How many probability distributions can we generate by imagining simple natural processes? In this post I use a simple binomial random number generator to produce different random variables with a variety of distributions. Using built in probability densities functions in R, I show how the simulated data (plot bars) approach the exact probability density (plot lines) and provide an intuitive interpretation of model parameters of commonly encountered distributions.
A biological example “Nothing in Biology Makes Sense Except in the Light of Evolution” - Theodosius Dobzhansky, 1973

For a given species, a simple mortality response to environmental conditions can represented with the probabilistic outcome (death), which occurs with probabilty (p). This simple process is know as a Bernoulli random variable.
A motivating example is how a pest responds to increasing doses of a pesticide. Invertebrate pests cause 10-20% of yield losses in modern food systems. While cultural practices such as crop rotatation and biological control through beneficial insects increasingly form a core component of effective and sustainable management, pesticides remain a widely used tool.

What if a growing population gets eaten by another population?
In a previous post I showed why we might expect a population to grow exponentially when not resource limited. We then extended this to the case where a population reaches some carrying capacity (using a simple and non-mechanistic logistic function).
But population growth can also be curtailed through interactions with another species population, such as a predator. In my area of study, we deal with a lot of herbivorous pests of agricultural systems.

Let’s derive some more population growth functions!
The logistic population growth function In a previous post we derived a function for population growth based on the vital rates of reproduction and mortality. We assumed that the growth rate was constant with respect to the number of individuals in the population or (\frac{dt}{dN} = rN). This led to the unrealistic prediction that populations will grow indefinitely. Of course, populations will eventually run into resource problems (e.

Let’s derive some population growth functions!
How to grow Populations grow. They grow positively, if rates of reproduction > mortality, or negatively, if reproduction < mortality. For an unconstrained population of size (N) this diffence in per capita reproduction and mortality is referred to as the intrinsic growth rate, (r) and has the units individuals per individual per time (N.N^{-1}.t^{-1}) . The value of (r) is a constant if the age-distribution is constant (e.

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