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Reproductive Potential
Selected Protocol Calculations
(Re: page 65 in the lab manual)  

General Background
Imaginary organisms called maldars live on a tiny, imaginary tropical island which just happens to be exactly like this laboratory but without a ceiling or walls. Although there are other plants on the island, maldars feed exclusively on thuswin nectar. Thuswins are an imaginary flowering plant, constructed just for this lab exercise. There is plenty of water on the island, and the maldars have no diseases or predators affecting them. In fact, the only limitation on the size of their population is the availability of thuswins. From hatching until egg laying time in the fall, a maldar requires five thuswins to survive.

Thuswins only grow on horizontal surfaces. In a good year, each square meter can support ten of them. The plants begin to bloom when the first maldar eggs begin hatching, and they don't go to seed until after the maldars lay their eggs. The soil on this island contains all the nutrients the thuswins will need, but their population density does vary from year to year mostly due to the weather. In one particularly bad year their average density was only one per square meter.

 1.       Calculate how many square meters of thuswin habitat are on this island? For purposes of this lab exercise, let’s assume the “island” is: 10m x 12m  or 120m²

2.       Assuming seven good years in a row (with thuswin populations of 10/m²) and starting with a single pair of maldars, plot a graph showing how their population changes over the next seven years.

With ten thuswins per m² ,  the island can grow 10 thuswins/m2 x 120 m² or 1200 thuswins.  In nature, there will be many more factors that influence the population that an area can support (the carrying capacity) than just the food supply. In this example, however, we are considering the food supply as the only limiting factor. Since each maldar requires 5 thuswins, the carrying capacity of the island is 1200 thuswins ¸ 5 thuswins/maldar or 240 maldars. The graph looks like this:

Beginning with just one pair of maldars, the population doubles each year for the seven good years. It reaches 128 maldars by the seventh year and this is still within the carrying capacity of the island.

 3.       Starting with a single pair of maldars, plot a graph showing how their population changes from year to year in the seven years when the average numbers of thuswins per square meter are: 3.0, 3.5, 3.2, 3.7, 3.3, 4.0 and 3.6.

First calculate the number of maldars these thuswins can support (i.e., the carrying capacity) for each of the years.  Then see what happens to the maldar population in these not-so-good years.

Ypo can see the maldar population did not reach it full potential of 128 organisms this time: the population stopped growing at 86 organisms, the limit set by the food supply.

Carrying the study further for a few more years having similar thuswin crops, we see how the food supply sets a ceiling on population size.

The maldar population has the reproductive potential to double each year, and it does double each year for the first six years. But, in the seventh year, there is only enough food to support 86 maldars. Of the 128 animals born that year, only 86 survive. Those eighty-six produce 168 offspring, but the limited food supply holds the actual survivors to 110 (the other 58 die). The struggle for existence begins in year seven when the organisms are competing for the limited food supply.