The Effect of Phosphorus Concentration on the Intrinsic Rate of Increase

for Salvinia minima

Aaron Jacobs

Partners: Andrew Watts Derek Richards Jen Thaete

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Introduction:

Salvinia minima is an aquatic fern, originally from South America, that has invaded

multiple states in the US. They are composed of horizontal shoots that connect multiple plants

together and floating leaves. The leaves, also known as fronds, are generally an oval shape and

are covered with coarse, white hairs. The hairs main purpose is to act as a water repellent to

keep the leaves from sinking when covered with water. Salvinia grows in ponds, lakes and slow

moving streams. This invasive species is known to block waterways by covering them with a

thick layer, some even 20cm thick, which can block boating and can have a serious impact on the

ecosystem of the waterway. The layer of thick vegetation blocks sunlight from deeper plants and

organisms and decreases the oxygen concentrations, which limits oxygen for fish and other

organisms living in the aquatic habitat. When the masses of plants die, they lower oxygen levels

even further. Salvinia are also responsible for clogging hydro power stations as well as irrigation

systems1. Salvinia aren’t all bad, they are showing potential as a plant for aquatic

phytoremediation.

There are few reasons why Salvinia are being more closely examined for

phytoremediation. Phytoremediation is the process of using plants as a tool to remove harmful

pollutants from the environment2. Salvinia have a wide habitat range and can survive in

temperatures from -3°C to 43°C. They are also capable of outgrowing duckweeds, due to their

high reproductive ability. They have a very high growth rate, which is why they are so

dangerous in waterways, but this same quality that is viewed as being harmful could potentially

be used in a positive way. It also has larger leaves, making it easier to harvest than duckweeds3.

Salvinia also work as a buffer for pH, they have the ability to change a rather acidic environment

into a neutral one in an extremely short amount of time. This means that they could be used for

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both the removal of excess and potentially harmful nutrients and the neutralization of pH in

waterways. Salvinia also possess another important quality, they store all the nutrients into their

leaf tissues, this would make them a great plant to harvest and be used as a potential fertilizer4.

This lab will examine population growth using exponential models, more specifically

geometric growth models since we are dealing with discrete time intervals and not a continuous

stream of data, as well as logistic growth models to analyze the data. When a population enters a

new habitat, that is rich with nutrients and the population density is low, the population will

follow a more exponential-like growth. This is due to density independent factors like the excess

nutrients, light intensity and the space available to grow. At some point though, a population

will be limited by the amount of individuals, these are density dependent variables. Density

dependent variables are limitations brought on by the close proximity of the individuals living in

a confined and limited environment. When these types of factors are at work, a population will

begin to decrease in growth, reaching that population’s carrying capacity, and will follow a

logistic model curve more closely5.

The purpose of the first part of this experiment is to examine the natural growth rate of

Salvinia and use this as a control group for comparison with the second part of the experiment as

well as comparing the differences scene when starting with different initial population sizes. The

purpose of the second experiment is testing whether adding nutrients, specifically phosphorus,

will alter the population’s ability to grow compared to the control. I hypothesize that the

Salvinia in the plain water, with no added nutrients, will show a lower growth rate, and a lower

carrying capacity, than the Salvinia with added nutrients, due to the lack of extra nutrients. Also,

the control population of 24 will grow faster than the control population of 12 plants, but both

will come to the same carrying capacity in the long run.

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Materials and Methods:

The experiment involves five separate plastic containers that hold the populations of

Salvinia plants. There are two control populations; both only contain water with no extra

phosphorus added. One of the controls started out with 12 Salvinia plants and the other control

container initially started with 24 plants. The independent variable in experiment one was the

amount of plants initially started with and the dependent variable being the resulting growth rate.

The other three containers housed the second part of the experiment; all three of these containers

initially started with 24 plants. All of these containers were then placed in a greenhouse, which

was kept at 21°C during the day and 18°C at night, to increase growth and to keep the

temperature consistent. The main difference between experiment two’s setup compared to

experiment one, was that experiment two containers had 2mL of phosphorus added to each of

them. The independent variable of experiment two was the addition of phosphorus, making the

dependent variable the resulting growth rates. 2mL of phosphorus were then added to the

experiment two containers once a week after that initial addition. All of experiment two was

identical; this was done to give a better pool of data that could be averaged together and

compared. After the plants had been added to the containers, the amount of leaves, or fronds,

were counted. Counting days occurred on the same day once a week, starting the second week,

day 14 of the experiment, until the 28th day of the experiment, which was the last day of

counting. Due to evaporation, the plants needed water added three times a week, also due to the

accumulation of algae the containers needed to be cleaned once a week. After data collection,

there were various data analysis techniques that were utilized, specifically the geometric growth

model and the logistic growth model. The geometric growth model was used because the data

was collected at discrete time intervals. The logistic growth model was used since the

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populations are limited by their environment, they will reach a limit of growth, which is known

as the carrying capacity. The exponential growth model was also used to find rmax values, under

the assumption of continuous growth. Lastly, the formula to find the geometric rate of increase

was used so that the carrying capacity could be calculated for the various populations5.

Geometric Rate of Increase: 𝜆 = !!!!!!

Exponential Growth Model: !"!"= 𝑟!"#𝑁

Logistic Growth Model: !"!"= 𝑟!"#𝑁

!!!!

Results:

Figure 1.

Figure 1. Scatter plot showing the growth rates of Salvinia control populations. This graph depicts the control population, the blue line representing the container starting with 12 Salvinia plants and the red line representing the container that started with 24 Salvinia plants.

0  

50  

100  

150  

200  

250  

300  

350  

400  

450  

0   5   10   15   20   25   30  

Num

ber  of  Fronds  

Time  (Days)  

Population  Growth  of  Salvinia  Control  Populations  

Count(12)  

Count(24)  

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Figure 2.

Figure 2. Scatter plot showing the natural log versus time for the control populations. This graph was made to use the slopes of the lines in order to find rmax. Figure 3.

Figure 3. Scatter plot of lambda versus population size for the control populations. This graph’s best-fit line equations were used to find carrying capacities of the populations.

y  =  0.0923x  +  3.2195  

y  =  0.0763x  +  3.9391  

0  

1  

2  

3  

4  

5  

6  

7  

0   5   10   15   20   25   30  

ln(N)  

Time  (Days)  

Ln(N)  vs.  Time  for  Control  Populations  

Count(12)  

Count(24)  

Linear  (Count(12))  

Linear  (Count(24))  

y  =  -­‐0.0882x  +  3.4867  

y  =  -­‐0.0062x  +  3.0739  

0  

0.5  

1  

1.5  

2  

2.5  

3  

3.5  

4  

0   50   100   150   200   250   300  

Lambda  Values  

Number  of  Fronds  

Lambda  Values  vs.  Nt  for  Control  Populations  

Count(12)  

Count(24)  

Linear  (Count(12))  

Linear  (Count(24))  

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Figure 4.

Figure 4. Scatter plot showing the growth rates of Salvinia for the control and experimental populations. This graph shows a red line representing the control container that started with 24 Salvinia plants and a pink line representing the average of the three containers for the experimental phosphorus plant populations. Figure 5.

Figure 5. Scatter plot of lambda versus population size for the control and experimental populations. This graph’s best-fit line equations were used to find carrying capacities of the populations.

0  

100  

200  

300  

400  

500  

600  

700  

0   5   10   15   20   25   30  

Num

ber  of  Fronds  

Time  (Days)  

Population  Growth  of  Salvinia  for  Experimental  Phosphorus  Populations  

Count(Phosphorus)  

Count(24)  

y  =  -­‐0.0043x  +  3.2999  

y  =  -­‐0.0062x  +  3.0739  

0  

0.5  

1  

1.5  

2  

2.5  

3  

3.5  

0   100   200   300   400   500  

Lambda  Values  

Number  of  Fronds  

Lambda  Values  vs.  Nt  for  Experimental  Phosphorus  Populaitons  

Count(Phosphorus)  

Count(24  control  

Linear  (Count(Phosphorus))  

Linear  (Count(24  control)  

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Table 1.

Carrying  Capacities  

Control  Group  (12)  

Control  Group  (24)  

Experimental  Group  (phosphorus)  

235   335   535  

Table 1. Chart representing carrying capacities found. The carrying capacities in this table are color coded with the data they came from, these values were found using the best-fit lines from the lambda vs. population size graphs.

Carrying Capacity Calculations

Control  Group    (12)  

Control  Group    (24)  

Experimental  Group  (Phosphorus)  

y  =  -­‐0.0882x  +  3.4867   y  =  -­‐0.0062x  +  3.0739   y  =  -­‐0.0043x  +  3.2999  Set  y=1  and  solve  for  x   Set  y=1  and  solve  for  x   Set  y=1  and  solve  for  x  1  =  -­‐0.0882x  +  3.4867   1  =  -­‐0.0062x  +  3.0739   1  =  -­‐0.0043x  +  3.2999  

x  =  235   x  =  335   x  =  535  

Table 2.

Carrying  Capacities  Using  Surface  Area  

Number  of  Layers   1   2   3  

Carrying  Capacity   207   414   621  

Table 2. Chart showing the carrying capacities found using surface areas. The carrying capacities in this table are based on the layering behavior of Salvinia.

Sample  Calculation  for  Surface  Area  Carrying  Capacities    

𝐾 =𝑆𝑢𝑟𝑓𝑎𝑐𝑒  𝐴𝑟𝑒𝑎  𝑜𝑓  𝐶𝑜𝑛𝑡𝑎𝑖𝑛𝑒𝑟  𝑆𝑢𝑟𝑓𝑎𝑐𝑒𝑆𝑢𝑟𝑓𝑎𝑐𝑒  𝐴𝑟𝑒𝑎  𝑜𝑓  𝑆𝑎𝑙𝑣𝑖𝑛𝑖𝑎  𝐹𝑟𝑜𝑛𝑑  

 

𝐾 =5809𝑚𝑚  !

28𝑚𝑚  !    

𝐾 = 207  

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Discussion:

The results showed that Salvinia minima could be a good candidate for phytoremediation.

The first component of the results focused on the population growth and how populations of

Salvinia react to different initial population sizes as well as the introduction of phosphorus.

Figure 1 qualitatively seemed to show that the populations starting at different initial amounts of

plants grow at the same rate. This figure also showed that starting with more plants consistently

shows a higher amount of plants as time continues. But when this data was more closely looked

at it told a different story. Figure 2 showed that the slopes, or rmax value, were not the same.

This means that the two control populations actually grew at different rates. The results show

that the control population that started at 12 grew at a faster rate than the starting at 24 group.

This means that my initial hypothesis was wrong, which looking back makes sense. The

population that started with 12 plants would have less initial competition and more resources

available to each plant, this would allow for a more exponential growth. For more information

about the population dynamics of these two groups I found the carrying capacities for the two

populations using the best-fit lines from figure 3 and the surface area of the water in the

container. Table 2 shows the carrying capacities found for the container using the surface area of

the container and seeing how many Salvinia fronds could fit into the space. The main problem

with using this method is that it doesn’t account for the behavior of the Salvinia; Salvinia has

round leaves, which don’t fit perfectly together so there are gaps between leaves. Another

behavior of Salvinia is that it forms layers under the surface of the water, I tried to account for

this by multiplying the carrying capacity for one layer by 2 and 3, this is shown in table 2. A

better method for finding the carrying capacity is using the best-fit line from figure 3. The

carrying capacity for the control group with 12 initial plants, as shown in table 1, was 235. This

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was compared to the carrying capacity of the control group starting at 24 plants, which was 335.

My initial hypothesis was that the carrying capacities would be the same, which should be seen

since the amount of space in the long run is equal, being that both groups are in the same size

containers. There are a few reasons that could explain this discrepancy. The trials only lasted

for 28 days, this is a relatively short amount of time and the populations may not have been

allowed to grow for a long enough time. Another explanation is that there was a build up of

algae in the containers, this algae could have been acting as competition for the plants causing

them to grow at a decelerated pace. Lastly poor counting could have been a reason for the

inconsistency, since a thick layer of Salvinia develops, it can become difficult to count the fonds

and some may have been over or under counted.

The second part of this experiment looked more into an aspect that could show if Salvinia

minima would make a good plant for phytoremediation. The second part of the results showed

how adding nutrient, specifically phosphorus, would alter the population dynamics of the

Salvinia populations when compared to a control group with no added nutrients. Figure 4

showed a how the population growth of the two populations compared to one another. The

control group that started with 24 plants showed a much slower rate of growth compared to the

experimental population. Initially the two populations showed the same rate of growth, which

could have been to a result of a time lag, but after that the added phosphorus populations grew at

a much more accelerated rate. This agrees with my hypothesis that the nutrient rich environment

would cause an increase in growth rate. This is a good sign that the Salvinia could be a good

candidate as a plant to use in the process of phytoremediation. The reason this is a good sign is

because the ability to hold nutrients and grow at an accelerated rate shows that Salvinia would be

able to take potentially harmful nutrients out of waterways at an accelerated rate and could then

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be harvested as a natural fertilizer due to it’s ability to hold nutrients. The results also looked

more into the long-term affect of adding phosphorus, by taking the carrying capacities of the two

populations into account and comparing them. The best-fit lines from figure 5 were used to

determine the carrying capacities as seen in table 1. The carrying capacity for the control group

was 335 and the carrying capacity of the experimental group was 535. These results make sense

since available space and resources limit carrying capacity, by increasing phosphorus the

experimental population was able to grow to a higher carrying capacity than the control group,

which agrees with my hypothesis. The sources of error for this part of the experiment are the

same as for the first part, with the addition of poor measuring of nutrient. It is possible that not

enough or to much nutrient was added to the experimental containers, which could have lead to

skewed results.

The purpose of this experiment was to determine if the Salvinia minima would make a

good plant for phytoremediation in waterways that contain elevated levels of possibly harmful

nutrients. The results showed that Salvinia minima could work in this situation, but further

research will need to be conducted to support these findings. In future experiments, more plants

should be tested since a possible source of error was the very small sample sizes. Phosphorus

should be further analyzed and tested, but since Salvinia minima showed such positive results

other nutrients should also be examined. It may turn out that Salvinia minima can absorb a large

amount of various harmful nutrients, making it a great candidate for phytoremediation.

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Reference:

1. Salvinia  minima  (aquatic  plant,  fern).  (2012,  October  4).  Retrieved  4  10,  

2013,  from  Global  Invasive  Species  Database:  

http://www.issg.org/database/species/ecology.asp?si=570&fr=1&sts=&lan

g=EN

2. Chaney,  R.  L.  (200,  June).  Phytoremediation:  Using  Plants  To  Clean  Up  Soils.  

Agricultural  Research  magazine  .

3. Eugenia  J.  Olguin,  G.  S.-­‐G.-­‐P.  (2007).  Assessment  of  the  Phytoremediaiton  

Potential  of  Salvinia  minima  Baker  Compared  to  Spirodela  polyyhiza  in  High-­‐

strength  Organic  Wastewater.  Water,  Air,  &  Soil  Pollution  ,  181,  135-­‐147.

4. Safaa  H.  Al-­‐Hamdani,  C.  B.  (2008).  Physiological  Responses  of  Salvinia  

Minima  to  Different  Phosphorus  and  Nitrogen  Concentrations.  American  Fern  

Journal  ,  98,  71-­‐82.  

5. Hass, C.A., D. Burpee, R. Meisel, and A. Ward. 2013. A Preliminary Study of the Effects

of Excess Nutrients and Interspecies Competition on Population Growth of Lemna minor

and Salvinia minima In A Laboratory Manual for Biology 220W: Populations and

Communities. (Burpee, D. and C. Hass, eds.) Department of Biology, The Pennsylvania

State University, University Park, PA.

Adapated from Beiswenger, J. M. 1993. Experiments To Teach Ecology. A Project of the

Education Committee of the Ecological Society of America. Ecological Society of

America, Tempe, AZ. pp. 83-105.