The Calculus Diaries - Jennifer Ouellette [56]
A FUNGUS AMONG US
Deep in the forests of West Central Africa lurks a species of parasitic fungus that targets a particular kind of ant. The fungus belongs to the Cordyceps family, scattering spores into the air, which then attach to the ant’s body to germinate. The spores work their way inside the poor insect’s body, sprouting long tendrils called mycelia that eventually reach into the ant’s brain and release chemicals that make the ant the fungus’s zombie slave.
The chemicals change how the ant perceives critical pheromones, altering its behavior. In this case, the ant feels less inclined to devour delicious brains and is instead compelled to climb to the top of the nearest plant and clamp its tiny jaws around a leafy stem. It is the fungus that plays the role of zombie now, devouring what little remains of the insect’s brain, then sprouting through the ant’s head as one final indignity. Those sprouts burst and release even more spores into the air, which go forth to infect even more unsuspecting ants. The entire horrific process can take four to fourteen days. Fear the fungus, my friends.
There are over four hundred different species of Cordyceps fungi, each targeting a particular species of insect, whether it be ants, dragonflies, cockroaches, aphids, or beetles. Consider Cordyceps an example of Nature’s own population control mechanism to ensure that ecobalance is maintained. The fungus proliferates when there is a large supply of hosts—that is, when the ant population flourishes and becomes so large that it threatens to overwhelm the resources available to the colony. As more ants fall victim to zombifying spores, their numbers dwindle until (a) there are once again sufficient resources to support what remains of the colony, and (b) there are far fewer ants available to serve as hosts, making it more difficult for the fungi to reproduce, so their numbers dwindle as well. And the whole population growth-and-decline cycle begins all over again. That is the essence of population dynamics in a nutshell.
An English clergyman named Thomas Robert Malthus was one of the earliest pioneers in modeling population dynamics. Malthus was born with a harelip and cleft palate—defects that ran in the family—and was intensely self-conscious about his appearance as a result. He had an unremarkable childhood in the Surrey countryside, earning a mathematics degree from Cambridge University before being ordained as an Anglican curate.
Malthus bemoaned the decline of living conditions in late eighteenth-century England and observed that in nature, plants and animals were capable of reproducing at far greater rates than the surrounding resources could support. This led him to develop his classic theory on population: If human population were allowed to grow unchecked, it would do so exponentially, and we would all too quickly outstrip our limited resources for subsistence. He believed this fundamental truth had been obscured by catastrophic events like disease, famines, or wars, which serve periodically to cull the herd, so to speak. “Epidemics, pestilence and plague advance in terrific array, and sweep off their thousands and ten thousands,” he wrote with considerable dramatic flourish. “Should success be still incomplete, gigantic famine stalks in the rear, and with one mighty blow, levels the population with the food of the world.”
In 1798, Malthus published The Principle of Population, in which he outlined his model for population growth. It’s based on the notion that the population for a given generation is dependent on the size of the previous generation, and that this number will be a multiple. We can denote population size (p) as a function of time (t), where t can represent any unit of time we choose: days, months, years, and so forth. The key parameter