Questions tagged [population-dynamics]

The scientific study of short- and long-term changes in the size and age composition of populations and the processes driving these changes.

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Finding genotype/allele frequencies of second generation in Hardy-Weinberg equilibrium given that the recessive allele is deleterious [duplicate]

A population in Hardy-Weinberg equilibrium has p=0.6 and q=0.4, and allele q (recessive) is deleterious. If 25% of heterozygous individuals and 50% of homozygous recessive individuals die before ...
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What proportion of the people who lived 1000 years ago have genetic descendants alive today?

For context, I've been wondering about this for a paper I'm writing (in philosophy). Really, I want to figure out the chances that someone alive today will end up still having descendants 1000 years ...
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Classes of Graphs used in Biology

I am a student of Mathematics.Since I found no better place to ask my question I post it here. I was looking for some classes of graphs which are used in biology. I came across this particular class ...
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How to check if a population density obeys replicator dynamics

Say we have a probability vector or population density $p = (p_1,...,p_n)$ with $p_i \geq 0$ and $\sum_i p_i =1$. Also assume we know the functions $g=(g_1,...,g_n)$ such that: $$p_i(t+1) = g_i(p(t))...
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Did the Broadbill Swordfish population fully recovered?

Regarding the Broadbill Swordfish Xiphias gladius: I read Richard Ellis "Swordfish: A Biography of the Ocean Gladiator", Chicago University Press, 2013. The chapter about industrial-strength fishing ...
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How do I determine this logistic growth model formula?

The Question Two yeast cells were placed into a special container to which food was continually added, to keep it at a constant concentration. All other factors were set for optimal yeast ...
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44 views

Does someone know of a website that keeps track of a species population?

I am planning on doing some math on population growth, but I need a reliable source of data on population growth of some species over time. Does anyone know of a resource (website/publications/public ...
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25 views

How should should I run a yeast experiment where I measure population growth?

Soon I will conduct an experiment involving the population growth of yeast. Nonetheless, I am not sure how long should I let my experiment running for, nor do I know at which intervals should I ...
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Two state exponential growth model

I want to write an expression to model exponential growth of a microbe that scholastically and irreversibly acquires a mutation at a fixed rate that slows growth. I can do it iteratively, but am ...
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Is there any example, where cooperative behaviour of predators induce fear in prey population?

I am basically from math background and doing Ph.D in mathematical biology. So I am not so efficient in biology. But my problem based on cooperative behaviour of animals during hunting which is ...
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52 views

Is a wild-type strain more “fit” than its mutant strains?

Question's context In the context of a presentation on mathematical models for antibiotic-resistance bacteria research, someone mentioned that wild type strain (WT) are expected to be more fit than ...
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Sampling of Species counting same member of species twice

As part of the biology class, we performed a sample on the number of red squirrels in a forest a few miles away from the classroom to estimate its population. When we returned to analyse our data, we ...
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315 views

Calculate growth rate of a population by Leslie matrix

We can calculate growth rate of a population by calculate the dominant eigen value of a Leslie matrix. What does this growth rate mean? I think that the growth rate N(t+1)/N(t) is depend on the age ...
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Genetic disease elimination: Possible?

This is a question having to do with my generation ship story but more specifically, genetics, and even more specifically, genetic disease. Here are the conditions as far as people with or without ...
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83 views

Spread of a benign virus in a population over time

This is a somewhat difficult (for me) population dynamics question and I wonder if someone with experience in this area could suggest a reasonable approach? My simplifying assumptions: As a gross ...
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131 views

How to give a biological interpretation to this phase portrait?

Consider the following system and analyze its behavior. $$\begin{array}{rl} \frac{dA}{dt} &= A \left( 2-\frac{A}{5000}-\frac{L}{100} \right)\\ \frac{dL}{dt} &= L \left(-\frac{1}{2}+\frac{...
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108 views

Mathematical model about the relationship between two animal species

I'd like to relate a mathematical model with two animal species. This is the model: $$ \begin{split} \frac{dN}{dt} & =rN-\frac{rN(N+M)}{k} \\ \frac{dM}{dt} & =r'M-\frac{r'M(N+M)}{k'} \end{...
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Value of r (intrinsic rate of natural increase)

What is the current value of 'r' (instrinsic rate of natural increase) in India? How do we calculate it? My book says that In 1981, the r value for human population in India was 0.0205. But this ...
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568 views

Do death rate and birth rate become equal at replacement fertility rate?

A population transitions from stage 3 to stage 4 when the fertility rate reaches the population replacement level of 2.1. My question is that if the population replacement level reached, shouldn't ...
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Human genetic diversity in Africa in comparison with the rest of the world

Background The claim ... Most of the genetic diversity in humans is in Africa ... is quite common. On Biology.SE, it is easy to find posts that make this claim. Consider for example: Do humans ...
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World population pyramid since 1800 [closed]

I am interested in understanding how the global population pyramid has changed in the last couple of centuries. I have two questions: 1) Has this been calculated? Are there estimates of population ...
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1answer
33 views

Properly changing the time scale of a parameter in a growth model

I have a two-population model, where one of the populations is a bacterial culture with its growth described as a logistic growth, with a reported growth rate of $2 \log\hbox{bacteria hour}^{-1}$ and ...
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Variance of Stochastic Growth Rate for Average Population Size Over Time

I'm interested in calculating the variance of the stochastic growth rate for the average population size over time, $$\ln \beta = \lim_{t\to\infty}\dfrac{1}{t}\ln V[N(t)]$$ which shows that the ...
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References concerning the relative population sizes of predator and prey

In an ecosystem, say there are two species in a predator-prey relationship. What is the most typical ratio of these species' population densities? For instance, it could be that for every fox, there ...
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What is the mechanism by which passive immunity works?

My idea is that passive immunity can be used to cure an individual who is infected with a certain disease. For example, for someone infected by clostridium tetani, you would inject them with an ...
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How can DNA profiling be used to determine the number of organisms from a specific species that is within a certain area?

Here is the tedious exam question that asks this: question 8(b). https://drive.google.com/drive/folders/0B23NLD5L6099VWJya3dfLVJpbmc The question states: In 2007, the brown bear was a threatened ...
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What is full form of r and K in r-selection species and K-selection species?

What is full form/ meaning of 'r' and 'K' in r-selection species and K-selection species? Does this 'r' means "Random" and the 'K' means "constant"?
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Is the basic reproduction number unique?

Given any epidemic model of an infectious disease, there are various ways of computing a basic reproduction number($R_0$) such as; the next-generation method, survival function, largest eigenvalue of ...
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243 views

Example of code with pypgen (python)

I have a VCF file and wish to calculate a few indices of population divergence over a sliding window. I consider using pypgen but the documentation is currently very limited. Can you please give me ...
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934 views

How can I measure bee and wasp population?

Bees and wasps in our garden disappeared suddenly last year - I asked a question about it at Why our bees might have suddenly disappeared. This year, I see that some bumblebees are active now. I'd ...
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139 views

Reproduction number of a SIR model with mortality

We know that reproduction number $\mathcal{R}_0$ is $\frac{\alpha}{\beta}$ for the following system, such that if $\mathcal{R}_0>1$, there is an epidemic in the population. Now, assume the system ...
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Is there a name for dominant-intraspecific competition?

Some ecological competition dynamics have particular names (e.g.: scramble competition, contest competition, ...). I wonder if there's such a name for competition dynamics where the interspecific ...
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68 views

Accurate surveys of urban pigeon and bird populations

I've been working on an assignment to develop mathematical models of urban pigeon populations. (As a disclaimer, this is part of a math course, not a biology course). I already understand the ...
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131 views

Why are there relatively more predators on the land than in the oceans? [closed]

Our biology teacher told us that among worse conditions one of the reason that intelligent life had actually evolved on land is that there is a more important selective pressure due to the bigger ...
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Calculation of Malthusian fertility and mortality from birth and death rates

In a simple Malthusian model, the population $p$ grows according to $p = p_0e^{rt}$, where $r = \beta - \mu$, $\beta$ is the "fertility" parameter and $\mu$ the "mortality" parameter. In the case of $\...
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441 views

What is a typical value of the selection coefficient s?

I am trying to gain an understanding of the real world effects of natural selection from the equations, especially comparing it with drift. However I have been unable to find any examples which give ...
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275 views

Parasite - host equations

The Lotka–Volterra equations describe how predator–prey interactions affect population growth. Do these equations describe parasite-host interactions? If not, how would they change by adding these ...
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Variance of frequency in expanding populations

I'm trying to understand the variance in frequency of some strain after some time as passed in a growing population. The idea is to then plug this in kolmorov foward equations and get the classic ...
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Modeling population growth - Variance

I've been studing population growth models, but there's something I can not find that's fustrating. That's a formula for the variance in population growth. I know that other models can be aplied, but ...
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Can we use differential equations for population that is discrete?

Population dynamics is often modeled using ODE. For example one common model is logistic growth model: $$\frac{dx}{dt} = k.x.\left(1-\frac{x}{C}\right)$$ where x is population size, k is rate ...
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Interspecies competition and pathogen

Following my answer to this question, a debate ensued on whether the loss in population of one species (namely red squirrels) due to its lesser resistance to a pathogen brought by a competing species (...
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Why our bees might have suddenly disappeared

We have a large garden in Bedfordshire, UK, next to woods and to arable fields currently planted with intensively farmed rape. We usually have many bees in the garden. Earlier this year, things were ...
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What happened to the gypsy moth epidemics in the Northeast US?

I remember that back in the 1980s, 1980-1984, gypsy moths were a veritable plague in the Northeast United States. They were literally everywhere. Sidewalks were covered with their squashed bodies (of ...
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doubt with a multiple choice question [closed]

Permanent decrease in population would occur due to- A) Migration B) Natality C) Emigration D) Mortality E) Territoriality . It's obvious that C) & D) options are possible . But I'm confused ...
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How much do urban pigeons move around cities?

Do they tend to live their lives in one area of the city or do they move around? For example, do pigeons born on London's Trafalgar Square live their whole lives centered around Trafalgar Square or ...
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1answer
178 views

Guide to learning about Population biology / ecology / dynamics for a non-Biologist

I'm an applied mathematician who works in the field of feedback control systems but has been becoming interested in looking at population biology (e.g. Lotka-Volterra, Mathusian growth,etc.) from a ...
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Population size and genetic drift - What are the evidences?

Wright-Fisher model From the Wright-Fisher model of genetic drift, the random sampling of allele from one generation to the next is taken from a binomial distribution with parameters $2N$ and $p$, ...
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Is $F_{ST}$ a probability and a correlation coefficient?

$F_{ST}$ is one of the most famous and most important statistics of all of evolutionary biology. Yet, many people misunderstand it or misuse the classical results from the literature on $F_{ST}$ (...
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Population dynamics ODE with Allee Effects

From reading about Allee effects, it appears that there is a modification of the one-dimensional logistic equation to account for an allee effect given by: $$\frac{dN(t)}{dt} = rN\left(1-\frac{N}{K} \...
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Would a colony with only one male and female collapse?

This is a thought experiment: If we form a population with only a single founder pair, can this population survive? What would happen? Would this inbreeding cause the population to go extinct? Could ...