## Fanciful mathematics and ecological fantasy

3 05 2010

Bear with me here, dear reader – this one’s a bit of a stretch for conservation relevance at first glance, but it is important. Also, it’s one of my own papers so I have the prerogative :-)

As some of you probably know, I dabble quite a bit in population dynamics theory, which basically means examining the mathematics people use to decipher ecological patterns. Why is this important? Well, most models predicting extinction risk, estimating optimal harvest rates, determining minimum viable population size and metapopulation dynamics for species’ persistence rely on good mathematical abstraction to be realistic. Get the maths wrong, and you could end up overharvesting a species (e.g., 99.99 % of fisheries management), underestimating extinction risk from habitat degradation, and getting your predictions wrong about the effects of invasive species. Expressed as an equation itself, (conservation) ecology = mathematics.

A long-standing family of models known as ‘phenomenological’ models (i.e., because they deal with the phenomenon of population size which is an emergent property of the mechanisms of birth, death and immigration) has been used to estimate everything from maximum sustainable yield targets, temporal abundance patterns, wildlife management interventions, extinction risk to epidemiological patterns. The basic form of the model describes the growth response, or the relationship between the population’s rate of change (growth) and its size. The simplest form (known as the Ricker), assumes a linear decline in population growth rate (r) as the number of individuals increases, which basically means that populations can’t grow indefinitely (i.e., they fluctuate around some carrying capacity if unperturbed). Read the rest of this entry »