l23- Pathogen Dynamics and Interspecific Competition Models

Ecological Observations and Instructional Context

• The lecture begins with a brief troubleshooting phase regarding the audio-visual system, referencing the Irish sitcom The IT Crowd and its catchphrase regarding turning systems off and on again to fix them.

• Observation of Oak Trees: The instructor notes that the feet of students entering the lecture hall are "sticky" due to conditions outside.

• Ecological Cause: The stickiness is attributed to oak trees outside the library and the C lecture theaters.

• Aphid Infestation: The trees are currently under attack by pest insects, specifically aphids (sap-sucking insects), which produce a substance called "honeydew."

• Honeydew Production: Similar to beech scale insects, these aphids feed on the sap of the oak trees and excrete the excess sugars as honeydew, which is currently "raining down" from the trees.

• System Imbalance: The lecturer suggests there are currently not enough natural enemies, such as parasitoids, to control the aphid population, leading to the abundance of honeydew.

Pathogens as Metapopulations

• Host-Patch Dynamics: Pathogens and parasites can be understood through the lens of metapopulation theory.

• Habitat Patches: In this model, individual hosts are viewed as patches of habitat. Pathogens are specialized to utilize these specific host patches.

• Colonization and Extinction: Populations of pathogens exist within a host. If the host's immune system clears the infection or the host dies, that specific "patch" population goes extinct.

• Dispersal: For the metapopulation to survive, the pathogen must constantly disperse from one host (patch) to another before extinction occurs.

The Net Reproductive Rate ($R_0$) in Pathogens

• Definition of $R_0$: While in general population models $R_0$ is the net reproductive rate, in the context of infectious disease, it specifically refers to the number of host individuals infected by a single primary case.

• Host-Level Focus: In fields like human health, veterinary science, and plant pathology, researchers are more interested in the infection rate at the host level rather than the population size of the virus or bacteria within a single host.

• Factors Influencing $R_0$:

  • Infection Probability: A constant rate representing how effectively an organism infiltrates a host.

  • Susceptible Host Availability: The number of new hosts available for infection by offspring.

  • Virulence: Represented as the disease-induced death rate of hosts. High virulence can lead to patch extinction before dispersal.

  • Natural Mortality: The background death rate of the host species.

  • Recovery Rate: The rate at which hosts clear the infection and become immune.

• Alternative Equation Elements:

  • $S$: The density of susceptible hosts.

  • Transmission rate of the disease.

  • $L$: The average time a host remains infectious.

• Thresholds for Spread: If $S$ (susceptible hosts) becomes too small, the disease dies out because there are no new patches to colonize. If $S$ is large, growth is rapid, especially with high transmission rates and high $L$.

Epidemiology and Case Studies

• Infectivity Comparisons: Different diseases have vastly different $R_0$ values:

  • Very High $R_0$: Measles and Pertussis (whooping cough). These spread extremely rapidly through unvaccinated populations, making high vaccination rates critical.

  • High $R_0$: Mumps and Malaria (Malaria has a broad range).

  • Lower $R_0$: Smallpox, Flu, SARS, and COVID-19.

• COVID-19 Context: Although its $R_0$ is lower than measles, it spread rapidly because the initial susceptible population ($N$) was the entire global population (no prior exposure).

• High Mortality/Low Spread: Dangerous diseases like Ebola and MERS have lower $R_0$ values, which limits their spread compared to more infectious but less lethal diseases.

• Population Cycles (The London Measles Example):

  • Pre-vaccination, measles in London showed a tendency to peak every two years.

  • The Mechanism: An outbreak would occur, reducing the number of susceptible individuals as survivors became immune.

  • Replenishment: New births would eventually create a large enough cohort of susceptible children (a new "susceptible population") to trigger another peak.

  • Vaccination Impact: After the introduction of vaccines, these peaks became significantly smaller.

Formalizing Parasitism vs. Pests

• Strict Definition of Parasite: To be considered a parasite in the strict sense used in this course, an organism must be specialized and rely on a host for at least one part of its life cycle, remaining on the host for a duration of time.

• Exclusion of Sandflies and Fleas: While often called parasites colloquially, sandflies and fleas are categorized as pests or vectors. Their interactions with hosts are too intermittent and they do not remain on the host to complete a life cycle stage in the way specialized parasites do.

Concepts of the Ecological Niche

• Etymology: The word "niche" comes from a French term meaning a small nook in a church wall designed to fit a specific statue.

• Ecological Definition: It represents the specific "place" or set of conditions where a species fits and thrives.

• Dimensions of the Niche:

  • Abiotic Factors: Temperature, salinity, humidity, etc.

  • Biotic Factors: Food size, competition, and predation.

• Hutchinson Hypervolume: A concept stating that a niche is defined by many different dimensions (abiotic and biotic gradients). As more detail is added, the hypervolume becomes a complex representation of the real world.

• Fundamental Niche: The physical conditions under which a species can survive and reproduce in the absence of interactions with other species (specifically competition).

• Realized Niche: The actual conditions and resources a species utilizes when restricted by interactions such as competition. This is typically smaller than the fundamental niche.

• Relationship Between Niches: While positive interactions (facilitation/anthropogenic changes) might theoretically expand a niche, the realized niche is traditionally considered the version of the fundamental niche that is constricted by competition.

Interspecific Competition

• Definition: A relationship between two or more species ($-/-$) where both are adversely affected as they compete for the same limiting resources.

• Simultaneous Competition: Species usually deal with intraspecific (within species) and interspecific (between species) competition at the same time.

• Examples:

  • Forestry/Restoration: When planting Kanuka, plants must be close enough to shade out weeds (interspecific competition with the seed bank) but not so close they compete with each other (intraspecific competition).

  • Woodlands: Chipmunks and squirrels in North America both competing for acorns.

Lotka-Volterra Competition Model

• Logistic Growth Foundation: The standard growth model is $\frac{dN}{dt} = rN \left( \frac{K-N}{K} \right)$.

• Adding Competition: To account for a second species, the equation for species 1 ($N_1$) is modified to include the population of species 2 ($N_2$).

• Perfect Competition Case: If two species are identical in resource use, the growth rate for species 1 becomes:

  • $\frac{dN_1}{dt} = r_1 N_1 \left( \frac{K_1 - (N_1 + N_2)}{K_1} \right)$

• Competition Coefficients (Alpha and Beta): Since species are rarely identical, we use coefficients to quantify the effect of one species on another.

  • $\alpha$: Represents the effect of species 2 on species 1.

  • $\beta$: Represents the effect of species 1 on species 2.

• Modified Lotka-Volterra Equations:

  • For Species 1: $\frac{dN_1}{dt} = r_1 N_1 \left( 1 - \frac{N_1 + \alpha N_2}{K_1} \right)$

  • For Species 2: $\frac{dN_2}{dt} = r_2 N_2 \left( 1 - \frac{N_2 + \beta N_1}{K_2} \right)$

Numerical Examples (The Antelope Scenario)

• Scenario 1: Species 1 Growth with No Competition

  • Variables: $r_1 = 0.15$, $N_1 = 400$, $N_2 = 0$, $K = 1000$.

  • Calculation: $0.15 \times 400 \times (1 - \frac{400+0}{1000})$.

  • Result: $60 \times 0.6 = 36$ individuals added.

• Scenario 2: Species 1 Growth with Perfect Competition ($\alpha = 1$)

  • Variables: $r_1 = 0.15$, $N_1 = 400$, $N_2 = 250$, $K = 1000$.

  • Calculation: $0.15 \times 400 \times (1 - \frac{400+250}{1000})$.

  • Result: $60 \times 0.35 = 21$ individuals added.

• Scenario 3: Species 1 Growth with Differential Competition ($\alpha = 0.5$)

  • Context: Species 2 is half the mass and eats half as much as species 1.

  • Variables: $r_1 = 0.15$, $N_1 = 400$, $N_2 = 250$, $K = 1000$, $\alpha = 0.5$.

  • Calculation: $0.15 \times 400 \times (1 - \frac{400 + (0.5 \times 250)}{1000})$.

  • Result: $60 \times (1 - 0.525) = 60 \times 0.475 = 28.5$ individuals added.

• Scenario 4: Species 2 Growth ($\beta = 2$)

  • Context: Species 1 is twice as large as species 2. Since species 2 is smaller, the environment's carrying capacity for them alone is higher ($K_2 = 2000$).

  • Variables: $r_2 = 0.15$, $N_2 = 250$, $N_1 = 400$, $K_2 = 2000$, $\beta = 2$.

  • Calculation: $0.15 \times 250 \times (1 - \frac{250 + (2 \times 400)}{2000})$.

  • Result: $37.5 \times (1 - \frac{1050}{2000}) = 37.5 \times 0.475 = 17.8125$.

Experimental Evidence of Competition

• Paramecium Study:

  • P. aurelia and P. caudatum have similar growth rates when grown separately.

  • When grown together, P. aurelia outcompetes P. caudatum, which reaches much lower densities. This supports the Lotka-Volterra predictions.

• Rocky Mountain Fish Study:

  • Elevation Distribution: Brook trout (high), Brown trout (middle), Creek chub (low).

  • Experimental Design: Fish were matched by size and tested at temperatures from $3^\circ\text{C}$ to $26^\circ\text{C}$. Food consumption was measured as an indicator of competitive success.

  • Results:

  • Brook Trout: Only outperformed others at very low temperatures ($3^\circ\text{C}$ - $4^\circ\text{C}$).

  • Brown Trout: Outcompeted brook trout starting at roughly $6^\circ\text{C}$.

  • Creek Chub: Dominated at temperatures above $24^\circ\text{C}$. High temperatures were detrimental to the trout species.

  • Conclusion: Abiotic conditions (temperature) mediate competitive ability, defining the realized niches along elevation gradients.

• Pennsylvania Grassland Study:

  • Seedlings were grown in PVC pipes with holes allowing varying degrees of root access to neighbors.

  • Results: As the percentage of the tube open to neighbors increased, root biomass of neighbors increased, and the total plant biomass of the subject plant decreased due to subterranean competition for resources.

Questions & Discussion

• Question: Can a realized niche be wider than a fundamental niche due to positive interactions?

• Answer: Theoretically yes, particularly in anthropogenic environments where facilitation occurs, though generally, competition constricts the niche. This is a topic explored further in third-year Community Ecology.

• Question: Are there shorter cycles for diseases?

• Answer: Yes, the London measles example focused on two-year cycles driven by the entry of new cohorts of susceptible children (e.g., entering kindergarten/school) rather than multi-generational cycles.