Tag Info

Hot answers tagged

21

The conservation biology literature has a great deal of information, particularly with reference to developing species survival plans (e.g., Traill et al. [2007] report a minimum effective population size of ~4,000 will give a 99% persistence probability of 40 generations). Because the question specifically mentions human populations, I'll focus my answer ...


17

A quick back-of-the-envelope answer to the number of generations that have passed since the estimated human-chimp split would be to divide the the split, approximately 7 million years ago (Langergraber et al. 2012), by the human generation time. The human generation time can be tricky to estimate, but 20 years is often used. However, the average number is ...


16

No, I don't think auto-regulation explain much in the population sizes of predators. Group selection may explain such auto-reagulation but I don't think it is of any considerable importance for this discussion. The short answer is, as @shigeta said "predators tend to starve to death as they are too many!" To have a better understanding of what @shigeta ...


10

Population dynamics occupies a whole subset of mathematical biology. Perhaps the most pragmatic uses for modelling population dynamics come from the fields of epidemiology for modelling disease infection and transmission through a population (one such article), or ecology modelling things like forestation, fishing dynamics, predator-prey relationships (an ...


8

Leonardo's already given you an excellent answer, but I thought I'd add my perspective. I'm a mathematical epidemiologist, so I'd at least like to believe these types of models are useful. For me, there are a number of things population dynamics models are especially useful for: Highlighting data requirements. Yes, models need data, as you've mentioned. ...


8

I think it does make sense - with a population density for finland that is so low, the disease with such a low beta cannot communicate to enough people to propagate. The number of people who have this disease will be fewer each week. I think this makes sense because at 16 / km^2, you can expect that practically nobody will ever see each other. This is ...


8

It is certainly possible to use general relationships to predict this. The relationship between population density/abundance and body size is an old topic in ecology, that fall within the field of allometrics (how different features of organisms scale with body size). Your assumption of a generally negative relationship between body size and abundance is ...


7

Two previous answers listed many applications of population dynamics models. I want to add that they are also important for conservation of endangered species. For example classical stage-class model (Crouse et al 1987, free copy) indicate that the most effective way to protect sea turtles is reducing mortality of large juveniles. Moreover, you don't have ...


6

it is impossible to know the exact number so here is my gross ballpark estimate of an upper bound - i.e. the maximum number of organisms that could have lived on earth in the extreme best case scenario. in practice it is probably much less, but this is to get an idea of what kind of numbers we are dealing with. The earth's volume is about 1.08321 * 10^12 ...


6

Mark-recapture is the most frequently used method for small mammals. It's best when combined with uncertainty estimates and population dynamics models (e.g. projection matrix). The fluctuations of small rodent populations have long fascinated scientists, and various models have been developed. Logistic regression models can be used to estimate likelihood ...


5

Remi.b's answer is an excellent one, and this should be taken as a supplement to it: It's possible your simulation is correct The Lotka-Volterra equations are what is known as a deterministic model, and it describes the behavior of predator-prey systems (in a somewhat simplified fashion) in large populations. Small populations are subject to what is known ...


5

One of the possible adjustments of these mathematical models is to introduce a "place to hide", making some (small) percent of the prey population not accessible (or much more difficult to access) for predators. After the number of predators decreases from starvation, prey individuals are relatively safer outside the "place to hide" and can grow over this ...


5

These equations describe how the haplotype frequencies will change over time due to a combination of recombination and natural selection. Before I proceed, I need to change your four $\delta X_i$ formulas above. Lewontin and Kojima (1960) writes the equations as: $$\Delta X_i = \frac{X_i(w_i - \bar w) \pm Drw_{14}}{\bar w}$$ where the minus sign is used ...


5

Your calculations are the following. Assuming non-overlapping generations, the number of ancestors you have in the last $t$ generation is given by: $$\sum_{i=1}^t 2^t$$ This sounds correct. But there are some very strong assumptions: Generations are non-overlapping. A more realistic model would need to consider $t$ as a continuous variable a give a ...


5

I guess you meant the population size stability. It is considered that the biosystems will increase their capacity of adaptation when evolving in very fluctuating environments. I believe the population stability is embedded in the adaptability of individuals. There is a measurement about it, evolvability, when the environment changes, the faster the ...


5

The chaotic behaviour you are referring to (at least the one described in your link in the comments) is a property of the discrete version of the logistic equation, where you get chaotic dynamics at growth rates above ~3.55 (see the logistic map). The behaviour of this equation has been described in a classic paper by Robert May (1976). As you increase ...


5

First of all, here is a program which simulates the evolution of the G-matrix over multiple generations, it's a few years old (they seem to have stopped developing it) and I've only played with it briefly. This could solve how to model the evolution of the G-matrix. Fisher's fundamental theorem is a great place to start off with the theory of this: The ...


4

This is a hard problem - estimates of total living things in an given environment are usually created by looking at the number of species and individuals found in a sample area and extrapolating. As far as estimating the number of living things in the world, there are still lots of species which are not known, making this number still unknown for the world ...


4

Classification of equilibrium points is done on the basis of the eigenvalues. If the two eigenvalues have no real parts, it is a hyperbolic fixed point and represents undamped oscillation. If both have a negative real part, it is a stable fixed point. If any of the eigenvalues has an imaginary part then it represents damped oscillations (in that case the ...


4

This is derived from studying how heterozygosity changes over time. The standard equation for change in heterozygosity ($H$) with constant population size ($N$) is: $H_t = \left(1 - \frac{1}{2N}\right)^tH_0$ When $N$ varies between generations you use the product of this formula: $H_t = \left(1 - \frac{1}{2N_0}\right)\left(1 - ...


4

You need to add Bell curves to your simulation. The most important curve to simulate is the nutritional quality of the prey though there are plenty more thing to curve like speed and virility for prey and predators both. Nature uses lots of Bell curves so they must be good for something, such as softening the harsh effects of pure exponential growth. I ...


4

An easy way to visualize the mistake in your thought experiment is to consider a bottleneck event, when the ancestral population was very small, maybe just a few individuals. This would mean that the entire current population is descending from just a few individuals. Your thought experiment is assuming that the "pyramid" of your ancentors is expanding all ...


4

Just need to solve the equation. p1 = X11 + X12; q1 = X11 + X21; 1 = X11 + X12 + X21 + X22. D = X11 - (X11 + X12) * (X11 + X21) D = X11 - (X11X11 + X11X21 + X11X12 + X12X21) D = X11 - X11X11 - X11X21 - X11X12 - X12X21 D = X11 * (1 - X11) - X11X21 - X11X12 - X12X21 D = X11 * (X11 + X12 + X21 + X22 - X11) - X11X21 - X11X12 - X12X21 D = X11 * (X12 + X21 + ...


4

Probably the best source to start would be Ilkka Hanksi's work, you can find a full list here: http://www.helsinki.fi/science/metapop/People/IlkkaPub2.htm. The seminal work would be "Ecology, Genetics and Evolution of Metapopulations" It gives a strong mathematical treatment


4

According to Hartl & Clark on population genetics: "Population genetics deals with Mendel's laws and other genetic principles as they apply to entire populations of organisms.... also includes the study of the various forces that result in evolutionary changes in species through time." According to Conner & Hartl also on population ...


4

Recap of the question: Looking at a single locus trait ($A$) controlled by two alleles, $A_1$ and $A_2$, the phenotypic mean is only affected by inbreeding depression, $f$ (Wright's inbreeding coefficient), if there is some degree of dominance, $d$. Why? Answer: If we take inbreeding as a higher than expected frequency of homozygotes, such that if the ...


4

There is one book that will perfectly suits your needs: A biologist's guide to Mathematical Modeling in Ecology and Evolution, by Sally Otto It is a very good book that is very easy to understand and in the meantime goes pretty far (It ends with the use of diffusion equation in Evolutionary Biology). I highly recommend it. It covers: How to create a ...


4

This book "A primer of conservation genetics" would suit quite well I think. In particular chapter five deals with "Genetics and Extinction" and is preceded by a lot of population genetics based theory. A beginner might also combine it with "A primer of ecological genetics" (Hartl & Conner) but you seem to have enough Pop gen knowledge to not need it! ...


4

I am presenting a speculative approach since nobody has mentioned about any existent models yet. Assuming that selection is based on performance in certain tasks; performance is a function of traits which in-turn is a function of genotype. Performance is a non-linear function of genotype and selection imposes a cutoff/bandpass filter on the performance ...


4

First of all, the $\mu$ is not expected time for a mutation to occur and get fixed; it is the rate at which mutations are fixed in the population. The basic result states that if neutral mutations arise at a locus at rate $\mu$ within individuals, mutations at this locus will be fixed in the population at rate $\mu$ as well. The expected time for a given ...



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