Three of six tracking fixes fall inside a habitat. That is half the recorded locations. It does not automatically mean that the animal spent half its time there, especially when the gaps between fixes are unequal.
The short answer is to keep the timestamps, define the habitat boundary and distinguish observed classifications from unobserved crossing times. A model can turn those gaps into estimates or bounds, but its assumptions must remain visible. A line on a map is not a continuous record of where the animal was.
This guide develops original fictional time records beneath the Wildlife subject guide. It uses no real nest, den, animal route or sensitive coordinate. Its interval models are teaching illustrations, not a validated ecological analysis or permission to approach, tag or disturb wildlife. The purpose is to explain what a residence-time claim needs before it can support a wider story about habitat use.
eduKateSG · Wildlife
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Choose the question closest to your task, or read the full lesson in order.
ROUTE 1 · CHAPTERS 1–4
Define the time question
Distinguish fixes, intervals and the observation window.
ROUTE 4 · CHAPTERS 16–18
Practise independently
Solve a changed timeline and diagnose the first error.
Chapter contents
Define the time question · Chapters 1–4
Build a bounded model · Chapters 5–9
Test the assumptions · Chapters 10–15
- 10. Add a fix and track which bound changes
- 11. Allow a boundary classification to remain uncertain
- 12. Keep habitat boundaries stable and meaningful
- 13. Separate time inside from preference or benefit
- 14. Treat gaps and deployment changes as evidence conditions
- 15. Compare pooled tracking time with an average animal proportion
Practise independently · Chapters 16–18
Continue responsibly · Chapters 19–21
CHAPTER 1 OF 21 · Define the time question
1. Define residence within a specific window
In this lesson, residence time means the total duration within a specified habitat boundary during a defined observation window. It does not necessarily mean one uninterrupted visit, a home range, feeding time or a preferred habitat.
Suppose an animal enters a mapped area, leaves and later returns. Its total time inside can combine several visits. A record of the first and last inside fixes does not establish that it stayed throughout the interval between them.
The window also matters. Twelve hours of tracking and a full migration season answer different questions. If the record begins while the animal is already inside, the total visit may have started earlier. If it ends inside, the visit may continue afterwards.
Write the question precisely: how much time did this fictional individual spend inside this defined area between t = 0 and t = 12 hours? That statement avoids silently turning a partial window into an entire visit.
The USGS wildlife tracking collection describes telemetry applications to movement, habitat use and time spent on behaviours. Our narrower exercise examines the time information between discrete fixes; it does not assume that an inside location identifies the animal’s behaviour or the ecological value of the area.
CHAPTER 2 OF 21 · Define the time question
2. Keep locations, classifications and durations separate
A tracking fix is a recorded location at a time, with whatever quality information the system supplies. A habitat classification assigns that location to a defined category. A duration concerns an interval, not an isolated point.
For the first mathematical model, assume that each supplied inside or outside classification is exact. This temporarily removes location error so that the timing problem can be examined on its own. We will add uncertain classifications later.
An inside fix at 03:00 establishes that classification at the observation time under the model. It does not alone show when entry occurred, whether the animal left soon afterwards or how long the previous visit lasted.
Likewise, an outside fix should not be replaced with absence from the broader landscape. The boundary may describe one habitat patch inside a much larger study area. The classification’s meaning follows the question and map, not the visual prominence of a point.
Use three columns in a learning record: supplied observation, derived quantity and interpretation. Put timestamps and exact model classifications in the first. Put interval lengths and conditional bounds in the second. Put the limited habitat-use conclusion in the third.
That separation protects the reasoning. A calculated number can be correct while the accompanying biological interpretation asks it to establish something the location-and-time record never measured.
Our main fictional record contains six fixes over twelve hours. Inside and Outside refer to one fixed boundary and the same individual throughout.
| Time | Classification | Interval until next fix |
|---|---|---|
| t = 0 h | Outside | 2 h |
| t = 2 h | Outside | 1 h |
| t = 3 h | Inside | 3 h |
| t = 6 h | Inside | 2 h |
| t = 8 h | Outside | 4 h |
| t = 12 h | Inside | End of window |
Three of six fixes are Inside, giving a point fraction of 50 per cent. The gaps are two, one, three, two and four hours. A simple fraction of points gives each fix equal weight even though the unobserved intervals have different durations.
Do not assign the final fix a four-hour duration merely because the preceding gap was four hours. It occurs at the end of the defined window. Any later time lies outside the supplied task.
Check the interval total independently: 2 + 1 + 3 + 2 + 4 = 12 hours. This confirms the window accounting before any habitat duration is assigned.
A useful learner question is what the 50 per cent actually describes. The supported answer is half the recorded fixes under the stated classification rule. Calling it half the animal’s time would require an additional timing or sampling argument.
CHAPTER 4 OF 21 · Define the time question
4. Explain what fixes alone leave unresolved
Without restrictions on movement between fixes, even two consecutive Inside observations do not prove continuous residence. The animal could leave and return before the next observation. Two Outside fixes could conceal a visit.
The same observation table can therefore fit different time histories. One history spends most of the window inside except near the Outside observations. Another spends very little time inside except near the Inside observations.
In this abstract exercise, exact classifications at isolated times alone provide no positive-duration lower bound and no useful upper bound smaller than the full window. This is a statement about missing model information, not a claim that real animals move without physical limits.
Actual movement, speed, landscape barriers and other sensors can constrain the possibilities. Those constraints must be supplied and justified. A plausible-looking straight map connector cannot silently provide all of them.
Ask learners to draw two inside/outside time strips through the same six observations. Include a hidden leave-and-return episode in one. Then identify what additional assumption would exclude it.
This first comparison matters because the later, narrower bounds will depend on a restriction. If the restriction is forgotten, the calculation can look like a direct observation of residence when it is really a model-dependent account.
Keep the distinction visible: the fixes establish classifications at their timestamps; a between-fix model establishes what histories are treated as admissible.
CHAPTER 5 OF 21 · Build a bounded model
5. Introduce a single-crossing model explicitly
For the main bounded exercise, assume that at most one inside/outside transition occurs between each adjacent pair of fixes. This is an invented mathematical condition for the lesson. It is not known to hold merely because tracking data exist.
Under that condition, two Inside endpoints imply an Inside interval apart from any boundary instants that do not affect duration. Leaving and returning would require two transitions, which the model excludes.
Two Outside endpoints similarly imply an Outside interval. Different endpoint classifications imply one transition, but its timing is unknown somewhere within the gap. The time inside can range from almost none of that interval to almost all of it.
For simple duration bounds, we use the closed interval endpoints zero and the full gap as limiting possibilities. Whether an exact boundary instant belongs to Inside does not change the total duration in this exercise.
This model makes the evidence more informative by excluding some possible histories. That is its role. It should not be described as a discovery made by the six fixes.
For a real ecological analysis, the appropriateness of movement and observation models requires competent assessment. Frequent crossings, complex boundaries, uncertain locations or a long gap can make the single-crossing condition implausible. A useful report should state the condition and discuss whether the actual evidence supports using it.
CHAPTER 6 OF 21 · Build a bounded model
6. Classify each interval before adding durations
Apply the single-crossing model to the five gaps. The first, Outside to Outside over two hours, contributes zero Inside time. The middle Inside-to-Inside interval from t = 3 to 6 contributes three hours.
The remaining gaps have different endpoint classifications. Their uncertain Inside contributions range from zero to their full lengths: one hour from t = 2 to 3, two hours from 6 to 8, and four hours from 8 to 12.
| Interval | Endpoint pair | Inside duration under the model |
|---|---|---|
| 0–2 h | Outside–Outside | 0 h |
| 2–3 h | Outside–Inside | 0–1 h |
| 3–6 h | Inside–Inside | 3 h |
| 6–8 h | Inside–Outside | 0–2 h |
| 8–12 h | Outside–Inside | 0–4 h |
The guaranteed contribution is three hours. The uncertain contributions can add at most seven. The compatible total residence range is therefore 3–10 hours, or 25 to approximately 83.3 per cent of the twelve-hour window.
This is a logical range under the specified model, not a confidence interval. It does not say that all values are equally probable, that the midpoint is expected, or that another individual would have the same residence.
An independent check uses Outside time. Two hours are fixed Outside and seven are uncertain, giving 2–9 hours Outside. Subtracting from twelve gives 3–10 Inside, agreeing with the direct calculation.
A bound is easier to trust when its relationship to possible histories is visible. To approach the lowest residence, place entry near t = 3, exit near t = 6, and the final entry near t = 12. The three-hour Inside-to-Inside span remains, while the transition intervals contribute almost no additional Inside time.
To approach the highest residence, place the first entry near t = 2, exit near t = 8, and final entry just after t = 8. The two-hour initial Outside-to-Outside span remains outside, while nearly all other time can be inside.
Each construction respects the one-transition-per-gap condition and the supplied classifications at the fixes. Boundary conventions can determine whether exact endpoint totals are attained or approached; the closed bounds remain a clear account of the admissible duration limits.
Do not connect the maximal history to a claim about the most likely behaviour. It was constructed to show the upper limit, not to represent a fitted movement model. The minimal history serves the corresponding lower-limit role.
For a learner, ask which interval controls the largest amount of uncertainty. The final four-hour transition gap contributes more uncertainty than the one-hour gap. This identifies where additional timing evidence could be valuable without pretending to prescribe an actual tag deployment.
The construction also reveals why a single plotted trajectory is only one choice among compatible histories. A neat path does not remove the alternatives unless additional evidence or a justified model excludes them.
CHAPTER 8 OF 21 · Build a bounded model
8. Compare carrying classifications forward and backward
One simple estimation rule carries each observed classification forward until the next fix. In the main record, Inside then runs from t = 3 until t = 8, producing five hours. The final Inside fix at t = 12 contributes no later time within this window.
A different rule carries the next classification backward over the preceding gap. It assigns Inside to t = 2–6 and t = 8–12, producing eight hours. Both methods use the same observations and reach different estimates.
Five and eight lie within the model’s 3–10 range. That does not make either the observed truth. The rules choose different crossing times: one delays a change to the next observation, while the other moves it to the earlier end of the gap.
| Timing convention | Estimated Inside time | What it assumes about transitions |
|---|---|---|
| Carry previous classification forward | 5 h | Change at the later endpoint |
| Carry next classification backward | 8 h | Change at the earlier endpoint |
| Midpoint of each transition interval | 6.5 h | Change at each gap’s midpoint |
The table is a comparison of conventions, not a menu of equally validated ecological methods. Their relevance depends on the actual question and evidence.
For a report, name the rule and retain the gap information. A reader should be able to distinguish five hours estimated by a carry-forward convention from five hours continuously established by suitable observations.
CHAPTER 9 OF 21 · Build a bounded model
9. Understand the midpoint estimate without giving it false certainty
Assign each transition to the midpoint of its gap. The one-hour Outside-to-Inside interval contributes half an hour. The two-hour Inside-to-Outside interval contributes one hour. The four-hour Outside-to-Inside interval contributes two hours.
Adding the fixed three hours gives 3 + 0.5 + 1 + 2 = 6.5 hours Inside. That is approximately 54.2 per cent of the twelve-hour window, which already differs from the 50 per cent point fraction.
The midpoint is a timing assumption. It is not established because a crossing happened somewhere in the gap. Interpreting it as an expected duration would require an additional probability model for crossing time; the interval record alone does not supply one.
Two compatible histories can place the crossing near opposite ends while retaining identical fixes. The midpoint convention chooses between them by a rule, not by observing the animal at the midpoint.
This does not forbid using a simple estimate for an explicitly illustrative task. It requires the estimate to carry its method and limitations. A sensitivity comparison with other admissible timings can show how much the conclusion depends on that choice.
Ask the learner to explain why 6.5 is not more authoritative merely because it has a decimal place. The precise arithmetic describes the chosen convention; it does not add precision to the unknown crossing times.
CHAPTER 10 OF 21 · Test the assumptions
10. Add a fix and track which bound changes
The longest uncertain gap runs from Outside at t = 8 to Inside at t = 12. Add an exact Inside classification at t = 10. Under the same single-crossing model, t = 10–12 is now a fixed two-hour Inside interval.
The earlier half, t = 8–10, remains a transition interval of up to two hours. The total lower bound rises from three to five hours, while the upper remains ten. The uncertainty width falls from seven to five hours.
Now consider the alternative new observation: Outside at t = 10. The t = 8–10 interval is fixed Outside, and t = 10–12 remains uncertain. The lower stays three while the upper falls from ten to eight. The uncertainty width is again five.
The same added timestamp can therefore improve the range in different directions depending on the observed classification. Additional data do not always move a result toward a preferred story about more habitat use.
For a learner, calculate the interval table again rather than adjusting the old percentage by intuition. The new fix changes the model’s allowed histories, which changes the supported duration range.
This exercise does not prescribe a field sampling schedule. Real choices involve animal welfare, device performance, resources and the ecological question. It simply demonstrates where a record’s uncertainty sits and what kind of additional observation could constrain it.
CHAPTER 11 OF 21 · Test the assumptions
11. Allow a boundary classification to remain uncertain
Location error can make a fix near the boundary difficult to classify. The recorded coordinate may fall just inside while an admissible error region overlaps both sides. Calling it definitely Inside would add certainty the location evidence does not provide.
For an original extension, keep the main record but mark the t = 6 classification Unknown. Suppose the supplied location evidence permits either Inside or Outside at that time. The remaining classifications are unchanged.
If t = 6 is Inside, the earlier 3–10 hour range applies under the single-crossing model. If t = 6 is Outside, the t = 3–6 interval becomes a three-hour transition, while t = 6–8 becomes fixed Outside. That version permits 0–8 hours Inside.
Across the two admissible classifications, the compatible overall range is 0–10 hours. The previously fixed three-hour Inside interval is no longer established. A single uncertain endpoint can therefore affect more than one adjacent interval.
This is not an instruction to classify every boundary point as missing. Use the actual location-quality information, spatial definition and appropriate analysis. The teaching point is to preserve the uncertainty when it is material.
Movebank's platform description connects individual locations with sensor information, study methods and data-quality management. A useful residence analysis likewise needs the quality context, not only the coordinate that makes the map easiest to draw.
CHAPTER 12 OF 21 · Test the assumptions
12. Keep habitat boundaries stable and meaningful
Inside means inside a particular boundary. Expanding the polygon can increase classified residence without any change in the animal’s behaviour. That may be a useful sensitivity analysis, but it is not evidence that habitat use increased over time.
Suppose two reports use the same tracking record but different mapped areas. One includes a surrounding strip that the other excludes. Their residence values can differ because the question changed. Compare the definitions before interpreting the numerical difference.
A boundary should relate to the ecological question and its evidence. A convenient map shape is not automatically a habitat of consistent quality. The animal’s presence inside also does not establish feeding, resting, breeding or benefit without additional information.
For a learner exercise, give two invented polygons and several non-sensitive points. Ask which classifications change and which stay the same. Then ask how the time intervals would need to be reconsidered under each boundary.
Keep map version and classification rules with the record. If an updated habitat map is scientifically justified, document the change rather than silently comparing it with a previous definition as though nothing changed.
This preserves an important distinction: movement can change, the observation method can change, and the habitat definition can change. A residence-time report should identify which of those produced the result before telling a story about the animal.
CHAPTER 13 OF 21 · Test the assumptions
13. Separate time inside from preference or benefit
An animal spending substantial time inside an area may be using it, passing through it, constrained there or responding to conditions the record does not describe. Residence is a measurement target, not an automatic explanation.
Preference needs an appropriate comparison with availability and other relevant factors. A large share of time in a widespread habitat does not by itself show selection for that habitat. The present interval ledger does not supply a full habitat-selection model.
Likewise, time inside a restored area does not alone establish improved survival, reproduction or population security. Those outcomes require suitable ecological evidence. The Wildlife Conservation guide provides the wider route from threats to conservation outcomes.
For a classroom claim-and-evidence check, compare three statements: the model supports 3–10 hours inside the boundary; the animal preferred this habitat; the restoration improved the population. Only the first follows from the supplied interval exercise.
The other statements may be worthwhile research questions. Their importance is a reason to obtain appropriate evidence, not a reason to stretch a location table until it seems to answer them.
A useful conclusion states the individual, window, boundary, model and range. It then names the next ecological question separately. This keeps a modest result valuable and prevents a visually compelling track from carrying an unsupported conservation claim.
CHAPTER 14 OF 21 · Test the assumptions
14. Treat gaps and deployment changes as evidence conditions
Tracking schedules can change, and some expected fixes may be absent. A gap can reflect the device, transmission, location acquisition or the available dataset. It should not automatically be interpreted as the animal leaving the habitat.
Preserve the actual timestamps rather than replacing a long gap with several invented evenly spaced points. Interpolated locations may be useful within a stated model, but they are not new observations.
If a device changes its schedule during the record, identify the break. A period with more fixes can yield a different point fraction even without an equivalent change in time spent inside. The observation process is part of the comparison.
The existing Wildlife Tracking, Telemetry and Migration Evidence guide develops the broader chain from animal and device to recorded trajectory. This lesson adds an explicit interval account for one duration question.
In the single-crossing classroom model, a longer transition gap directly widens the possible duration contribution. In a real analysis, the same gap may also make that model less credible because multiple crossings become more plausible. Do not treat the mathematical range as a complete representation of model uncertainty.
The practical habit is to retain observed fixes, quality information and modelling choices separately. A reader should be able to see which parts of the residence result come from data and which come from assumptions about the unobserved periods.
CHAPTER 15 OF 21 · Test the assumptions
15. Compare pooled tracking time with an average animal proportion
Combining individuals introduces another denominator question. An average of individual residence proportions gives each individual equal weight. A pooled time proportion gives each tracked hour equal weight. They can differ when windows have different lengths.
Take the main individual’s twelve-hour window with a conditional 3–10 hours Inside. A second fictional individual has a four-hour window with a separately established 1–2 hours Inside under its stated model.
Pooling the windows gives sixteen tracked hours and 4–12 hours Inside. The pooled proportion range is 25–75 per cent. Averaging individual proportions instead gives a lower value of (3/12 + 1/4)/2 = 25 per cent and an upper of (10/12 + 2/4)/2, approximately 66.7 per cent.
The matching lower endpoints are coincidental. The upper endpoints differ because the twelve-hour animal receives more weight in the pooled result.
Neither summary automatically describes a species or population. The animals, selection, seasons, windows and models still matter. Choose the summary according to the actual question and state how the weighting works.
For a learner, calculate both summaries before deciding which one answers a sentence such as proportion of observed animal-hours inside. That sentence points toward pooled time. A sentence about an equally weighted average across the two supplied individuals asks a different question.
CHAPTER 16 OF 21 · Practise independently
16. Try an independent residence-time record
Here is a changed fictional record for one individual over ten hours. Its classifications are Outside at t = 0, Inside at t = 1, Inside at t = 4, Outside at t = 5, Outside at t = 9 and Inside at t = 10.
Assume exact classifications and, only for this exercise, at most one transition in each adjacent-fix interval. Calculate the point fraction Inside, the fixed Inside duration, fixed Outside duration and total uncertain transition duration.
Use those interval categories to bound total residence. Check the result independently by subtracting the compatible Outside-time range from the ten-hour window.
Then calculate the carry-forward, carry-backward and midpoint estimates. Identify which assumptions place the crossing times and which quantities were actually supplied as observations.
Next add an exact Inside fix at t = 9.5. Recalculate the lower and upper residence bounds. Explain why the new half-hour Inside-to-Inside interval changes one endpoint of the range.
Finally, remove the single-crossing assumption. Explain why the earlier fixed Inside and Outside spans are no longer established merely by matching endpoint classifications.
Write the conclusion with the words under the stated model where appropriate. That phrase is doing real work: without it, an interval result can be misread as a continuous observation of the animal.
Three of six fixes are Inside, so the point fraction is 50 per cent. The Inside-to-Inside interval from t = 1 to 4 contributes three fixed hours. The Outside-to-Outside interval from 5 to 9 contributes four fixed hours.
The three transition gaps, 0–1, 4–5 and 9–10, are each one hour. Their total uncertainty contribution is three hours. The compatible residence range is therefore 3–6 hours, or 30–60 per cent of the window.
| Independent-record quantity | Result |
|---|---|
| Fixed Inside time | 3 h |
| Fixed Outside time | 4 h |
| Transition-gap total | 3 h |
| Compatible Inside range | 3–6 h |
| Carry-forward estimate | 4 h |
| Carry-backward estimate | 5 h |
| Midpoint estimate | 4.5 h |
The Outside range is 4–7 hours. Subtracting from ten gives 3–6 Inside, agreeing with the direct result.
With the added Inside observation at t = 9.5, the final half-hour becomes fixed Inside. The earlier half-hour remains a transition gap. The lower bound rises to 3.5 hours and the upper stays six.
Without the single-crossing assumption, an Inside-to-Inside gap can contain a leave-and-return episode and an Outside-to-Outside gap can contain a visit. The fixed spans used in the calculation no longer follow from endpoint classifications alone. The record needs another justified model or additional evidence before retaining those narrower bounds.
If a learner treats half the points as half the time, return to the timestamps. Ask them to compare a one-hour gap with a four-hour gap and explain why equal point weights do not automatically represent equal duration.
If they count the entire first-to-last Inside span, insert an observed Outside fix between those endpoints. The claim of uninterrupted residence should now be visibly incompatible with the record.
If they correctly derive 3–10 hours but forget the single-crossing assumption, ask for a hidden exit and return between two Inside fixes. That drawing shows which histories the model deliberately removed.
If they call the midpoint estimate measured time, ask where the crossing was observed. The midpoint is supplied by a convention, not by a fix at that moment.
If the numbers are correct but the conclusion declares habitat preference or successful conservation, separate the duration question from the ecological explanation. Name the additional comparison or outcome evidence required.
Finish with a new boundary or observation schedule and ask the learner to rebuild the interval table independently. A person who can identify which assumption changed the result has learned more than one particular percentage. They can now question a residence claim in another setting without dismissing the value of tracking altogether.
The repair route uses a paper timeline with Inside and Outside cards at irregular times. Begin with what is observed, then ask learners to draw alternative histories. Keep the task fictional and free of sensitive wildlife locations.
The stabilisation route adds the explicit single-crossing rule, classifies intervals and checks residence from both Inside and Outside totals. Compare a point fraction, a bound and an estimated duration so that the different claims remain visible.
The extension route introduces uncertain locations, changed boundaries, missing fixes and different individual windows. Add one complication at a time. The learner should explain what remains valid and which earlier conclusion needs to be weakened or recalculated.
For teachers, the useful assessment is a supported explanation: individual, boundary, window, observation process, model, result and limitation. A polished animation without those elements can hide more than a simple table reveals.
For actual ecological work, use the relevant permissions, animal-welfare arrangements, data controls and competent methods. A classroom interval exercise is not a deployment plan or a validated habitat-use analysis.
The practical next step is to inspect one residence statement and underline its time window and model. If neither is visible, ask for them before treating a precise percentage as a complete account of the animal’s time.
Do three Inside fixes out of six mean half the time inside?
They mean half the recorded fixes were classified Inside. Translating that fraction into time requires a suitable observation or modelling argument.
Do two Inside fixes prove the animal stayed between them?
Not without further evidence or a restriction such as the classroom single-crossing model. Hidden exits and returns are otherwise possible.
Is the midpoint crossing time the most likely one?
The supplied interval record does not establish that. It is a convention unless a justified probability model supports an expected-time interpretation.
Are the duration ranges confidence intervals?
No. They are logical bounds under explicit assumptions, not probabilities about paths or a complete treatment of ecological uncertainty.
Does more time inside establish preference?
No. Availability, movement context, observation conditions and the relevant ecological alternatives need consideration. Presence also does not identify behaviour automatically.
Should precise real locations be published for checking?
Use the project’s data-sharing rules and appropriate protection for sensitive information. This lesson uses fictional records and needs no real wildlife coordinates.
CHAPTER 21 OF 21 · Continue responsibly
21. Continue through the connected movement and conservation guides
Follow the animal, instrument and inference
The Wildlife root connects ethical observation with habitat and population questions. Wildlife Tracking, Telemetry and Migration Evidence explains the broader measurement chain. Kinematics: Sampled Position Data, Hidden Reversals and Measurement Error owns the different problem of travel distance and sampled motion; this article does not retitle that path-length lesson.
Keep conservation claims proportionate
Wildlife Conservation develops the route from threats and interventions to outcomes. A bounded time-inside calculation is one possible piece of evidence, not a substitute for that wider ecological assessment.
The USGS Alaska wildlife tracking collection and Movebank's platform description were checked on 22 October 2026 for their tracking, habitat-use and data-context information. All timelines, crossing assumptions, classifications and bounds here are original fictional teaching models, not methods endorsed for a particular study.
Continue through Education: learning that transfers into life and How X Works. Before reading a residence percentage as an animal’s continuous history, ask how the unobserved intervals were treated.