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FC001: The Grass Growth Rate

Dave Volek
Food Chain Inventor
March 2012
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Abstract

Many organisms can be divided into r-types and K-types. This experiment will determine which pattern the Food Chain grass follows more closely.

Objective

This experiment will determine whether the grass in the Food Chain simulation has an exponential growth characteristic, thus being classified as an r-selected organism. If it does, the experiment will identify the duration of this exponential growth. When the growth rate declines, this indicates the population is reaching the carrying capacity of the ecosystem.

Research

Organisms can be classified by their population growth patterns. R-selected organisms are characterized by early exponential growth of population numbers (Nelson, p 650). R-selected organisms as if they have unlimited resources.

Many insects and unicellular organisms are classified as R-type organisms. These organisms have a characteristic that allows them for rapid and exponential growth when they seem to have unlimited resources. They can increase their populations very quickly under the right conditions.

The growth rate can be modeled with this equation:

dN / dt = rN (1- N/K)

R-selected organisms have a relatively high r-value, and a low K-value.

K-selected organisms have a low relatively r-value and a high K-value.

For r-selected organisms, their exponential growth usually lasts a short time. Eventually the number of organisms reaches a point where the organisms start competing with each other for resources and waste byproducts cannot be removed fast enough. Predators are attracted to this new source of food. The growth rate declines.

Procedure

Using the Food Chain Laboratory, only 100 turns were planted. All other spaces were left vacant.

The initial seed density, number of biology students, and mice of all stages were set to zero.

Turns were not counted in the bionumbers, bioenergy, or biomass totals. All other stages, from seedling to header, were calculated.

The experiment went for 25 months.

Observations & Data

The data is tabled and graphed below:

Table 1: Raw Data
Month Bionumbers Bioenergy (kelovs) Biomass (kg)
2 27 3 2
3 69 11 7
4 120 30 21
5 174 77 52
6 229 168 104
7 283 317 165
8 307 398 198
9 313 436 212
10 315 447 215
11 325 444 212
12 355 437 210
13 409 441 217
14 492 476 243
15 605 568 296
16 738 715 372
17 882 901 465
18 1029 1108 566
19 1176 1321 668
20 1326 1530 767
21 1490 1731 864
22 1678 1931 962
23 1907 2149 1074
24 2190 2412 1211
25 2535 2744 1384

Calculations were done to determine the rate of growth in biomass, bioenergy, and biomass by using this formula:

% Growth Rate=(This Month -Last Month) ÷Last month 100%

These calculations are tabled and graphed below:

Table 2: Growth Rate
(% change from previous month)
Month Bionumbers Bioenergy Biomass
2
3 158% 256% 256%
4 73% 180% 180%
5 45% 153% 153%
6 31% 119% 98%
7 23% 89% 59%
8 9% 26% 20%
9 2% 9% 7%
10 1% 3% 1%
11 3% -1% -1%
12 9% -2% -1%
13 15% 1% 3%
14 20% 8% 12%
15 23% 19% 22%
16 22% 26% 26%
17 20% 26% 25%
18 17% 23% 22%
19 14% 19% 18%
20 13% 16% 15%
21 12% 13% 13%
22 13% 12% 11%
23 14% 11% 12%
24 15% 12% 13%
25 16% 14% 14%

Conclusions

If the Food Chain grass is indeed an r-selected organism, the growth rate should be a horizontal line, eventually declining when the ecosystem starts approaching its carrying capacity. Instead the graph shows an oscillation of high and low growth rates. So this experiment did not prove this hypothesis, although the growth rate seems to be more stabilized towards the end. Some scientists may call the shape of this graph “harmonic decline.”

However, when the data was more closely inspected, the experimenter could see waves of one stage having a high number, and this high number moving to the next stage each month. When the wave moved from headers to turns, there was a dramatic decline in bionumbers, bioenergy, and biomass because the old headers were removed from the totals (or the new turns were not included). It took a couple of months for the new turns to indirectly create more seedlings, and this is why there seems to be a two-month lag between bionumbers and the values for bioenergy and biomass.

This would indicate that the original experimental setup of “100 turns” is not really a stabilized starting point and is conducive to producing these oscillations. More of the other stages should be present in this initial starting point. More research needs to be done to prove or disprove whether the Food Chain grass is an r-selected organism.

If there is an exponential growth rate, it seems to be about 15% per month.

Other Observations

It took two months for seedlings to start. The first month seems to have knocked down some turns to put seeds onto the ground. The second month was when some of these seeds found suitable locations to sprout.

From the bionumbers data for each stage, the first wave of sprouts could be seen moving in its entirety from each stage each month , i.e., the actual number of plants did not change as the stages progressed. So it seems that each grass stage takes one month to progress from one stage to the next. This means a grass plant needs six month to progress from seedling to turn.

At the end of the experiment, 96% of the Laboratory space was still vacant. This suggests that the grasses were not yet competing with each other for sunlight.

Bibliography

  • Nelson Biology, Various Authors, Nelson Publishing, 2004.
  • r/K Selection Theory <http://en.wikipedia.org/wiki/R/K_selection_theory>, Various authors, Wikipedia, updated 2011.

Author

Dave Volek graduated from Tilley School in 1977. He attended his first year of engineering at Medicine Hat College and completed his engineering degree in 1982 at the University of Alberta.

Since graduation, Dave had taken on a variety of occupations and a ten-year illness limited his workplace abilities. These days, Dave is working as a math and science tutor at the Brooks Campus of Medicine Hat College. When he has some space time and energy, he keeps putting up his “inventions” on his website. He is hoping that Food Chain will be his first breakthrough as a recognized innovator.

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