aspx?si=3501//applications/images/app_image_blank_lg.jpg" alt="Dynamics of arthropod predator-prey systems" style="max-width: 25%;" align="left"/>This application describes the dynamics of arthropod predator-prey systems where the first part explores the standard density independent and dependent models. The second part is concerned with a more general (algebraic) eigenvalue analysis of both the original and the density dependent models. The last part investigates the stability analysis from a graphical point of view, giving an idication why the jacobian matrix is used. https://www.maplesoft.com/applications/view.aspx?SID=3501&ref=FeedMon, 18 Jun 2001 00:00:00 ZMatt MillerMatt MillerBiological populations and ecological models
https://www.maplesoft.com/applications/view.aspx?SID=3500&ref=Feed
This Maple worksheet is designed to illustrate two papers: Biological populations with nonoverlapping generations: stable points, stable cycles and chaos and Bifurcations and dynamic complexity in simple ecological models.<img src="https://www.maplesoft.com/view.aspx?si=3500//applications/images/app_image_blank_lg.jpg" alt="Biological populations and ecological models" style="max-width: 25%;" align="left"/>This Maple worksheet is designed to illustrate two papers: Biological populations with nonoverlapping generations: stable points, stable cycles and chaos and Bifurcations and dynamic complexity in simple ecological models.https://www.maplesoft.com/applications/view.aspx?SID=3500&ref=FeedMon, 18 Jun 2001 00:00:00 ZMatt MillerMatt MillerBiological populations with non-overlapping generations: stable points, stable cycles and chaos
https://www.maplesoft.com/applications/view.aspx?SID=3499&ref=Feed
This worksheet on Biological populations with non-overlapping generations has three parts. In the first two parts we look at the model itself, and especially at the long term behaviour of the trajectories and how this may depend on initial conditions, growth parameters, etc. In section 1 we consider the dynamics of a single species; in section 2 we consider two competing species. The third part (originally bifurc.ms) introduces the idea of a bifurcation diagram, which is a record of the repeated "stable points" that occur for different growth parameter values.<img src="https://www.maplesoft.com/view.aspx?si=3499//applications/images/app_image_blank_lg.jpg" alt="Biological populations with non-overlapping generations: stable points, stable cycles and chaos" style="max-width: 25%;" align="left"/>This worksheet on Biological populations with non-overlapping generations has three parts. In the first two parts we look at the model itself, and especially at the long term behaviour of the trajectories and how this may depend on initial conditions, growth parameters, etc. In section 1 we consider the dynamics of a single species; in section 2 we consider two competing species. The third part (originally bifurc.ms) introduces the idea of a bifurcation diagram, which is a record of the repeated "stable points" that occur for different growth parameter values.https://www.maplesoft.com/applications/view.aspx?SID=3499&ref=FeedMon, 18 Jun 2001 00:00:00 ZMatt MillerMatt MillerPredator-prey models
https://www.maplesoft.com/applications/view.aspx?SID=3498&ref=Feed
Using Maple's DEtools, this application studies solutions of the Lotka-Volterra system and its refinements.<img src="https://www.maplesoft.com/view.aspx?si=3498//applications/images/app_image_blank_lg.jpg" alt="Predator-prey models" style="max-width: 25%;" align="left"/>Using Maple's DEtools, this application studies solutions of the Lotka-Volterra system and its refinements.https://www.maplesoft.com/applications/view.aspx?SID=3498&ref=FeedMon, 18 Jun 2001 00:00:00 ZMatt MillerMatt Miller