Expanding the view on the production and dietary diversity link: Scale, function, and change over time

Biodiversity describes the variety of living things at multiple organizational levels: genetic, species and ecosystem diversity. Species diversity includes all branches of the evolutionary tree from single-celled prokaryotic organisms, bacteria, and archaea, to the eukaryotic kingdoms: plants; animals; fungi; and protists. To date, there have been about 1.75 million species identified, and new species are discovered every week.

An increasing function exhibits a rise in output values as input values increase. This behavior is depicted graphically as a curve or line that slopes upward from left to right. Such a function satisfies the condition that if x1 < x2, then f(x1) < f(x2), indicating that the function values grow with increasing inputs. This concept is fundamental in understanding growth trends across various domains, such as population dynamics, financial investments, or resource consumption.The...

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.

How animals obtain and eat their food is called foraging behavior. Foraging can include searching for plants and hunting for prey and depends on the species and environment.

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

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