AP Syllabus focus:
‘Relationships among populations can be modeled as positive or negative interactions, such as predator–prey and cooperation.’
Interactions among species shape community structure by changing survival, reproduction, and resource access. Ecologists model these effects using sign conventions and simple equations that predict how one population’s growth changes when another population is present.
Why model species interactions?
Models translate observations into testable predictions about population change under different interaction types. In AP Biology, emphasis is on identifying positive, negative, and neutral effects and interpreting what they imply for population trends over time.
Interaction “signs” (net effects)
A convenient first model uses the net effect of each species on the other:
(+/+) both benefit (often cooperation/mutual benefit)
(+/−) one benefits, the other is harmed (predator–prey; also many parasite–host cases)
(−/−) both are harmed (competition)
(+/0) one benefits, the other is largely unaffected (commensal-like outcomes)
(−/0) one is harmed, the other is largely unaffected (amensal-like outcomes)
(0/0) neither is detectably affected (neutral in the measured context)
Modeling with interaction coefficients
To move beyond signs, ecologists assign coefficients that represent the direction and strength of effects on per-capita growth.
Interaction coefficient: A parameter describing how the presence of one species changes the growth rate of another species; its sign indicates whether the effect is beneficial (+) or harmful (−), and its magnitude reflects effect strength.
Because coefficients summarise net outcomes, they can change with environment, density, age structure, or resource levels; models are always tied to stated conditions and timescales.
General two-species interaction model (conceptual)
A common framework adds an interaction term proportional to encounters between species.
= population size of species 1 (individuals)
= population size of species 2 (individuals)
= intrinsic per-capita growth rate of species 1 (time)
= intrinsic per-capita growth rate of species 2 (time)
= effect of species 2 on species 1 (time·individual)
= effect of species 1 on species 2 (time·individual)
In this model, predator–prey interactions are captured when one coefficient is positive and the other is negative; cooperation is captured when both coefficients are positive.
Predator–prey as a (+/−) interaction
Core idea
Predators gain energy (higher survival/reproduction) from consuming prey: predator benefits (+).
Prey experience reduced survival and/or reproduction: prey harmed (−).
What models help you predict
If predator numbers rise, prey growth rate decreases (more negative effect on prey).
If prey numbers rise, predator growth can increase (more food), often producing coupled population changes.
The strength of the interaction (coefficient magnitude) affects stability: strong effects can produce large oscillations; weaker effects can dampen fluctuations.
Key interpretation skills
From a graph, identify which population changes first and which follows (a time lag is common in predator–prey dynamics).
Time-series dynamics from a Lotka–Volterra predator–prey model, showing prey and predator abundances oscillating through time. The offset between the curves illustrates the typical lag: prey increases first, then predator increases in response to increased food availability. Source
Explain outcomes in terms of changed birth/death rates rather than “intent” or “need.”
Cooperation as a (+/+) interaction
Core idea
Cooperation increases fitness for both interacting populations (or groups) via shared benefits such as improved resource acquisition or defence.
Examples of mutualism: termites with gut protozoa (cellulose digestion) and lichen (fungus + photosynthetic partner). These pairings illustrate a (+/+) net effect, where each partner gains resources or services that increase survival and/or reproduction. Source
Modeling cooperation
Both coefficients are positive: and .
Cooperation can raise effective growth when partners are present, but real systems often include limits (space, nutrients), so benefits may plateau as density increases.
How to justify a (+/+) claim using evidence
Show that each population has a higher growth rate, survival rate, or reproductive output when the other is present versus absent.
Control for alternative causes (e.g., shared abiotic conditions) to avoid confusing correlation with interaction.
Using models responsibly (assumptions and limits)
Net-effect simplification: signs/coefficients may hide multiple mechanisms (e.g., a predator also reduces competitors of the prey).
Context dependence: the same pair can shift from (+/+) to (+/−) if resources become scarce.
Scale: short-term behavioural effects may not match long-term population outcomes.
Testing: model predictions should be compared to data (population counts, survival, fecundity) under defined conditions.
FAQ
They separate immediate mechanisms (e.g., consumption) from mediated pathways (e.g., predator reduces a herbivore, indirectly benefiting plants).
Useful approaches include:
Removal/addition experiments
Path analysis or causal diagrams
Comparing outcomes across multiple community contexts
Yes. The interaction term is modified so predation pressure does not rise linearly with prey density.
Common outcomes:
Stabilised dynamics if refuges reduce predation at low prey density
Slower predator growth when predators saturate at high prey density
If conditions change so that one partner imposes costs exceeding benefits (e.g., resource scarcity, overcrowding, or partner “cheating”).
Models may shift coefficients from $+$ to $-$ as net fitness effects reverse.
You need demonstrated fitness changes attributable to the partner’s presence.
Evidence may include:
Increased survival/fecundity in paired treatments
Mechanistic links (e.g., shared defence behaviour)
Controls for abiotic variables and resource availability
Delays between prey increase and predator reproduction can create cycles even if average conditions are stable.
Time lags arise from:
Gestation/development time
Seasonal breeding
Delayed numerical response of predators to prey abundance
Practice Questions
In a predator–prey relationship, state the sign of the effect on each species and briefly justify each sign. (2 marks)
Prey experiences a negative effect (−) because predation reduces prey survival and/or reproduction. (1)
Predator experiences a positive effect (+) because consuming prey increases predator energy intake, survival and/or reproduction. (1)
A two-species model uses interaction coefficients and . Describe the expected signs of these coefficients for (i) predator–prey and (ii) cooperation, and explain what the magnitude of the coefficients represents. (5 marks)
Predator–prey: one coefficient positive and the other negative (e.g., prey affected negatively by predator so if species 2 is predator; predator benefits from prey so the other coefficient ). (2)
Cooperation: both coefficients positive, and . (1)
Magnitude represents strength of per-capita effect on growth rate (larger absolute value = stronger effect). (1)
Coefficients summarise net effects under stated conditions (can vary with context). (1)
