Population Ecology: Carrying Capacity and Predator-Prey Dynamics
Population Ecology
A population is a group of organisms of the same species living in the same area at the same time. Population ecology studies the factors that determine population size, density, and distribution, and how populations change over time.
Population Growth
Exponential (Geometric) Growth
When a population has unlimited resources and no predation, disease, or competition, it grows exponentially — the rate of increase is proportional to the current population size. The population doubles in each equal time period, producing a J-shaped curve.
This occurs when:
- Resources (food, water, space) are abundant
- There are no predators or parasites
- There is no competition (intraspecific or interspecific)
- Environmental conditions are favourable
In nature, exponential growth occurs briefly when a population colonises a new, resource-rich environment (e.g. bacteria in fresh culture medium, organisms introduced to an island with no competitors).
Logistic Growth and Carrying Capacity
In reality, resources are finite. As a population grows, it increasingly encounters environmental resistance — the sum of factors that limit population growth. The population growth rate slows and eventually stabilises at the carrying capacity (K).
Carrying capacity (K) is the maximum population size that the environment can sustain indefinitely given the available resources.
The logistic growth curve is S-shaped (sigmoidal) and has three phases:
1. Lag phase — population is small; growth is slow as individuals adapt to the environment and begin reproducing. Few reproductive individuals.
2. Log (exponential) phase — abundant resources; birth rate greatly exceeds death rate; population grows rapidly. The rate of increase is close to the maximum (rmax).
3. Stationary phase — population reaches the carrying capacity. Birth rate ≈ death rate. The population fluctuates around K as resources are consumed and replenished. Growth rate approaches zero.
Factors Affecting Carrying Capacity
| Factor | Effect |
|---|---|
| Food/nutrient availability | Directly limits population size |
| Water availability | Essential for all organisms |
| Space/territory | Limits nesting sites, territories |
| Predation | Removes individuals; increases death rate |
| Disease/parasitism | Increases death rate, especially in dense populations |
| Accumulation of waste | Toxic byproducts can limit growth (e.g. ethanol in yeast cultures) |
Density-Dependent and Density-Independent Factors
Density-Dependent Factors
These factors become more significant as population density increases:
- Intraspecific competition — competition for resources between members of the same species. As density increases, per-capita resource availability decreases, reducing birth rate and/or increasing death rate. This is the primary mechanism that regulates population size around K.
- Predation — predators may target denser prey populations more heavily
- Disease — pathogens spread more easily in dense populations (more frequent contact)
- Parasitism — increased transmission at higher densities
- Waste accumulation — more individuals produce more waste
Density-dependent factors provide negative feedback, stabilising the population near K.
Density-Independent Factors
These affect populations regardless of their density:
- Natural disasters — floods, fires, volcanic eruptions
- Weather events — droughts, severe winters, storms
- Human activities — habitat destruction, pollution, pesticides
These can cause sudden population crashes that are unrelated to population size.
Predator-Prey Relationships
Predators and their prey populations often show linked oscillations in population size, producing a characteristic pattern of out-of-phase cycles.
The Classic Pattern
1. When prey numbers are high, food is abundant for predators → predator numbers increase (more food → higher birth rate, lower death rate)
2. As predator numbers increase, more prey are consumed → prey numbers decrease
3. As prey numbers decline, food becomes scarce for predators → predator numbers decrease (starvation, lower birth rate)
4. As predator numbers decline, fewer prey are consumed → prey numbers recover
5. The cycle repeats
The predator population peaks and troughs lag behind the prey population — typically the predator curve is offset by a quarter to a half cycle.
The Lotka-Volterra Model
The mathematical model predicts that predator and prey populations oscillate indefinitely. In reality, oscillations may be:
- Damped — decreasing in amplitude over time toward a stable equilibrium
- Driven by external factors — weather, disease, or other species complicate the simple two-species model
- Chaotic — unpredictable fluctuations in complex ecosystems
Real-World Example: Lynx and Snowshoe Hare
The best-documented example comes from Hudson's Bay Company fur trapping records in Canada, spanning over 100 years (1845-1935):
- Snowshoe hare populations cycle with a period of approximately 9-11 years
- Canadian lynx populations follow with a similar period, peaking 1-2 years after the hare peaks
- The cycles are driven by a combination of predation and food supply for the hares (vegetation availability)
Factors That Complicate Simple Predator-Prey Models
| Factor | Effect |
|---|---|
| Multiple prey species | Predator can switch to alternative prey when one species declines |
| Multiple predator species | Prey population is affected by several predators |
| Refuges | Some prey can hide or escape, preventing total elimination |
| Migration | Immigration of prey or emigration of predators can alter dynamics |
| Time lags | Reproduction takes time; prey populations can overshoot or undershoot K |
| Human intervention | Hunting, habitat change, and introduction of species disrupt natural cycles |
Interspecific Competition and the Competitive Exclusion Principle
Interspecific competition occurs between individuals of different species that share the same resources.
The competitive exclusion principle (Gause's principle) states that two species competing for the same ecological niche cannot coexist indefinitely — one will outcompete the other, leading to local extinction of the weaker competitor.
Coexistence is possible when species occupy different niches (even if there is overlap) — they use different resources, feed at different times, or occupy different microhabitats. This is called resource partitioning or niche differentiation.
Measuring Populations
Sampling Methods
- Quadrats — square frames placed randomly in a habitat; count individuals or estimate percentage cover within each quadrat. Used for sessile (non-moving) organisms such as plants.
- Transects — a line (or belt) along which quadrats are placed at regular intervals; used to study how species distribution changes along an environmental gradient (e.g. across a rocky shore, up a hillside)
- Mark-release-recapture — used for mobile animals:
Lincoln index (mark-release-recapture):
N = (n₁ × n₂) / n₃
Where:
- N = estimated population size
- n₁ = number caught, marked, and released in first sample
- n₂ = total number caught in second sample
- n₃ = number of marked individuals recaptured in second sample
Assumptions:
- No immigration, emigration, births, or deaths between sampling events
- Marks do not affect survival or behaviour
- Marked individuals mix randomly with the unmarked population
- Marks are not lost between samples
- Sampling methods are equally likely to capture marked and unmarked individuals
Exam Tips
- AQA commonly asks you to interpret population growth curves — identify the lag, log, and stationary phases and explain what is happening at each stage
- When describing predator-prey cycles, always state that predator peaks lag behind prey peaks
- For mark-release-recapture calculations, show your working and state the assumptions — marks are often given for identifying assumptions that are violated
- Distinguish clearly between density-dependent factors (regulate population via negative feedback) and density-independent factors (cause random population changes regardless of density)
- When discussing carrying capacity, define it as the maximum population the environment can sustain INDEFINITELY — the word "indefinitely" or "long-term" is important