System analysis: Competition

Intro

• 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.

About the example

• 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.

Load the model

• The model is part of the rodeoEasy package. You may open the respective workbook on your local computer.

rm(list=ls())                                      # initial clean-up

#remotes::install_github("dkneis/rodeoEasy")       # if not installed yet
library("rodeoEasy")

workbook <- system.file("models/coexistence.xlsx", # contains the model
  package="rodeoEasy")

m <- build(workbook)                               # build model object

Functions in detail

• 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.

times <- 0:96
plot(range(times), c(0,2), type="n", xlab="time", ylab="N:P")
lines(times, N2Pin(times, mini=1, maxi=1, interval=24), col="black")
lines(times, N2Pin(times, mini=0, maxi=2, interval=24), col="steelblue")
lines(times, N2Pin(times, mini=0, maxi=2, interval=48), col="darkorange")

Case 1: Identical competitors

• Default parameters were chosen such that species A and B are identical.

x <- run.scenarios(m, times=0:100)

Case 1: Identical competitors

• 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.

Case 2: Superiority of one species

• 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.

common <- c(hP_A=0.005, hP_B=0.01)                # hP_A < hP_B
sc <- list(
  P.limitation=c(common, minN2P=10, maxN2P=10),   # excess of N 
  N.limitation=c(common, minN2P=3, maxN2P=3)      # excess of P
)
x <- run.scenarios(m, times=0:100, scenarios=sc)

Case 2: Superiority of one species

• 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.

Case 3: Contrasting advantages

• 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.

Case 3: Contrasting advantages

• 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.

common <- c(tau=5, hP_A=0.01, hP_B=0.02, hN_A=0.2, hN_B=0.1)
sc <- list(
  low.N2P=  c(common, minN2P=5,   maxN2P=5),
  high.N2P= c(common, minN2P=9.5, maxN2P=9.5),
  var.N2P=  c(common, minN2P=5,   maxN2P=9.5, intN2P=20)
)
x <- run.scenarios(m, times=0:300, scenarios=sc)

Case 3: Contrasting advantages

• 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.

Multiple mechanisms control diversity (1)

Multiple mechanisms control diversity (2)

Multiple mechanisms control diversity (3)

Multiple mechanisms control diversity (4)

• 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).