Competition is common in all kinds of (eco)systems.
Competition requires limited essential resources like nutrients, light, or space.
Species coexistence and thus biodiversity are necessarily linked to competition.
Models can gain insights into the nature of competition and the conditions for coexistence.
Compared to experiments, we can perfectly disentangle / control all involved mechanisms.
We consider a pair of two planktonic algae species in shallow lake (i.e. a continuous flow stirred tank reactor).
We assume competition for the essential nutrients P and N but ignore light as another factor.
We do not account for mortality but consider flushing (i.e. outflow from the lake) as the only loss process.
name | unit | description | default |
---|---|---|---|
A | mg C / L | Biomass of algae spec. A | 1.00 |
B | mg C / L | Biomass of algae spec. B | 1.00 |
P | mg P / L | Dissolved bioavailable phosphorus | 0.06 |
N | mg N / L | Dissolved bioavailable nitrogen | 1.20 |
name | unit | description | rate | P | N | A | B |
---|---|---|---|---|---|---|---|
gr_A | mg C / L / h | growth of A | muA * min(P / (P+hP_A), N / (N+hN_A)) * A | -1/cp | -1/(cp/np) | 1 | 0 |
gr_B | mg C / L / h | growth of B | muB * min(P / (P+hP_B), N / (N+hN_B)) * B | -1/cp | -1/(cp/np) | 0 | 1 |
tr_P | mg P / L / h | im-/export | 1/tau * (Pin - P) | 1 | 0 | 0 | 0 |
tr_N | mg N / L / h | im-/export | 1/tau * (Pin * N2Pin(time, minN2P, maxN2P, intN2P) - N) | 0 | 1 | 0 | 0 |
tr_A | mg C / L / h | im-/export | 1/tau * (Ain - A) | 0 | 0 | 1 | 0 |
tr_B | mg C / L / h | im-/export | 1/tau * (Bin - B) | 0 | 0 | 0 | 1 |
name | unit | description | default |
---|---|---|---|
muA | 1 / day | Growth rate constant of spec. A | 3.000000 |
muB | 1 / day | Growth rate constant of spec. B | 3.000000 |
np | g / g | N:P mass ratio (for 16:1 mol/mol) | 7.225807 |
cp | g / g | C:P mass ratio (for 106:1 mol/mol) | 41.032258 |
hP_A | mg / L | Half. sat. constant for P, spec. A | 0.010000 |
hP_B | mg / L | Half. sat. constant for P, spec. B | 0.010000 |
hN_A | mg / L | Half. sat. constant for N, spec. A | 0.100000 |
hN_B | mg / L | Half. sat. constant for N, spec. B | 0.100000 |
tau | days | Residence time | 14.000000 |
name | unit | description | default |
---|---|---|---|
Ain | mg / L | Abundance of species A in inflow | 0.000000 |
Bin | mg / L | Abundance of species A in inflow | 0.000000 |
Pin | mg / L | P concentration in inflow | 0.060000 |
minN2P | g / g | Lowest N:P mass ratio in inflow | 7.225807 |
maxN2P | g / g | Highest N:P mass ratio in inflow | 7.225807 |
intN2P | days | Cycle duration of N:P variation | 10.000000 |
name | code |
---|---|
min | # intrinsic function |
N2Pin | # N:P mass ratio in the inflow in units of g N / g P |
N2Pin | # The function can return constant values or a cyclic dynamics |
N2Pin | # depending on the choice of arguments. |
N2Pin | # time: will be set by the integration routine internally |
N2Pin | # mini: the lowest possible value |
N2Pin | # maxi: the largest possible value |
N2Pin | # interval: duration of a full cycle (e.g. from maxi to maxi) |
N2Pin | N2Pin <- function(time, mini, maxi, interval) { |
N2Pin | mini + 0.5(sin(time/interval 2 * 3.1415) + 1) * (maxi - mini) |
N2Pin | } |
N2Pin
represent the N:P ratio in the reactor’s input.
Ratio is constant if mini
and maxi
argument are equal.
Set mini < maxi
to create regular temporal variation.
Species A and B coexist in the reactor.
This is true for arbitrary non-zero initial values.
No surprise, because A and B are indistinguishable.
We grant an advantage to species A with regard to one resource (here: Phosphorus).
The advantage is reflected by the lower half-saturation constant (hP_A
< hP_B
).
We let A and B compete under two scenarios: P limitation and N limitation.
If P is the limiting resource, the superior competitor (species A) dominates the system while species B goes extinct. The winner takes it all.
If N is the limiting resource, we still experience coexistence (because hN_A
= hN_B
).
Hence, superiority regarding the uptake of a resource only pays out if that resource is actually limiting. No advantage from unnecessary skills.
In classical theory, coexistence requires niches (i.e. each species is adapted to the specific conditions in a sub-habitat or capable of exploiting an exclusive resource).
But here, species A and B exploit identical resources (P, N) and in a fully homogeneous environment (mixed tank).
However, if suitable habitats for two distinct species do not exist in the spatial domain they can still exist in the time domain.
We equip A and B with contrasting advantages (hP_A
< hP_B
but hN_A
> hN_B
).
Depending on N and P supply, either A or B is the better competitor.
We study different scenarios of nutrient supply, including a periodical switch between P and N limitation.
In a constant environment, there is no coexistence.
Temporal variability in forcings can lead to coexistence.
Amplitude and frequency must be in a suitable range to actually serve both competitors with a sufficient niche.
The maintenance of species diversity through temporal variation has many facets.
You may want to read about the intermediate disturbance hypothesis (IDH). In that context “disturbance” is used in a broad sense and includes, e.g., the reset of successions.
Mechanism | Explanation |
---|---|
Diversity of resources | Supports the coexistence of specialists, each of them expoiting a unique resource. |
Temporal variability | Causes switches between superiority and inferiority of competitors (recall the example and the IDH). |
Spatial structures | Allow for different habitate conditions, possibly on very small spatial scales. Exchange between habitats (e.g. partial mixing) results in apparent coexistence. |
Mechanism | Explanation |
---|---|
Continuous immigration | Rivers receive input (e.g. bacteria) from soil and groundwater. Lakes and seas are inoculated with river-borne organisms. Invaders may persist for long times. |
Dormant states | Microorganisms survive long periods of unsuitable conditions in a metabolic inactive state. This avoids or delays extinction of inferior competitors. In suitable conditions, populations recover. |
Mechanism | Explanation |
---|---|
Top-down control | In some circumstances, predation may promote coexistence, because prey species can differ with respect to grazing resistence and defense (kind of niches). |
Mutual dependence | Even competitors may depend on each other. E.g., bacterium A mobilizes a resource co-exploited by species B. At the same time, B produces an exoenzyme protecting A from antibiotics. |
Consider this review paper to learn more about the mechanisms of (bacterial) competition.
In real-word ecosystems, it is often difficult to disentangle the reasons of apparent coexistence.
In aquatic systems, you will often find a combination of both co-existence (niches) and mere co-presence (import from external habitats through hydrological connections).