General insight: more coexistence under stronger within-species limitation than between-species limitation
General insight: Relative interaction strengths shape competitive outcomes
We address this gap by developing a pathogen invasion theory (PIT) based on modern ecological coexistence theory and testing the resulting framework against empirical systems. […] PIT unifies existing ideas about pathogen co-circulation, offering a quantitative framework for predicting the emergence of novel pathogen strains
In the previous unit, we explored how a reductionist approach can be applied to the study of species competition:
What can we learn from a similar approach to consumer–resource dynamics?
Consider the dynamics of a “consumer” species \(C\) and a “resource” species \(R\)
The resource species has plenty of resources available and can grow exponentially…
… but it is suppressed by the consumer.
The consumer is a specialist (only eats the “resource” species)
(If there is no resource around, the consumer population dies out)
The consumer loses energy at some rate (maintenance cost)
How should the abundances of consumers and resources change over time? (\(\frac{dR}{dt}\) and \(\frac{dC}{dt}\))
\[\frac{dR}{dt} = \text{exponential growth - loss to consumer}\]
\[\frac{dR}{dt} = rR - aRC\]
\[\frac{dC}{dt} = \text{growth from consumption - energy loss}\]
\[\frac{dC}{dt} = eaRC - mC\]
\[\frac{dR}{dt} = rR - aRC\]
\[\frac{dC}{dt} = eaRC - mC\]
Some “obvious” takeaways:
\[\frac{dR}{dt} = rR - aRC\]
\[\frac{dC}{dt} = eaRC - mC\]
Some more takeaways:
Given the consumer–resource dynamics equations:
\[\frac{dR}{dt} = rR - aRC\]
\[\frac{dC}{dt} = eaRC - mC\]
Where does equilibrium occur?
\[\frac{dR}{dt} = rR - aRC = 0\]
\[rR = aRC\]
\[C^* = \frac{r}{a}\]
Interpretation: There is a set abundace of the consumer \(C\) that would cause the resource \(R\) to be at equilibrium.
\[\frac{dC}{dt} = eaRC - mC = 0\]
\[eaRC = mC\]
\[R = \frac{m}{ea}\]
Interpration: There is a set abundance of the resource \(R\) that would cause the consumer to reach equilibrium
This suggests that populations should cycle. Do they?
Image from “Population cycles: generalities, exceptions and remaining mysteries”, Meyers 2018 in Proc. Royal Soc. B.
Image from Blasius et al. “Long-term cyclic persistence in an experimental predator–prey system”, 2020, in Nature. These authors were studying a lab population of an aquatic rotifer (consumer) and a grean algae (resource)