notes/competition_basics.html

Competition Basics

Phytoplankton have been used to study competition for resources and competitive exclusion. In homogeneous aqueous media, these studies have been able to focus on just the physiological parameters that relate nutrient uptake to growth.

One classical references is:

Tilman, David. 1982. Resouce Competition and Community Structure. Princeton University Press.

 

Nutrient uptake parameters

Transport and assimilation of nutrients, such as NO3^-, PO4^3-, and silicic acid, can be described with an equation that is based on the Michalelis-Menten equation for enzyme kinetics.If the algae are nutrient limited, i.e. if their growth rate is dependent on the uptake of new nutrients AND if they don't change the amount of cellular nutrient per cell, this equation can be stated very simply:

growth_rate = maximum_growth_rate * nutrient_conc/(nutrient_conc + half_sat_K)

growth_rate = new cells/(per cell *time) and has units of time^-1

maximum_growth_rate is the maximum growth rate under these temperature conditions

nutrient concentration = mol L^-1

half_sat_K is the half saturation constant, a constant equivalent to the value of the concentration when the growth_rate would equal 1/2 of the maximum_growth_rate.

For half_sat_K = 10 and maximum_growth_rate = 10

figure 1 - uptake kinetics

 

K1/2 or half_sat_K and Maximum_growth_rate are shown on the figure below.

figure 1b - graphical representations of the constants half_sat_K and maximum_growth _rate

 

Ideally these kinetic characteristics can be determined on cells that have all been grown in the same conditions (but nutrient limited) and then divided up into sub-cultures that are identical except for the nutrient concentration. Then the instantaneous uptake rate calculated over a short time period, short enough that the algae both 1) don't change the concentration in the media and 2) don't change their own physiological response to the nutrient because of accumulation of nutrient.

 

Nutrient uptake and depletion

If a small innoculum of healthy algae are placed into medium with a high concentration of nutrients they will take up the nutrients and grow. Under the simplest models used here, these algae will have the same kinetics and cell content for the entire growth phase. As they take up the nutrients, the nutrient concentration will decrease. The following two graphs relate this relationship.

figure 2a. Increase in cell number and decrease in nutrient with time

figure 2b. uptake kinetics per cell that result in the upper curve (maximum_growth_rate = 0.2 day^-1, half_sat_K = 5 umol/L Nitrogen)

The two figures are related directly. You can follow the growth rate decrease by moving from right to left in Figure 2b. The rate is high at first and then decreases as the nutrient concentration is decreased.

 

Steady state growth

Before we can explain competitive exclusion in algae, we have to modify our simple models for nutrient concentration and growth rate to include a loss term that is due to dilution of the culture with "fresh" media. In each time interval (or continuously) some small amount of culture is taken out and replaced with the same volume of media with full nutrient concentration. This dilution rate is a loss term for the population that is alreatdy there. This loss terms is given as volume_removed/(total_volume * time), and has units of time^-1, the same as the growth rate.

For example, if we set the dilution rate to 0.05 day^-1 this is roughly equivalent to taking out 5% of the volume each day and replacing it with fresh media (it is not exactly the same because if usually happens continuously).

 

Figure 3. Nutrient uptake, growth and dilution. The same characteristics as the Figure 2 but with a dilution of fresh media at 5% day^-1.

It's difficult to see in this graph, but the nutrient doesn't deplete all the way to zero. It reaches a value that just supports the growth rate of 0.05.

Figure 4. An expansion of the nutrient uptake kinetics to show the steady state solution where the growth rate just equals the loss rate. The nutrient concentration required for cells to grow just this fast is 1.6.

The steady state values of nutrients and cells that are reached is self adjusting. If the nutrient concentration is above 1.6, then the cells will grow a little faster than the dilution rate, take up more nutrient and bring the nutrient concentration back down to 1.6. If the nutrient concentration is less than 1.6, the cells will grow more slowly than the dilution rate, take up relatively less nutrients than is being put back in through dilution and the concentration will increase back up to 1.6.

At the steady state nutrient concentration there is zero net growth. The number of cells will remain constant because growth rate is exactly balanced by loss through dilution.

 

Finally, competition

We can finally describe competition between two algal species that have different kinetics for nutrient uptake. Competitive exclusion won't happen unless there is a loss term. The outcomes of all the competitions that I will describe below are heavily dependent on the loss rate.

The kinetic parameters and growth parameters are given table 1.

Species "A" has a lower half_sat_K (which is a good thing) but also a lower maxium_growth_rate.

  A B
half_sat_K 5 10
maximum_growth_rate 1 2
     
fresh media concentration 200
dilution rate 0.1

 

 

Figure 5a. Graphical comparison of the kinetic parameters for species A and B

 

Figure 5b. Expanded region at low concentrations. Species A will grow faster at concentrations lower than a concentration of 6.

From this figure you can't predict which species will win unless you know the loss and dilution rate.

Interestingly, competitive exclusion doesn't happen because one species grows faster, but rather that one species can have a zero net growth rate in a region of concentration that forces the other species to have a negative growth rate. For example at a dilution rate of 0.4, species A can have a zero net growth rate at a nutrient concentration of 1.3, but species B will only be able to support a growth rate of 0.23 at that concentration and with a loss of 0.4 this means that species B will be washed out at a net rate of -0.17.

Similar logic applies to dilution rates. It isn't that B can grow faster but that at dilution rate of 1.0 for example, B can grow that fast at a nutrient concentration of only 10 but A will have a net growth rate at 10 of -0.17 (0.83-1.0).

Rate of competitive exclusion

Competitive exclusion can happen rapidly if there is a wide discrepancy in the kinetic parameters of the competing species, but most likely it will happen very slowly because the relative kinetics are close and the net negative growth rate of the looser is very small.

Below are several examples of the time course of competition between Species A and B.

Figure 6. A and B both start at populations of 10. Dilution rate = 0.4 day^-1. You can see that species B starts off strongly but as the concentration is pushed down below B's zero net growth level, B decreases and A continues to increase. After 20 days, this competition still hasn't come close to exclusion.

 

Figure 7. At a dilution rate of 0.8 day^-1. B grows quickly and A fails to get going. You can see that the concentration of nutrients remains significantly above zero in order to support the rapid growth by B.

 

accompanying Excel worksheet = competition.xls

 

John Rueter
ESR473
2003.04.06