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en:ecovirt:roteiro:den_ind:di_ed_base [2017/09/19 17:56] melina.leite |
en:ecovirt:roteiro:den_ind:di_ed_base [2022/09/19 13:43] (current) |
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===== Only deaths ===== | ===== Only deaths ===== | ||
- | Let's start with a population of $N_0$ individuals in which there are no births and no migration. Individuals die at a //per capita// [[ecovirt:roteiro:den_ind:di_rcmdr#taxa_instantanea_de_crescimento|instantaneous rate]] of $\mu = 0,693 \ \text{yr}^{-1}$. The simplest model to figure out the population size over time is the [[ecovirt:roteiro:den_ind:di_rcmdr|exponentia modell]]: | + | Let's start with a population of $N_0$ individuals in which there are no births and no migration. Individuals die at a //per capita// [[ecovirt:roteiro:den_ind:di_rcmdr#taxa_instantanea_de_crescimento|instantaneous rate]] of $\mu = 0,693 \ \text{yr}^{-1}$. The simplest model to figure out the population size over time is the [[ecovirt:roteiro:den_ind:di_rcmdr|exponential model]]: |
$$N(t)=N_0e^{(\text{births}-\text{deaths})t} \ = \ N_0 e^{-0,693t}$$ | $$N(t)=N_0e^{(\text{births}-\text{deaths})t} \ = \ N_0 e^{-0,693t}$$ | ||
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We can test this by simulating several populations with initial size $N_0=20$ and averaging the time they take to reach $N=10$. Set the simulation to: | We can test this by simulating several populations with initial size $N_0=20$ and averaging the time they take to reach $N=10$. Set the simulation to: | ||
- | * ''Maximum time'': 3 | + | * ''Maximum time'': 3 |
- | * ''Number of simulations'': 1000 | + | * ''Number of simulations'': 1000 |
- | * ''Initial size'' : 20 | + | * ''Initial size'' : 20 |
- | * ''birth rate'' : 0 | + | * ''birth rate'' : 0 |
- | * ''death rate'': 0.693 | + | * ''death rate'': 0.693 |
The graph will be covered with lots of lines, but we are interested in the value of //Halving time//. Is it near the theoretical value? Now change the population initial size to 80, keeping the other options unchanged and run the simulation again. | The graph will be covered with lots of lines, but we are interested in the value of //Halving time//. Is it near the theoretical value? Now change the population initial size to 80, keeping the other options unchanged and run the simulation again. | ||
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====== To learn more ====== | ====== To learn more ====== | ||
- | * Renshaw, E. (1991). Modelling biological populations in space and time Cambridge University Press. //This tutorial is inspired on the second chapter of this book, which is a great introduction for stochastic models of births and deaths//. | + | * Renshaw, E. (1991). Modelling biological populations in space and time Cambridge University Press. //This tutorial is inspired on the second chapter of this book, which is a great introduction for stochastic models of births and deaths//. |
- | * Akçakaya H.R., Burgman M.A & Ginzburg, L.V. (1999). [[http://www.ramas.com/apppopn.htm|Applied population ecology - Principles and computer exercises using RAMAS EcoLab]]. //Another very didactic book, with computer exercises using the proprietary software [[http://www.ramas.com/ecolab.htm|RAMAS ecolab]]. The chapter two is a great introduction on the sources of stochasticity in population dynamics.// | + | * Akçakaya H.R., Burgman M.A & Ginzburg, L.V. (1999). [[http://www.ramas.com/apppopn.htm|Applied population ecology - Principles and computer exercises using RAMAS EcoLab]]. //Another very didactic book, with computer exercises using the proprietary software [[http://www.ramas.com/ecolab.htm|RAMAS ecolab]]. The chapter two is a great introduction on the sources of stochasticity in population dynamics.// |
- | * [[http://cmq.esalq.usp.br/BIE5781/doku.php?id=01-discretas:01-discretas|R tutorials]] about the discrete probability distributions, from the course on [[http://cmq.esalq.usp.br/BIE5781|Statistical Modeling]] of the graduate program in ecology from the University of São Paulo. These include tutorials about the binomial and negative binomial distributions. | + | * [[http://cmq.esalq.usp.br/BIE5781/doku.php?id=01-discretas:01-discretas|R tutorials]] about the discrete probability distributions, from the course on [[http://cmq.esalq.usp.br/BIE5781|Statistical Modeling]] of the graduate program in ecology from the University of São Paulo. These include tutorials about the binomial and negative binomial distributions. |