Populations
They describe the growth of a population at a constant rate. Therefore, there is no regulation associated with its growth. They are the simplest models of population dynamics, and they serve as a basis for other more complex models,
Here you will learn about the basic models of dense-independent dynamics. You will also understand the difference between a discrete and continuous time model, and how to make the equivalence between them.
These models predict that the rate at which the population grows is influenced by the size of the population. For example, population growth may be restricted by its overcrowding and resource constraints, or the population may have its mortality rate decreased by some clustering effect. We present here two models that represent these examples.
With the inclusion of the Allee effect, logistics now have more than one equilibrium point, with a sudden transition between them.
Models that classify individuals in a population by life stages, which can be age classes or developmental stages. Population changes due to class stay, class change, or death.
The growth of an age-structured population can be projected using matrix algebra. Leslie matrices contain information about the birth and death rates of different age groups in a population and are a robust way of calculating population growth and making population projections for different scenarios. A generalization of the Leslie matrix occurs when the population is classified by stages (Leftkovicth matrix), where an individual of a given class can, in addition to dying, growing and reproducing, remain in the same stage over time cycles. In this generalization, the basic vital rates (growth, survival and reproduction) are embedded in the values of the transition matrices where we compute the effect that each state (or size) class has on the others in the next time cycle. The objective of this exercise is to understand how we can treat structured populations with matrix models.
An important tool in matrix analysis is to understand how the probabilities of transition and permanence of each class affect population growth. Knowing which vital rates are most important for population stabilization or growth is a powerful tool, both for understanding different life history strategies and for managing threatened populations or for the sustainable use of plant resources. ….