Biology · Behaviour, Communication & Social Life
Foraging, navigation, migration and decision-making
A forager can collect more from a patch by staying longer, yet the return per unit of total time may fall. On its way home, knowing a direction may still leave it without the information needed to locate home. Both problems depend on what is counted and what information is available.
Nervous Systems, Senses & Movement supplies the sensory and motor context. Evolutionary Processes & Adaptation introduces heritable variation, selection and fitness. Begin with the first lesson and the ordinary numerical examples; return to those chapters when a mechanism or evolutionary comparison needs more detail. Animal Reproduction, Development & Life Histories is an optional return path for reproductive timing and the distinction between resource expenditure and lifetime outcomes.
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Use explicit currencies and spatial information to reason about food acquisition, orientation and migration without assuming a universal optimum.
More food and a higher rate are different comparisons
Foraging includes finding, acquiring and using food resources. A decision model identifies a currency: for example, resource amount per unit of time. It then states constraints such as travel, handling, digestive capacity or risk. Different currencies and constraints can favour different actions.
Optimal foraging models describe predictions under assumptions. They do not require an animal to calculate a ratio consciously, and they do not establish that every observed action is the best possible one. A fit to one prediction also does not verify all of the model's assumptions.
The original patch table assigns cumulative resource gains of five, eight, ten and eleven after one, two, three and four residence units. Travel adds two time units to each visit. Gains keep increasing, but later increments are smaller. The whole visit's rate includes travel as well as residence.
More cumulative gain can accompany a lower rate
Read the diagram in words
Residence times 1/2/3/4 give gains 5/8/10/11 and total times 3/4/5/6. Rates are 5/3, 2, 2 and 11/6. The maximum among supplied options is two, shared by residence two and three.
| Residence option | Cumulative gain | Gain added since previous residence value | Travel plus residence time | Cumulative gain divided by total time |
|---|---|---|---|---|
| 1 | 5 | 5 | 3 | 5/3 |
| 2 | 8 | 3 | 4 | 8/4 = 2 |
| 3 | 10 | 2 | 5 | 10/5 = 2 |
| 4 | 11 | 1 | 6 | 11/6 |
Travel plus residence time: 2 + Residence time
Two listed options tie for the largest rate: 2, 3; Gain per total time unit: 2
Assigned time units; Assigned resource units
Connections join listed residence options only
Original discrete gains, four residence options, fixed travel time and resource-per-total-time currency. No empirical intake, risk, continuous optimum, future fitness or conscious calculation.
The best row belongs to the stated problem
The supplied rate is cumulative gain divided by travel plus residence time. Staying for two or three residence units gives the largest rate among the four listed options. The model has a tie, so it does not identify one unique departure time.
A different travel cost, resource schedule or objective could change the ranking. Reducing exposure to predators, obtaining a particular nutrient and maximising energy intake are different problems. They may also be limited by uncertainty about what another patch contains.
Observed foraging can test a model's predictions, and departures from a prediction can reveal missing constraints. The rate table contains no measurements, future reproductive outcomes or proof that natural selection produced the illustrated choice. It helps expose the assumptions before extending an explanation to an animal.
A compass is useful information, not an address
Orientation concerns direction. A compass provides a reference for heading, while navigation to a goal may also require information about the goal's location relative to the current position. An animal using a familiar landmark route need not use exactly the same information as one crossing unfamiliar terrain.
Path integration accumulates information about movements to estimate position relative to a starting point. The original route goes three assigned distance units along one axis and four along the other. The endpoint is displaced five units from the start, while the travelled route totals seven.
The return vector points three units in the negative first-axis direction and four in the negative second-axis direction. Two animals at different positions can adopt the same compass heading and still reach different destinations. Errors in estimated movements can accumulate, and a geometric record does not identify which sensory cues an animal uses.
A travelled route differs from displacement
Read the diagram in words
The route moves from 0, 0 to 3, 0 and then 3, 4. Its leg lengths sum to seven; the start-to-end straight distance is five. Returning to the start reverses the displacement to −3, −4.
| A travelled route differs from displacement | First conceptual spatial coordinate | Second conceptual spatial coordinate |
|---|---|---|
| Starting point | 0 | 0 |
| Turning point | 3 | 0 |
| Endpoint | 3 | 4 |
| Travelled legs | Assigned distance units |
|---|---|
| Starting point → Turning point | 3 |
| Turning point → Endpoint | 4 |
| Travelled legs | 7 |
|---|---|
| Start-to-end displacement | Starting point (0, 0) → Endpoint (3, 4); (3, 4); 5 |
| Displacement needed to return | Endpoint (3, 4) → Starting point (0, 0); (-3, -4); 5 |
These coordinates do not identify an animal's sensory information
Original two-dimensional geometry and assigned distance units. No actual animal route, compass error, movement timing, map or migration mechanism.
Movement across a season can combine several capacities
Migration involves directed movements linked to a life cycle or changing conditions, often between recurring regions. Distance alone is not enough to classify every journey as migration. Species differ in schedules, routes, the proportion of individuals moving and the contributions of development and experience.
Animals can use combinations of landmarks, celestial information, odours, magnetic information and other cues in different settings. Detecting a directional reference and estimating location are distinct tasks. A successful journey does not by itself tell us which information was decisive.
In a selected honeybee system, recruited flight paths provide evidence that waggle dances convey direction and range information. That example connects navigation with communication, but it does not make every bee or every migrating animal share one code. A behaviour can use information without having human-like language or conscious map calculations.
Worked example
Include travel before comparing rates
At residence two, the assigned gain is eight and the total time is two travel units plus two residence units. The rate is 8/4 = 2 resource units per time unit. At residence three,10/(2 + 3)=2 also.
Residence four gives the largest cumulative gain, eleven, but its rate is 11/6, approximately 1.83. Taking more total resource is therefore compatible with a lower rate. The equal rates at two and three are the complete answer for the listed alternatives.
For the route, total travelled distance is 3 + 4 = 7. Straight displacement is the square root of 3²+4², which is five. The return vector reverses both components. These are different descriptions of one original geometric record, not measured migration performance.
Check your understanding
Which residence options maximise the supplied resource rate when travel takes two time units?
Show reasoning
Residence two and three tie at two resource units per total time unit:8/4 and 10/5. The table supplies no unique winner and no lifetime-fitness ranking.
Why can a longer stay yield more resource but a lower rate?
Show reasoning
The numerator and denominator both grow. At residence four, gain eleven is spread over six total time units; the resulting rate is lower than eight over four or ten over five.
Does a correct compass heading alone identify the route to home?
Show reasoning
No. Heading specifies a direction. Reaching a location may also require positional, landmark or other information; the same heading from different starting points can lead to different endpoints.
What to carry forward
A behavioural model becomes interpretable when its currency, constraints, location and information are explicit.
References
Resources supporting this lesson’s explanations and examples.
- Foraging in a patchy environment by a predatory net-spinning caddis larva: A test of optimal foraging theory (Oecologia 47(2):219–221, 1980; doi: 10.1007/BF00346824)C. R. Townsend and A. G. HildrewPrimary research article
- A mathematical framework for optimal foraging of herbivores (Journal of Mathematical Biology 33(4):365–387, 1995; doi: 10.1007/BF00176378)S. Focardi and P. MarcelliniOriginal mathematical analysis
- Long-distance navigation and magnetoreception in migratory animals (Nature 558:50–59, 2018; doi: 10.1038/s41586-018-0176-1)Henrik MouritsenScientific review
- The flight paths of honeybees recruited by the waggle dance (Nature 435:205–207, 2005; doi: 10.1038/nature03526)J. R. Riley, U. Greggers, A. D. Smith, D. R. Reynolds and R. MenzelPrimary research article