Competition occurs when two or more organisms vie for the same limited resources, such as food, space, or mates. This interaction can be intraspecific, occurring between members of the same species, or interspecific, happening between different species.

Types of Competition:

• Exploitative Competition: Organisms indirectly compete by consuming shared resources, reducing availability for others.
• Interference Competition: Direct interactions occur where organisms actively prevent others from accessing resources.

Competitive Exclusion Principle: Proposed by G.F. Gause, this principle states that two species competing for the same limiting resource cannot coexist indefinitely. One species will outcompete and exclude the other.

Niche Partitioning: To reduce competition, species may adapt to utilize different resources or occupy different niches within the same environment. This can involve temporal separation (using resources at different times) or spatial separation (using resources in different areas).

Lotka-Volterra Competition Model: This mathematical model describes the dynamics of biological systems in which two species compete for the same resources. The equations are:

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

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

Where:

• $N_1$, $N_2$: Population sizes of species 1 and 2.
• $r_1$, $r_2$: Intrinsic growth rates of species 1 and 2.
• $K_1$, $K_2$: Carrying capacities for species 1 and 2.
• $\alpha$, $\beta$: Competition coefficients measuring the impact of one species on the other.

These equations illustrate how the presence of one species can limit the growth of another, leading to potential dominance of one species in the environment.

Predation involves a predator organism consuming a prey organism. This interaction is a form of consumer-resource relationship and plays a critical role in regulating population sizes and maintaining ecosystem balance.

Types of Predation:

• Facultative Predation: Predators that do not rely exclusively on a single prey species for survival and can switch to other food sources if necessary.
• Obligate Predation: Predators that depend on a specific prey species for their nutritional needs and cannot survive without it.

Functional Response: Describes how the rate of prey consumption by a predator changes with prey density. The three types are:

• Type I: Linear increase in prey consumption until satiation.
• Type II: Rapid increase in consumption that slows as the predator becomes satiated.
• Type III: Sigmoidal relationship where consumption accelerates at intermediate prey densities.

Lotka-Volterra Predation Model: A set of equations that describe the dynamics between predator and prey populations:

$$\frac{dN}{dt} = rN - aNP$$

$$\frac{dP}{dt} = baNP - mP$$

Where:

• $N$: Prey population size.
• $P$: Predator population size.
• $r$: Intrinsic growth rate of prey.
• $a$: Predation rate coefficient.
• $b$: Conversion efficiency of prey into predators.
• $m$: Predator mortality rate.

These equations demonstrate how prey populations can support predator populations, while predators help regulate prey numbers, creating cyclical population dynamics.

Symbiosis refers to a close and long-term biological interaction between two different biological organisms. These relationships can vary in nature, ranging from mutually beneficial to harmful.

Types of Symbiotic Relationships:

• Mutualism: Both organisms benefit from the interaction. Example: Bees pollinating flowers while obtaining nectar.
• Commensalism: One organism benefits while the other is neither helped nor harmed. Example: Barnacles attaching to whales.
• Parasitism: One organism (the parasite) benefits at the expense of the other (the host). Example: Ticks feeding on the blood of mammals.

Facilitation: A form of symbiosis where one species has a positive effect on another, often making the environment more favorable. Example: Certain plants releasing chemicals that inhibit the growth of competing species.

Obligate vs. Facultative Symbiosis:

• Obligate Symbiosis: Both or one of the organisms cannot survive without the other. Example: Lichen formation between fungi and algae.
• Facultative Symbiosis: The organisms can survive independently but may benefit from the association. Example: Clownfish and anemones.

Evolutionary Implications: Symbiotic relationships can drive evolutionary changes, leading to coevolution where two or more species reciprocally affect each other's evolution. This can result in specialized adaptations that enhance the symbiotic partnership.

• Competition, predation, and symbiosis are fundamental ecological interactions shaping ecosystems.
• Competition can be intraspecific or interspecific, leading to competitive exclusion or niche partitioning.
• Predation involves predator and prey dynamics, influencing population cycles and ecosystem balance.
• Symbiotic relationships range from mutualism to parasitism, affecting the survival and evolution of involved species.
• Understanding these interactions is essential for comprehending ecological niches and the intricate web of life.