prey. In 1925, the American mathematician Alfred J. Lotka developed simple equations for predator–prey interactions in his book on biomathematics. The following year, the Italian mathematician Vito Volterra, made a statistical analysis of fish catches in the Adriatic and independently developed the same equations. It is one of the earliest and most recognised ecological models, known as the Lotka-Volterra model: where N is the prey and P is the predator population sizes, r is the rate for prey growth, taken to be exponential in the absence of any predators, α is the prey mortality rate for per-capita predation (also called ‘attack rate’), c is the efficiency of conversion from prey to predator, and d is the exponential death rate for predators in the absence of any prey. Volterra originally used the model to explain fluctuations in fish and shark populations after fishing was curtailed during the First World War. However, the equations have subsequently been applied more generally. Other examples of these models include the Lotka-Volterra model of the snowshoe hare and Canadian lynx in North America, any infectious disease modeling such as the recent outbreak of SARS and biological control of California red scale by the introduction of its parasitoid, Aphytis melinus . A credible, simple alternative to the Lotka-Volterra predator–prey model and their common prey dependent generalizations is the ratio dependent or Arditi-Ginzburg model. The two are the extremes of the spectrum of predator interference models. According to the authors of the alternative view, the data show that true interactions in nature are so far from the Lotka–Volterra extreme on the interference spectrum that the model can simply be discounted as wrong. They are much closer to the ratio-dependent extreme, so if a simple model is needed one can use the Arditi–Ginzburg model as the first approximation. Host–pathogen interaction The second interaction, that of host and pathogen, differs from predator–prey interactions in that pathogens are much smaller, have much faster generation times, and require a host to reproduce. Therefore, only the host population is tracked in host–pathogen models. Compartmental models that categorize host population into groups such as susceptible, infected, and recovered (SIR) are commonly used. Host–parasitoid interaction The third interaction, that of host and parasitoid, can be analyzed by the Nicholson–Bailey model, which differs from Lotka-Volterra and SIR models in that it is discrete in time. This model, like that of Lotka-Volterra, tracks both populations explicitly. Typically,