Science / Limitations Of Population Growth

Limitations Of Population Growth

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Autor:  anton  21 November 2010
Tags:  Limitations,  Population,  Growth
Words: 1845   |   Pages: 8
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There are a number of factors that can contribute to the growth of a population and these trends can be seen in a number of species. It is generally believed, from an ecological perspective, that populations will display either an exponential of logistic growth rate. If optimal environments are consistently maintained with no biotic or abiotic limiting factors (excess food, excess space availability, optimum climactic environment, no predation, etc) then a population will grow in an exponential direction. Species with high maximal relative growth rates do not occupy infertile habitats because their physiologies are more sensitive to suboptimal habitats and so their relative growth rates decrease more rapidly as fertility of the environment decreases (Shipley, 1988). A logistic curve will occur in population growth if the population is exposed to at least one limiting factor. The logistics model is and empirical description of how a population tends to grow when environmental conditions are not optimal. Although these two models can be seen in some species of organisms such as bacteria, they are rarely exhibited in natural occurring populations in the wild. In nature population growth in organisms is seen as more or less regular oscillations with high and low points, termed, the time lag model. In the time lag model there is a lag between a change in the environment and a corresponding change in the rate of population growth. These cyclic oscillations are influenced by the environment which the organism inhabits. Changes in the environment can affect numerous functions of an organism including natality (amount of births in a population) and mortality (number of deaths in a population). Laboratory populations of Daphnia are a good example of the effect of time lags on population growth (BOOK)!!!!!!. In this experiment Daphnia magna were utilized to observe the direct relationship of one limiting factor (food in this case) on the dynamics of growth in a population.

Daphnia are found in many kinds of water bodies, including rock pools on the island in the Gulf of Finland (Hanski, 1983). Daphnia exhibit some interesting adaptations to various limiting factors such as low food abundance. If energy and nutrients are limited, the number and size of offspring produced by an organism will depend on how these resources are allocated between reproduction and other life functions (Glazier, 1992). In this experiment there are two different populations of Daphnia, one which received food weekly (food is not a limiting factor) and one that did not receive food. Effects of food availability and toxic stress on maturation in female Daphnia magna are presented (Enserink, 1995). As food levels increase, the developmental rate approaches a maximum (Eneserink, 1995). It is also interesting to note that when food is scarce, some Daphnia eggs develop into males (weeeeeb). Because males are not the components that are responsible for population growth (females are) the addition of males should reduce the amount of offspring adding to the population. Overpopulation can lead to intraspecific competition for resources that are now limited like food availability. This adaptation of adding more males to the population seems to have evolved to curtail overpopulation that can occur in an optimal environment. The descriptive null hypothesis is there will be no difference in population growth between the supplemented treatments versus the unsupplemented treatments. Because of the evident sensitivity of Daphnia to limitation of food, the supplemented group should exhibit a greater population growth then that of the unsupplemented. It is expected that there will be significantly more Daphnia in the supplemented group over the 8 week time span of the experiment then in the unsupplemented group.

Materials and Methods

This experiment was conducted at the Texas State University Biology Department and lasted a full 8 weeks. Ten groups obtained two 1 liter bottles of clear plastic. One bottle was labeled “supplemented” and the other was labeled “unsupplemented”. Each bottle was filled 3/4 full with spring water from the San Marcos River. The water levels in the bottles were marked for future reference. Ten large Daphnia magna were carefully placed n each bottle along with a pinch of Spirulina (powdered algae). For the duration of the experiment, only the supplemented group of Daphnia magna received food weekly, the unsupplemented did not. Spring water was added periodically to the bottles when the water levels were below the line marked previously. Each week the numbers of Daphnia were counted utilizing a light source in order to illuminate the Daphnia and allowed them to be visible. The daphnia were placed in the designated lab area that maintained at room temperature. The data for a total span of 8 weeks was pooled and recorded. The data was then used for various types of statistical analysis including weekly means, per capita growth rates, t-tests, etc.


According to the data collected, the Daphnia magna population in neither the supplemented treatment nor the unsupplemented treatment portrayed either the exponential or logistic growth model. The supplemented group showed a steady decline in the population while the unsupplemented group at first began with a significant drop off at first but then also became a steady decline. The week with the highest maximum growth rate for the supplemented group was week 7 and for the unsupplemented group was also in week 7. The supplemented group had an average maximum growth rate of 1.2 during week 7 and the unsupplemented group had a maximum growth rate of .3 during week 7. It is evident that the supplemented group showed a much higher max growth rate then the unsupplemented group. The t-test utilizing the maximum growth rates revealed a t-critical value less the t-calculated value and the decision to reject the null hypothesis. There is a difference between the growth rates between the supplemented group and the unsupplemented group. When analyzing the per capita values, the control group (unsupplemented group) had its highest value of .429 in week 7 and the treatment group (supplemented group) had its highest value of .39 in week 7. When comparing the two values against each other, the unsupplemented group had a higher per capita value.

Table A- Shows the statistical analysis conducted on the Supplemented data. The statistical calculations above include the mean of each week, the standard deviation of each week, the growth rate means for each week and the per capita growth rate for each week


Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8

Mean (N)

10 10.9 9 5.3 3.7 2.7 3.1 4.3

Std. Dev. 0 2.28 4.76 3.95 2.83 3.02 3.96 5.27

Growth Rate (Means) 0.9 -1.9 -3.7 -1.6 -1 0.4 1.2

Per Capita G.R. 0.09 -0.17 -0.41 -0.302 -0.27 0.148 0.39

rm 0.327


Table B- Shows the statistical analysis performer on the unsupplemented data collected. It includes the weekly mean, standard deviation, mean growth rate and per capita growth rate.


Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8

Mean (N)

10 0 4.6 2.1 0.6 0.8 0.7 1

Std.Dev. 0 3.77 3.13 2.73 1.08 1.75 1.57 2.83

Growth Rate (Means) -1 -4.4 -2.5 -1.5 0.2 -0.1 0.3

Per Capita G.R. -0.1 -0.489 -0.54 -0.71 0.33 -0.13 0.429

rm 0.357

Table C- Shows the t-test results utilizing the maximum growth rates.

Supp Unsupp

Mean 9.44 3

Variance 7.12 6.72

Observations 10 10

df 18

t Stat 2.72

t Critical one-tail 1.73

Reject Null

Graph 1- Portrays the population growth within the 8 week time interval for both supplemented and unsupplemented treatments.

Graph 2- Shows the per capita growth rate versus the population growth rate for the supplemented group.

Graph 3- Represents the per capita growth rate versus the population growth rate for the unsupplemented group.


According to the data the null hypothesis was rejected; the t-test calculated value was found to be greater then the critical value. The two treatments showed a difference in population growth rates. The supplemented group overall showed a significantly higher increase in the population. It also maintained a larger population then the unsupplemented group for the 8 week period. The supplemented group consistently had a larger amount of Daphnia weekly. Both the populations did show a decrease in population size with or without food supplement. But the supplemented group portrayed a larger population growth rate which can be assumed to be due to the food availability. The per capita growth rate of the supplemented group should eventually level off which would be due to the fact that their growth is a density dependent factor, meaning that the population will be maintained once the population has reached the level that has only enough resources for a certain amount of individuals to survive. Once the population has leveled off in growth rate the carrying capacity can be estimated. The per capita growth rate of the unsupplemented group portrays density independent characters because the environment was not in optimal conditions and therefore the population never reached a size that impacted the growth rate. Similar studies involving different organisms have shown a similar as Daphnia to resource availability. The predicted increase in egg or newborn size in response to resource depletion or to increased population density has been observed in copepods and terrestrial isopods (Glazier, 1992).

Daphnia also portray limitations to abiotic factors such as the temperature gradient that were not taken into account. This may be an explanation of the variation of per capita rates amongst the supplemented and unsupplemented treatments. Generally the life span increases as temperature decreases, due to metabolic activity (webbbbbb). The optimum temperature for Daphnia magna is 18-22_ C (webb). This may mean that growth rates portrayed by the Daphnia could have been due to limiting factors other then food abundance. It is possible that because the Daphnia were observed at room temperature (32_C), their growth rates were skewed and their life spans were actually limited/decreased because they were not at their optimal temperature to meet maximum longevity. Also, because it is hard to measure or know exactly what all optimal factors for the Daphnia magna are (ex- dissolved oxygen level of the water, mineral content of the water) and because the Daphnia were maintained in basically the same water for 8 weeks, there may be unseen factors that may have altered the data. In order to improve the outcome of the experiment, all factors (with the exception of food) that may alter the Daphnia’s population growth must be well known and eliminated. The biology of the Daphnia should be known in depth and optimal environments should be replicated exactly. The results would also be more precise if the data was measured over a longer period of time.

Literature Cited

Enserink, M. J., Kerkhofs M. J., Baltus C. A., and J. H. Koeman. 1995. Influence of food quantity and lead exposure on maturation of Daphnia magna; evidence for a trade-off mechanism. Functional Ecology 9:175-185

Glazier, D. S. 1992. Effects of food, genotype, and maternal size and age on offspring investment in Daphnia magna. Ecology 73:910-926

Hanski, I., and E. Ranta. 1983. Coexistence in a patchy environment: three species of Daphnia in rock pools. The Journal of Animal Ecology 52:263 -279

Shipley, B., and P. A. Keddy. 1988. The relationship between relative growth rates and sensitivity to nutrient stress in twenty-eight species of emergent macrophytes. Journal of Ecology 76:1101-1110

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