Ecological Interactions and Competition Modeling

Administrative Updates and Lab Report Expectations

• Lab Report Grading Policy: The instructor identifies as an "extremely easy" grader on lab reports, provided students put in a genuine effort.

• Submission Quality: Turning in "trash" or high-effort results that appear to have been finished five million minutes before the deadline negatively impacts grades. The goal is to reward those who perform the work and avoid equating low-effort submissions with high-quality work.

• Open Communication: Students are encouraged to ask questions, even if the same question has already been addressed multiple times. It is preferable to provide clarity than to receive poorly executed reports.

• GPS Data and Laboratory Timeline:

  • Students are required to check and correct the GPS data for their trees immediately, as several entries contain "janky" or "screwy" numbers that prevent others from completing their reports.

  • The deadline for lab reports has been extended by one week to accommodate the time needed to fix the data set.

Introduction to Species Interactions: The Cod Example

• The "Trifecta" Cod: A fisherman in Canada recently published a photo of a large Cod that had consumed two other Cod simultaneously on a single hook.

• Nature of the Interaction: This is a primary example of cannibalism, which is categorised as a specific type of predation.

• Intraspecific Competition: In this context, it also represents intraspecific competition. A larger individual consumes smaller members of its own species to gain resources and eliminate competitors in its "daily business."

Taxonomy of Biological Interactions

Species interactions are defined by how each party is affected (benefited, harmed, or unaffected):

• Mutualism ($+/+$): Both species benefit from the interaction.

  • Symbiosis: Often used interchangeably with mutualism, though it specifically refers to a form where both parties receive a benefit.

• Parasitism ($+/-$): One species (the parasite) benefits at the expense of another (the host).

  • Strategy: A successful parasite does not kill its host because it wants the host to live as long as possible to provide a consistent resource.

  • Examples: Tapeworms weaken but rarely kill the host; mosquitoes feed off a host for a duration without causing death.

• Commensalism ($+/0$): One party gains a benefit while the other is completely unaffected.

  • Orchids: In rainforests, orchids live high on trees to reach sunlight. Their roots do not penetrate the tree or steal nutrients; they simply use the tree's physical structure as a home.

  • Butterflies and Caimans: Butterflies land on caimans to sun themselves in a safe, elevated position. The caiman is typically unaffected. (While one could argue it is mutualism if the butterfly attracts birds that the caiman then eats, it is generally classified as commensalism).

• Amensalism ($-/0$): One species is harmed, while the other is unaffected.

  • Example: A small flower growing in the deep shade of a large tree suffers from lack of sunlight, while the large tree is indifferent to the flower's presence.

• Neutralism ($0/0$): Two species live together but do not interact or share resources in any capacity.

• Predation ($+/-$): The goal is the immediate consumption of the prey. Unlike parasitism, the outcome for the prey is death (e.g., a ladybug eating aphids).

The Ecological Niche

• Definition: Scientifically defined as an n-dimensional hyper volume.

  • n: Represents the number of environmental factors important to the survival and reproduction of a species.

• Practical Explanation: A niche is what it takes for an organism to perform its "daily business," including water, resources, shelter, and sunlight.

• Dimensions of a Niche:

  • Food Particle Size: The specific range of food sizes an organism can utilize (some are too small, some too big).

  • Foraging Height: The vertical range an animal can reach (e.g., too short or too tall).

  • Light Intensity: The specific amount of light required (not too little, not too much).

• The Snail Example: A snail\'s niche is defined by eating algae and bacteria and its requirement for moisture. While it can live on land or in water, it cannot survive in a desert because it would dry out.

Categorization of Competition

• Symmetric Competition: The classic definition where both parties lose ($-/-$). Competing for the same resources means both individuals expend more energy to get fewer resources.

• Asymmetric Competition: Relates to amensalism; one species is significantly more impacted than the other.

• Interference Competition: Direct, often aggressive, interaction that prevents others from using a resource.

  • Example: Geese protecting nests will aggressively chase humans or other animals away, functionally preventing them from utilizing that space.

• Exploitation Competition: Indirect competition for limited resources.

  • Example: Plants in a forest compete for sunlight, water, and nitrogen. The plant that grows the fastest and shades out others "wins" by exploiting the limited sunlight better than its neighbours.

Strategies for Avoiding or Mitigating Competition

• Creosote Bushes: These plants grow in close proximity in the Southwest, but their roots avoid each other. When a root encounters another individual\'s root, it turns away, allowing same-species (conspecific) plants to share space without massive competition.

• Herd Behavior: Animals like cattle or wildebeest move as a group to new pastures. Their positions within the herd often rotate so that the leading edge constantly finds new food, preventing a static disadvantage for individuals in the back.

• Social Hierarchies: Hyenas establish a dominance order (e.g., Female A eats first, then B, then Male A). Establishing this hierarchy avoids the need to fight over every meal, thereby reducing overall competition energy costs.

Competitive Exclusion and Niche Dynamics

• The Competitive Exclusion Principle: Two species with identical niches cannot coexist indefinitely; one will eventually outcompute the other.

• Realized vs. Fundamental Niche:

  • Fundamental Niche: The entire range of conditions under which a species could potentially survive and reproduce (e.g., humans can live in the Arctic or the Sahara).

  • Realized Niche: The actual subset of the fundamental niche that a species occupies, often restricted by predators or competitors.

  • Shrinking the Niche: Mountain gorillas are physically capable of eating meat (they have the teeth and digestive capacity), but they choose not to. This makes their realized niche smaller than their fundamental niche.

• Expanding the Niche (Rare cases): Occasionally, the presence of one species makes an area inhabitable for another. Humans cannot digest wood, but if termites are present to convert wood into termite biomass, humans can survive in a woody area by eating the termites.

• The Date Palm: Date palms allowed human societies (like Bedouins or Berbers) to inhabit deserts by providing a high-sugar, transportable food source in otherwise uninhabitable wadis.

Mathematical Modeling: The Lotka-Volterra Competition Equations

To understand interspecific competition, we modify the logistic growth equation:

$\frac{dN}{dt} = rN\left(\frac{K-N}{K}\right)$

The Competition Coefficients ($\alpha$)

For two species (1 and 2), we account for the impact of one on the other using $\alpha$:

• Species 1 Growth: $\frac{dN_1}{dt} = r_1N_1 \left( \frac{K_1 - N_1 - \alpha_{12} N_2}{K_1} \right)$

• Species 2 Growth: $\frac{dN_2}{dt} = r_2N_2 \left( \frac{K_2 - N_2 - \alpha_{21} N_1}{K_2} \right)$

• Weighting Interactions: If 1 deer eats as much as 5 groundhogs, the impact of a groundhog on the deer\'s carrying capacity ($\alpha$) is $\frac{1}{5}$ (or $0.2$). If calculating the impact of a deer on groundhogs, the coefficient is $5$.

Competition Scenarios based on $\alpha$

• \alpha < 1: The impact of the other species is small; intraspecific competition is more significant than interspecific competition.

• \alpha > 1: The impact of the other species is large; interspecific competition is more significant.

• $\alpha = 1$: Intra- and interspecific competition are equal.

Isoclines of Zero Population Growth

• Definition: An isocline is a set of population abundances for which the growth rate of a species is zero.

• Graphical Representation: For Species 1, the x-axis intercept is $K_1$ (carrying capacity with zero competitors). The y-axis intercept is $\frac{K_1}{\alpha_{12}}$ (the number of Species 2 individuals required to completely exclude Species 1).

• Utility: Plotting these lines on the same chart allows ecologists to predict whether species will coexist, whether one will exclude the other, or if the outcome depends on initial population sizes.