21
votes
Why aren't native predators in Australia able to handle the mice problem?
The mice aren't invading Australia, they are invading the wheat producing zones, where the tractors are leveling the land and putting on pesticides. The local frog, amphibian and snake populations ...
- 10.3k
14
votes
Accepted
Is global life expectancy normally distributed?
Let's see!
I took the most recent WHO data from here and did a quick an dirty analysis in R. Here is the histogram as well as a normal distribution with the same mean and standard deviation as the ...
- 1,244
12
votes
Are there real world examples of one way isolation between two populations?
You might want to look for asymmetric dispersal.
Asymmetric dispersal has been found in many freshwater fishes (such as bullhead; Junker 2012), freshwater mussel (Terui et al., 2014) and in marine ...
- 68k
11
votes
Accepted
What is full form of r and K in r-selection species and K-selection species?
This article discusses the origin of the terms. They come directly from the equation used to describe population dynamics. As Canadianer mentioned the Wiki also covers it quite well.
"r" stands for "...
- 14.3k
8
votes
Accepted
Population dynamics ODE with Allee Effects
First, Allee effects (also positive density dependence) can be modelled in several different ways, and the equation you give is one example. The terms weak and strong Allee effects are in my ...
- 16.7k
8
votes
Why our bees might have suddenly disappeared
We call it Colony Collapse Disorder (CCD).
Consequences
The phenomenon is observed worldwide and is pretty serious. Northern Ireland lost 50% of its beehives for example. Between 1997 and 2003, 10 ...
- 68k
8
votes
Can we use differential equations for population that is discrete?
You can make the continuous approximation when the population size is large. As mentioned by arboviral, there are algorithms that allow you to perform stochastic simulations with discrete variables. ...
- 35.2k
8
votes
What is the mechanism by which passive immunity works?
I commented on this question, but the OP's response prompted me to think again. Here is the graph from the document that the OP linked to:
Clearly what is confusing is that the parameter referred to ...
- 22.7k
7
votes
What is the mechanism by which passive immunity works?
As Alan Boyd says, the relatively slow rise is due to gradual uptake of the injected antibody.
If you deliver the antibodies by intravenous injection or another mode that allows rapid uptake (I use ...
- 14.2k
7
votes
Accepted
Human genetic diversity in Africa in comparison with the rest of the world
Here is a tree based on mitochondrial DNA variations in human populations.
van Oven M, Kayser M. Hum Mutat. 2009 Feb;30(2):E386-94.
Updated comprehensive phylogenetic tree of global human ...
- 2,964
7
votes
Accepted
Understanding expected mean number of breeding seasons
It's just a continuous version of the discrete calculation. The discrete version is the (infinite series) sum
$$
\sum_{i = 0}^\infty S^i \cdot bp
$$
adding up every (chance of survival to season $i$) ...
- 1,709
7
votes
Understanding expected mean number of breeding seasons
I think your explanation is correct. The expected value of the exponential distribution is:
$$t \sim \text{e}^{-\lambda t} \implies \langle t \rangle = \int_0^\infty t \ \text{e}^{-\lambda t} \; \text{...
- 1,923
7
votes
Accepted
Refuge impact on growth rate
The answer to this depends a lot on what kind of question you're asking. Adding more context/clarifying your question might help you get more useful answers.
If you run a short-term experiment ...
- 5,324
6
votes
How do I determine this logistic growth model formula?
The growth of the yeast can be studied with a Logistic model (i.e. differential equation) as follows:
$$
\frac{dX}{dt}=\mu X \left(1 - \frac{X}{X_{max}} \right)
$$
This is an ordinary differential ...
5
votes
Stochastic parameters in population growth equations
Since you are asking for the biological interpretations about these parameters, it is important to realize that the model you are presenting is a non-dimensionalized version of this model:
$$ \frac{...
- 16.7k
5
votes
Can we use differential equations for population that is discrete?
I'd hardly call myself an expert on this topic by any stretch of the imagination, but you can actually come up with good approximations based on ODE-based models by rounding off to the nearest whole ...
5
votes
Human genetic diversity in Africa in comparison with the rest of the world
I've found two papers that provide some information on this, but no definitive answer.
The 1000 Genomes Project Consortium (2015) analysed whole genomes and found that "28% of novel variants" were ...
- 149
5
votes
Accepted
Mathematical model about the relationship between two animal species
The model you present here is a special case of the Lotka-Volterra competition equations, where the two species have the same effect on each other (i.e., symmetric competition). Some things to think ...
- 5,324
5
votes
Accepted
How is the carrying capacity of a logistic growth model calculated?
@Remi.b is correct that you haven't given us very much information, but I think we can reconstruct what's going on. Suppose the population growth rate is written out as
$$
\frac{dN}{dt} = N ( b - \...
- 5,324
5
votes
Accepted
What could be a refuge in host-parasitoid models
The most typical situation is a size refuge, i.e. prey/hosts that are too large or too small to attack (or possibly too small to be useful) are not attacked, or are attacked less, than hosts that are ...
- 5,324
4
votes
Accepted
Genetic Diversity and Adaptation
It is a good question. The question is hard to answer though because
The answer is not completely resolved
There are many influential parameters hidden behind this question.
Your question, as I ...
- 68k
4
votes
Is the Basic Reproduction Number in epidemiology dependent on population size?
From what I understand (as an ecologist/population modeller), $R_0$ in epidemiology is not dependent on host population size per se, at least not in its basic form. It is also not dependent on the ...
- 16.7k
4
votes
Would a colony with only one male and female collapse?
Populations founded by a single pair are quite common in the lab
The Drosophila Genetic Reference Panel, one such example of high artificial inbreeding, is a series of inbred lines where the ...
- 16k
4
votes
Is global life expectancy normally distributed?
A few people thought it would be interesting to see what the distribution looked like if we plotted the number of people dying at each age, so I took data from the SSA (which admittedly isn't global ...
- 470
4
votes
Accepted
What happened to the gypsy moth epidemics in the Northeast US?
It appears that the gypsy moths were controlled by pesticide spraying by the US Forestry Service.
The defoliation areas measured peaked at 12 million acres in 1981 and again at 7 million acres in ...
- 9,432
4
votes
Can we use differential equations for population that is discrete?
Yes, you can. For example, the Gillespie algorithm (Gillespie-Doob algorithm) generates a statistically correct trajectory of a discrete population from a system of differential equations. This is ...
- 3,346
4
votes
Modeling population growth - Variance
If $W$ is a parameter, I'd expect (in the simplest case) that $W$ itself is a constant (i.e. it doesn't have a distribution). (By the way, I would normally use $T_{1/2}$ to denote the doubling time, $\...
- 5,324
4
votes
Accepted
Modeling population growth - Variance
Check out Kendall (1949), section 2. He shows that the pdf is a geometric distribution. In your notation, it's $P_n(t) = N(0)W^{-t}\left(1-W^{-t}\right)^{n-1}$, which implies that the mean is indeed $...
- 641
4
votes
Value of r (intrinsic rate of natural increase)
NCERT shows per capita value is divided by 1000, not hundred (%). So the data you see is 22.50 per thousand! So, the per capita rate is 22.50/1000 = 0.02250 that is almost equal to 0.0205 given in ...
- 41
4
votes
What proportion of the people who lived 1000 years ago have genetic descendants alive today?
Expanding on @heracho's answer and Wikipedia, assume pi denotes the probability of having (exactly) i children, and that dm denotes the probability of extinction by the mth generation (note that this ...
- 141
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