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 ...
bandybabboon's user avatar
  • 10.4k
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 ...
Remi.b's user avatar
  • 68.1k
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 "...
John's user avatar
  • 14.7k
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. ...
WYSIWYG's user avatar
  • 35.6k
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 ...
Remi.b's user avatar
  • 68.1k
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 ...
fileunderwater's user avatar
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 ...
Alan Boyd's user avatar
  • 22.8k
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 ...
iayork's user avatar
  • 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 ...
Willk's user avatar
  • 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 $i$) ...
Armand's user avatar
  • 1,711
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{...
Domen's user avatar
  • 1,932
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 ...
Ben Bolker's user avatar
  • 5,354
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 ...
Alejandro Vignoni's user avatar
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 ...
EJoshuaS - Stand with Ukraine's user avatar
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 ...
JCThomas's user avatar
  • 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 ...
Ben Bolker's user avatar
  • 5,354
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 - \...
Ben Bolker's user avatar
  • 5,354
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 ...
Ben Bolker's user avatar
  • 5,354
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 ...
rg255's user avatar
  • 16.1k
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 ...
Remi.b's user avatar
  • 68.1k
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 ...
March Ho's user avatar
  • 9,452
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 ...
arboviral's user avatar
  • 3,344
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 $...
Daniel Weissman's user avatar
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, $\...
Ben Bolker's user avatar
  • 5,354
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 ...
YASH PATHAK's user avatar
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 ...
Kahovius's user avatar
  • 141
4 votes

Overly stabilised population dynamics model

In a deterministic system, there are 2 options: equilibrium or collapse. It sounds like you've found an equilibrium. This is probably expected! Classic Lotka-Volterra makes specific deterministic ...
Maximilian Press's user avatar
3 votes
Accepted

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

I wouldn't say conditions on land are poorer... just more unstable, less predictable over a span of a million years. And an unstable environment appears to be one of the factors in the evolution of ...
JayCkat's user avatar
  • 2,926
3 votes

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

There are three seminal works that will give you an excellent grounding in the study of dynamical systems in population biology. The first details the foundations of population genetics: Crow, ...
Michael Andrew Bentley's user avatar
3 votes
Accepted

Interspecies competition and pathogen

No, you cannot for certain ascribe it to competition, without further information. The mediation by a pathogen is similar to the effects on prey species that are indirectly caused by shared predators (...
fileunderwater's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible