Each guide begins with a short answer and follows one original record through definitions, calculations, evidence checks, changed contexts, misconceptions and bounded reporting.
The worked numbers are stipulated for learning. Authoritative sources define the operational methods; the examples show how to keep their boundaries visible.
The worked records are original teaching examples. Each keeps the observation, method boundary, calculation and decision in separate fields so the reader can see exactly where a conclusion begins and where it stops.
A changed-context check alters one consequential condition while leaving the other inputs fixed. This makes transfer visible and prevents the original numerical answer from becoming a rule without a scope.
Keep a compact evidence receipt: object, sampling or measurement method, units, reference condition, transformation, result and nearest rival explanation. A future reader should be able to reproduce the narrow claim from that receipt.
The five reading routes move from definitions to mechanism, evidence, transfer and reporting. Readers may enter by task, but the examples stay connected so the explanation does not become a list of detached tips.
The practical standard is an answer that can be checked. Preserve raw inputs, intermediate calculations, exclusions and versioned sources; then state one stronger claim that the evidence still cannot support.
Before choosing a formula, name the reader job in one sentence. A process check, research comparison, operational report and teaching exercise may use the same observation differently.
Every central case includes a near-match with one familiar surface feature and a different mechanism underneath. The pair matters because a definition becomes useful only when a learner can reject the tempting substitute.
The evidence route treats missing information honestly. An unknown method, interval, calibration or boundary stays blank until a source supplies it; a plausible assumption may complete arithmetic while weakening the conclusion.
The transfer route changes scale, timing, composition or sampling without silently changing every other field. Predict the direction first, then calculate or inspect the result.
The reporting route keeps measurement and judgement separate. State what was observed, what rule produced the derived value, what uncertainty remains and which action follows only under the declared conditions.
The final reader check is practical: someone entering through the short answer should know the distinction, someone following the worked example should reproduce it, and someone opening the sources should see where the example ends.
A useful misconception test constructs two cases with the same headline number and different underlying records. If their interpretations differ, the omitted condition belongs in the result.
Where a standard leaves behaviour to a competent laboratory, observing authority, analyst or software workflow, the article says so directly. That boundary tells the reader which conclusion can travel.
The examples avoid hidden precision. Rounded display values remain linked to the unrounded calculation, and stipulated inputs are labelled as teaching data.
A complete explanation keeps three layers apart: the thing in the world, the method that turns it into a value, and the decision made from that value. Numerical agreement between layers is evidence to investigate rather than permission to merge them.
For each central example, sketch the boundary before calculating. Mark what enters, what is retained or excluded, what the instrument or algorithm can observe, and what must be inferred.
This specialist guide belongs to the Wildlife root. It also connects to The Gold Standard of Education | Learning That Transfers into Life and the How X Works hub. The worked cases are original teaching examples; their numbers are stipulated so that the reasoning can be checked.
eduKateSG · Wildlife
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Read the short answer first: MCP encloses selected outer fixes with one convex boundary; a kernel method estimates a utilization-distribution surface whose stated contour encloses a chosen share. Report estimator, fix rules, bandwidth, contour and time window.
ROUTE 1 · CHAPTERS 1–4
Define the quantities
Name the quantities, reference conditions and reporting rules.
ROUTE 3 · CHAPTERS 9–12
Audit the evidence
Check instruments, algorithms, assumptions and rival explanations.
ROUTE 5 · CHAPTERS 17–20
Report and continue
Repair shortcuts, answer questions and follow verified routes.
Chapter contents
Define the quantities · Chapters 1–4
1. Name the two home-range objects
Work the mechanism · Chapters 5–8
5. Work the central two-cluster case
Audit the evidence · Chapters 9–12
Transfer the reasoning · Chapters 13–16
13. Transfer to a hard habitat boundary
Report and continue · Chapters 17–20
17. Repair the smaller-is-better shortcut
18. Repair the polygon-shows-use shortcut
A minimum convex polygon is the smallest convex hull containing the selected locations, usually reported as an enclosed area. A kernel utilization distribution estimates a spatial probability density, from which contours such as 95 percent and 50 percent are derived.
Write the evidence in the order a reader can audit: the Wildlife quantity, its reference object, the observation or browser rule, the transformation, and the decision being made. Keeping those fields visible prevents a familiar label from hiding a changed basis.
The same 120 fixes produce a 42 ha MCP, a 36 ha 95 percent kernel contour and a 9 ha 50 percent core. Store all three as method-specific outputs.
First-principles test: ask what physical, observational or algorithmic operation produces each value in this chapter. Then ask whether the second value could change while the first stays fixed. If it can, the two labels are not substitutes. For Wildlife, this counterfactual is often clearer than a definition learned in isolation.
Keep the fixes fixed and change only the estimator. The reported area can change without any animal movement.
Evidence check: another reader should be able to reproduce the narrow result from the stored definitions, inputs and intermediate steps, then identify the nearest stronger claim that the evidence does not support.
Home range is a study construct tied to sampling period, estimator and settings.
CHAPTER 2 OF 20 · Define the quantities
2. Separate boundary from probability surface
MCP draws one convex outer boundary and assigns no graded use inside it. A kernel UD represents relative use across space before a contour is selected. Equal areas therefore need not describe equal spatial use.
Trace the mechanism before interpreting the result. For Wildlife, mark which value belongs to the source, which belongs to the measurement or layout algorithm, and which is a reported summary. A calculation is useful only when those roles remain attached.
Draw an MCP containing a lake the animal never visits, then overlay a kernel surface with low density over the lake.
Practical transfer: build two records that share the headline number but differ in the condition discussed here. If the correct interpretation changes, the omitted condition is decision-relevant and belongs in the report. This test turns a vocabulary distinction into a reusable Wildlife checking habit.
Keep the outer area equal while move probability mass between two habitat patches.
Practical check: keep one counterexample beside the worked case. If the wording fails when that one condition changes, narrow the sentence until it describes only the evidence actually in hand.
A contour is a summary of an estimated surface, not direct observation of continuous presence.
A kernel area is incomplete without its isopleth or probability contour. A 95 percent range and 50 percent core answer different spatial-use questions even from the same UD.
Use a compact decision table with columns for condition, input, operation, result and limit. This makes the comparison reproducible and exposes where a missing field would force an assumption instead of an observation.
Report 36 ha at 95 percent and 9 ha at 50 percent for the central animal.
Misconception check: a plausible output does not prove the right reference, denominator, ancestor, spectrum or observation rule was used. Reconstruct one intermediate step and one changed-context prediction. If either cannot be stated, keep the result provisional rather than strengthening its wording.
Change only the contour from 95 to 90 percent and predict a smaller enclosed area.
Transfer check: repeat the reasoning with one consequential condition changed while holding the rest fixed. State what changes, what stays comparable and why the original label alone was insufficient.
Contour conventions vary and should not be treated as natural cutoffs.
MCP area depends strongly on which locations are included and whether a percentage MCP excludes extreme fixes. A 100 percent MCP and 95 percent MCP are distinct operations.
Preserve the raw inputs beside the derived result. If a later reader changes one condition, the original Wildlife reasoning should still be recoverable without reverse-engineering a rounded headline or an unlabeled screenshot.
One excursion fix expands a 95 percent MCP from 38 to a 100 percent MCP of 70 ha.
Evidence design: retain both a positive case and a near-miss. The positive case shows when the rule applies; the near-miss changes one consequential condition and shows when the conclusion fails. Together they teach the boundary of the Wildlife mechanism better than another unlabelled example.
Remove the excursion under a predeclared rule and recompute.
Audit check: retain the source version, units, settings, exclusions and rounding rule. A future correction should be able to alter one field without rebuilding the entire explanation from memory.
Post-hoc point removal can conceal real movements or measurement errors.
The central teaching animal uses two wooded patches separated by an open reservoir. A convex hull bridges the patches; a kernel surface can preserve two high-use lobes depending on bandwidth.
Ask what would have to stay fixed for the comparison to be fair. Record those controls explicitly, then name the first uncontrolled condition that could reverse the conclusion. This is the practical transfer step, not an optional footnote.
Map 60 fixes in each patch. Record MCP area 42 ha, kernel 95 percent area 36 ha and two 50 percent cores totaling 9 ha.
Communication test: replace any sentence that says two things are “the same” or “different” with a sentence naming the operation, reference condition and supported consequence. The extra words are useful when they let a future reader repeat the decision without access to the original author.
Move one cluster closer while retaining each cluster’s internal spread. Predict the MCP bridge shrinks.
Decision check: end with an action or interpretation that follows from the stated conditions, followed by a boundary sentence explaining when a specialist rule, local procedure or additional measurement is needed.
The numbers are stipulated and do not represent a real species.
The hull is controlled by outermost vertices; many interior fixes can be added without changing its boundary. It is simple and comparable when rules match, but insensitive to internal intensity.
Write the evidence in the order a reader can audit: the Wildlife quantity, its reference object, the observation or browser rule, the transformation, and the decision being made. Keeping those fields visible prevents a familiar label from hiding a changed basis.
Add 500 fixes at the centre of the 42 ha MCP. Its area stays 42 ha.
First-principles test: ask what physical, observational or algorithmic operation produces each value in this chapter. Then ask whether the second value could change while the first stays fixed. If it can, the two labels are not substitutes. For Wildlife, this counterfactual is often clearer than a definition learned in isolation.
Move one boundary fix outward by 500 m and observe a potentially large area change.
Evidence check: another reader should be able to reproduce the narrow result from the stored definitions, inputs and intermediate steps, then identify the nearest stronger claim that the evidence does not support.
Location error and rare excursions can dominate an MCP.
Kernel density estimation places a smooth kernel around fixes and sums their contributions. Bandwidth controls smoothing: too small can fragment the surface, while too large can merge separate use areas and spill over barriers.
Trace the mechanism before interpreting the result. For Wildlife, mark which value belongs to the source, which belongs to the measurement or layout algorithm, and which is a reported summary. A calculation is useful only when those roles remain attached.
Compute fictional 95 percent areas of 28, 36 and 55 ha under narrow, selected and broad bandwidths.
Practical transfer: build two records that share the headline number but differ in the condition discussed here. If the correct interpretation changes, the omitted condition is decision-relevant and belongs in the report. This test turns a vocabulary distinction into a reusable Wildlife checking habit.
Keep fixes and contour fixed while changing bandwidth.
Practical check: keep one counterexample beside the worked case. If the wording fails when that one condition changes, narrow the sentence until it describes only the evidence actually in hand.
Kernel choice, grid extent and boundary treatment must be documented.
CHAPTER 8 OF 20 · Work the mechanism
8. Keep area and utilization probability separate
A 95 percent kernel contour encloses a region associated with a stated share of the estimated UD, not 95 percent certainty that a true boundary lies there. The probability belongs to use under the model.
Use a compact decision table with columns for condition, input, operation, result and limit. This makes the comparison reproducible and exposes where a missing field would force an assumption instead of an observation.
Explain why a 36 ha 95 percent contour is not a confidence interval for 36 ha.
Misconception check: a plausible output does not prove the right reference, denominator, ancestor, spectrum or observation rule was used. Reconstruct one intermediate step and one changed-context prediction. If either cannot be stated, keep the result provisional rather than strengthening its wording.
Bootstrap locations and compare estimator uncertainty as a separate layer.
Transfer check: repeat the reasoning with one consequential condition changed while holding the rest fixed. State what changes, what stays comparable and why the original label alone was insufficient.
Statistical uncertainty requires methods beyond the contour label.
Both estimators can change as fixes accumulate. MCP often expands with new extremes, while kernel estimates and bandwidth selection can be unstable with sparse data.
Preserve the raw inputs beside the derived result. If a later reader changes one condition, the original Wildlife reasoning should still be recoverable without reverse-engineering a rounded headline or an unlabeled screenshot.
Calculate cumulative areas at 20, 60 and 120 fixes and plot whether either estimate approaches a plateau.
Evidence design: retain both a positive case and a near-miss. The positive case shows when the rule applies; the near-miss changes one consequential condition and shows when the conclusion fails. Together they teach the boundary of the Wildlife mechanism better than another unlabelled example.
Keep animal movement fixed and halve the sampling frequency.
Audit check: retain the source version, units, settings, exclusions and rounding rule. A future correction should be able to alter one field without rebuilding the entire explanation from memory.
No universal minimum fix count applies across movement processes and estimators.
High-frequency tracking fixes are often autocorrelated. Treating them as independent can distort uncertainty and conventional bandwidth selection even though the path information may be valuable.
Ask what would have to stay fixed for the comparison to be fair. Record those controls explicitly, then name the first uncontrolled condition that could reverse the conclusion. This is the practical transfer step, not an optional footnote.
Compare a location every minute with one every six hours from the same route. Store effective sampling and estimator assumptions.
Communication test: replace any sentence that says two things are “the same” or “different” with a sentence naming the operation, reference condition and supported consequence. The extra words are useful when they let a future reader repeat the decision without access to the original author.
Keep duration fixed and increase fix frequency one hundredfold.
Decision check: end with an action or interpretation that follows from the stated conditions, followed by a boundary sentence explaining when a specialist rule, local procedure or additional measurement is needed.
Modern movement-informed estimators may be preferable when autocorrelation is material.
GPS error can push fixes across a boundary, inflate a hull or broaden a kernel surface. Error varies with canopy, terrain, device and filtering.
Write the evidence in the order a reader can audit: the Wildlife quantity, its reference object, the observation or browser rule, the transformation, and the decision being made. Keeping those fields visible prevents a familiar label from hiding a changed basis.
Give each fix a 15 m error model, then examine a single apparent lake location before treating it as habitat use.
First-principles test: ask what physical, observational or algorithmic operation produces each value in this chapter. Then ask whether the second value could change while the first stays fixed. If it can, the two labels are not substitutes. For Wildlife, this counterfactual is often clearer than a definition learned in isolation.
Increase error while holding true path fixed.
Evidence check: another reader should be able to reproduce the narrow result from the stored definitions, inputs and intermediate steps, then identify the nearest stronger claim that the evidence does not support.
Filtering errors post hoc needs predeclared evidence and sensitivity analysis.
Seasonal, breeding, migration and lifetime ranges can differ. Combining fixes across unequal durations can make estimator differences look biological when the study windows are mismatched.
Trace the mechanism before interpreting the result. For Wildlife, mark which value belongs to the source, which belongs to the measurement or layout algorithm, and which is a reported summary. A calculation is useful only when those roles remain attached.
Calculate the central outputs for a 30-day breeding period and a full year as separate records.
Practical transfer: build two records that share the headline number but differ in the condition discussed here. If the correct interpretation changes, the omitted condition is decision-relevant and belongs in the report. This test turns a vocabulary distinction into a reusable Wildlife checking habit.
Keep method fixed and extend the observation into migration.
Practical check: keep one counterexample beside the worked case. If the wording fails when that one condition changes, narrow the sentence until it describes only the evidence actually in hand.
Cross-animal comparisons require aligned biological and calendar windows.
Ordinary kernels may smooth probability across rivers, cliffs or fenced areas that the animal cannot cross. MCP can also include inaccessible space because convexity bridges around boundaries.
Use a compact decision table with columns for condition, input, operation, result and limit. This makes the comparison reproducible and exposes where a missing field would force an assumption instead of an observation.
Overlay the central range on a reservoir shoreline and count excluded or low-use area under each method.
Misconception check: a plausible output does not prove the right reference, denominator, ancestor, spectrum or observation rule was used. Reconstruct one intermediate step and one changed-context prediction. If either cannot be stated, keep the result provisional rather than strengthening its wording.
Add a verified crossing point and update the barrier assumption.
Transfer check: repeat the reasoning with one consequential condition changed while holding the rest fixed. State what changes, what stays comparable and why the original label alone was insufficient.
Boundary-corrected or movement-based methods need validated implementation.
A rare, verified trip can dramatically expand MCP while contributing only a small tail to a kernel UD. Whether it belongs depends on the reader job, not convenience.
Preserve the raw inputs beside the derived result. If a later reader changes one condition, the original Wildlife reasoning should still be recoverable without reverse-engineering a rounded headline or an unlabeled screenshot.
Add one confirmed breeding excursion 4 km away. Report its effect under both estimators.
Evidence design: retain both a positive case and a near-miss. The positive case shows when the rule applies; the near-miss changes one consequential condition and shows when the conclusion fails. Together they teach the boundary of the Wildlife mechanism better than another unlabelled example.
Label the point as GPS error instead and show why evidence, not area preference, decides treatment.
Audit check: retain the source version, units, settings, exclusions and rounding rule. A future correction should be able to alter one field without rebuilding the entire explanation from memory.
Excursion exclusion rules must be declared before comparing animals.
Animals can use several discrete patches. A single MCP merges them into one polygon, while a kernel contour may remain disjoint or merge them depending on bandwidth and level.
Ask what would have to stay fixed for the comparison to be fair. Record those controls explicitly, then name the first uncontrolled condition that could reverse the conclusion. This is the practical transfer step, not an optional footnote.
Three forest fragments yield one 60 ha hull and three kernel lobes totaling 31 ha.
Communication test: replace any sentence that says two things are “the same” or “different” with a sentence naming the operation, reference condition and supported consequence. The extra words are useful when they let a future reader repeat the decision without access to the original author.
Widen the gap between fragments while preserving within-patch use.
Decision check: end with an action or interpretation that follows from the stated conditions, followed by a boundary sentence explaining when a specialist rule, local procedure or additional measurement is needed.
Neither method automatically identifies ecological corridors.
Comparing species or groups requires the same estimator, contour, bandwidth approach, fix schedule, duration and inclusion rules. Otherwise a method effect can masquerade as a biological difference.
Write the evidence in the order a reader can audit: the Wildlife quantity, its reference object, the observation or browser rule, the transformation, and the decision being made. Keeping those fields visible prevents a familiar label from hiding a changed basis.
Group A has a 40 ha MCP and group B a 35 ha 95 percent kernel area. Refuse to rank them until methods align.
First-principles test: ask what physical, observational or algorithmic operation produces each value in this chapter. Then ask whether the second value could change while the first stays fixed. If it can, the two labels are not substitutes. For Wildlife, this counterfactual is often clearer than a definition learned in isolation.
Reprocess both with one declared workflow.
Evidence check: another reader should be able to reproduce the narrow result from the stored definitions, inputs and intermediate steps, then identify the nearest stronger claim that the evidence does not support.
Different movement processes can still require model-specific sensitivity checks.
A smaller kernel contour does not automatically mean it is more accurate than a larger MCP. The estimators describe different objects and respond to settings differently.
Trace the mechanism before interpreting the result. For Wildlife, mark which value belongs to the source, which belongs to the measurement or layout algorithm, and which is a reported summary. A calculation is useful only when those roles remain attached.
The 36 ha kernel is smaller than the 42 ha MCP because it downweights low-use bridge space; that does not prove the MCP wrong.
Practical transfer: build two records that share the headline number but differ in the condition discussed here. If the correct interpretation changes, the omitted condition is decision-relevant and belongs in the report. This test turns a vocabulary distinction into a reusable Wildlife checking habit.
Broaden bandwidth until the kernel becomes larger than the MCP.
Practical check: keep one counterexample beside the worked case. If the wording fails when that one condition changes, narrow the sentence until it describes only the evidence actually in hand.
Accuracy needs an estimand, validation strategy and uncertainty analysis.
All interior points of an MCP are geometrically inside the hull, but the polygon does not say the animal used every location or used them equally.
Use a compact decision table with columns for condition, input, operation, result and limit. This makes the comparison reproducible and exposes where a missing field would force an assumption instead of an observation.
Mark the reservoir inside the 42 ha hull as never observed and avoid calling it occupied habitat.
Misconception check: a plausible output does not prove the right reference, denominator, ancestor, spectrum or observation rule was used. Reconstruct one intermediate step and one changed-context prediction. If either cannot be stated, keep the result provisional rather than strengthening its wording.
Add dense fixes around the reservoir margin without any fixes on water.
Transfer check: repeat the reasoning with one consequential condition changed while holding the rest fixed. State what changes, what stays comparable and why the original label alone was insufficient.
Habitat use needs fix evidence, resource selection or movement modelling.
Store animal and period, fix count and cadence, coordinate system, error filtering, estimator and version, inclusion percentage, kernel type, bandwidth, grid, contour, area, uncertainty and sensitivity outputs.
Preserve the raw inputs beside the derived result. If a later reader changes one condition, the original Wildlife reasoning should still be recoverable without reverse-engineering a rounded headline or an unlabeled screenshot.
Package the 42/36/9 ha case with data checksum and maps so another analyst can reproduce every boundary.
Evidence design: retain both a positive case and a near-miss. The positive case shows when the rule applies; the near-miss changes one consequential condition and shows when the conclusion fails. Together they teach the boundary of the Wildlife mechanism better than another unlabelled example.
Delete the bandwidth and ask whether the 36 ha kernel result is reproducible.
Audit check: retain the source version, units, settings, exclusions and rounding rule. A future correction should be able to alter one field without rebuilding the entire explanation from memory.
A map image without settings is not a reusable analytical record.
A defensible statement names estimator, settings, area and study window and avoids turning either output into a literal territory boundary.
Ask what would have to stay fixed for the comparison to be fair. Record those controls explicitly, then name the first uncontrolled condition that could reverse the conclusion. This is the practical transfer step, not an optional footnote.
Write: “Across the 30-day period, 120 fixes yielded a 42 ha 100 percent MCP and a 36 ha 95 percent kernel contour under the declared bandwidth; the estimands differ.”
Communication test: replace any sentence that says two things are “the same” or “different” with a sentence naming the operation, reference condition and supported consequence. The extra words are useful when they let a future reader repeat the decision without access to the original author.
Change the estimator or period and reset the comparison.
Decision check: end with an action or interpretation that follows from the stated conditions, followed by a boundary sentence explaining when a specialist rule, local procedure or additional measurement is needed.
Ecological decisions require species knowledge, sampling design and appropriate movement analysis.
Continue through the verified reading route
Home-range overlap and recorded contact
Home-range overlap and recorded contact. Use this for spatial overlap versus observed co-occurrence.
Site occupancy and animal abundance
Site occupancy and animal abundance. Use this for occupied sampling units versus numbers of animals.
Animal abundance and biomass
Animal abundance and biomass. Use this for counts of animals versus total biological mass.
Frequently asked questions
Why can MCP include unused habitat?
Convexity joins outer fixes and gives no use gradient, so barriers and gaps may fall inside the hull.
Is a 95 percent kernel contour a confidence interval?
No. It is a contour of the estimated utilization distribution; estimator uncertainty is a separate question.
Which method is best?
Choose an estimator for the reader job and movement process, then report sensitivity, sampling and settings rather than ranking methods by area alone.
Authoritative sources and further reading
U.S. Geological Survey: LoCoH home ranges and utilization distributions. Compares convex-hull and kernel approaches and discusses hard boundaries.
U.S. Geological Survey: Effects of sample size on kernel home-range estimates. Examines sample size, smoothing and accuracy of kernel estimates.
U.S. Geological Survey: Autocorrelation and bias in home-range estimation. Compares MCP, kernel and movement-aware estimators under autocorrelated tracking data.
Return to the Wildlife subject guide, The Gold Standard of Education, or the How X Works hub.