Population Growth

Have you ever considered the environmental effects of farm-raised, or wild-caught fish? We can study the ecological impacts of these practices, by looking at population growth. A group of individuals of a single species, living in an area at the same time, is called a population.

In nature, fish populations grow at a high rate, when resources are plentiful. However, population growth slows down when its size nears the carrying capacity, k, which is the maximum population size allowed by the resources in a habitat. This type of population growth is known as logistic growth. If we know the population size of the current generation, or Nt, the maximum growth rate, r-max, which is the reproductive rate of one individual when no competition exists, and the carrying capacity, we can use the logistic growth formula to estimate the population size of the next generation.

At fish farms, resources like extra food and oxygen are artificially added to a relatively small living area, allowing population densities above natural carrying capacities. However, overcrowding releases excess biomaterials, and this can lead to algal blooms. If these resources remain high, cyanobacteria, or blue-green algae can continue to divide at the same growth rate. And this growth is not limited to a carrying capacity. Due to the continuous increase of resources. Therefore, it increases exponentially, and the size of the next generation in exponential growth can be calculated using this formula. Algal blooms like this deplete dissolved oxygen in the water and are detrimental to farmed fish and the ecosystem around the facility, necessitating cautious farming practices.

Fishing wild populations may impact ecosystems as well. If fishermen remove individuals faster than the population can replenish them with new fish, then the populations become smaller, and may struggle to rebound if predation pressure continues at the same rate. This may, in turn, disrupt the balance between predator and prey species. Scientists can estimate the sizes of future prey and predator populations, or Vt +1, and Ct +1, respectively, as long as they know current sizes of both populations, Vt and Ct, predator and prey growth rates, f, and r, and the predators' attack and starvation rates, a, and q. Typically, a large predator population reduces the prey population size. But then, the smaller available pool of prey will in turn reduce the predator population. Having less predators allows prey to thrive again, and the two populations will naturally oscillate back and forth, over time. The oscillation rule is a good way to visualize many natural predator-prey interactions, but, occasionally, the rule does not apply.

In invasive species, like the lionfish in the Atlantic and the Caribbean, far from their native waters of the Indo-Pacific oceans, they have no natural predators, and can reproduce all year long. But as a generalist predator, the consume numerous native species at unsustainable rates, permanently altering the Atlantic and Caribbean ecosystems. Applying the exponential growth model, that we saw in the algae example, scientists determined that approximately one quarter of the entire lionfish population would have to be removed every month, to keep their growth sustainable. Therefore, eating wild-caught Atlantic lionfish, and other edible invasive species, actually supports the health of the ecosystems.