eduKateSG · The Gold Standard · Zoology
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Choose the closest question, or follow the expanded chapters in order.
ROUTE 1 · CHAPTERS 1–2
Define state and observation
Decide whether the question concerns sites or animals.
ROUTE 2 · CHAPTERS 3–5
Work through repeated visits
See why one visit cannot resolve both probabilities.
ROUTE 3 · CHAPTERS 6–8
Inspect histories and assumptions
Keep the visit history instead of only its total.
Full chapter index · Work through the evidence · Zoology subject guide
A pond can contain a species that a survey never records. If that happens more often at one pond than another, a map of sightings can become a map of visibility as much as a map of animals.
The short answer: repeated detection and non-detection records can help separate site occupancy from the chance of detecting a species when it is present. A zero is an observation under a method. To interpret it as evidence about absence, specify the site, period, observation process and model assumptions.
This guide develops a numerical question beneath the Zoology root. It uses invented sites and probabilities to explain occupancy, repeated visits and the meaning of an all-zero history. It is not a wildlife-handling protocol or permission to conduct research. The examples can be studied entirely through paper records, without disturbing an animal or revealing a sensitive location.
The Gold Standard of Zoology · Learning That Transfers into Life · How X Works
Chapter index
Define state and observation · Chapters 1–2
Work through repeated visits · Chapters 3–5
Inspect histories and assumptions · Chapters 6–8
Compare and practise · Chapters 9–10
CHAPTER 1 OF 14 · Define state and observation
1. Decide whether the question concerns sites or animals
Suppose a class wants to understand a fictional frog’s distribution across twenty ponds. One question is how many ponds the species occupies during a defined study period. Another is how many individual frogs live in those ponds. They are related biological questions, but they require different quantities and potentially different methods.
An occupancy observation records whether the species was detected at a site under the chosen method. One detected frog and ten detected frogs can both produce the same binary entry: detected. That loss of individual-count detail is intentional when the question concerns site use rather than abundance.
Define the spatial unit before interpreting a percentage. A pond, one bank of a pond and a grid square containing several ponds are different sites. The fraction occupied can change when the unit changes, even if the animals have not moved. A coarse map and a fine map are not automatically competing measurements of the same quantity.
Define the period too. Occupancy over a short season differs from “ever recorded during ten years”. A pond used briefly during migration and one used throughout a breeding period may both count as occupied under one definition but require further distinctions for another question. The model and biological interpretation must fit the chosen period.
Use a measurement sentence: “We want the fraction of these defined sites occupied by this species during this period.” Then identify what each visit can record. If the actual question is breeding success, individual survival or population abundance, do not silently substitute site detection because it is easier to collect.
This distinction also prevents overinterpreting a conservation headline. A stable occupied-site fraction can coexist with changes in the number of animals within sites. A rising fraction can reflect broader distribution without telling us whether every local population is secure. Occupancy is informative when it answers its own question, rather than serving as an unexplained synonym for all aspects of wildlife condition.
CHAPTER 2 OF 14 · Define state and observation
2. Separate the hidden state from the observation
Let psi represent the probability that a randomly selected site from the defined population is occupied under the model. Let p represent the probability of detecting the species during one specified visit, conditional on the site being occupied. These parameters describe different stages of the observation process.
For a simple example, suppose psi is 0.60 and p is 0.50. Among many comparable sites, about 60% would be occupied in the model. Among visits to occupied sites, the method would detect the species on about half of visits. The chance of a detection on a single randomly selected site visit is psi times p: 0.60 × 0.50 = 0.30.
The multiplication follows the chain: the site must first be occupied, and the method must then detect the species there. It is not an assumption that occupancy and detection are independent. Detection probability is explicitly conditional on occupancy.
In this chapter’s simplified model, an unoccupied site cannot produce a valid positive detection. That rules out false positives for the exercise. A real study must consider identification errors and whether its records justify that assumption. We will return to this limit later.
| Quantity | Fictional value | Meaning |
|---|---|---|
| Occupancy probability psi | 0.60 | Chance the defined site is occupied |
| Conditional detection p | 0.50 | Chance of detection on one visit if occupied |
| Single-visit detection probability | 0.30 | psi × p for a randomly selected site |
What does a single non-detection mean? It can arise because the site is unoccupied, or because it is occupied and the method misses the species. In this model those probabilities are 0.40 and 0.60 × 0.50 = 0.30. Together they give a 0.70 chance of recording no detection.
This is why subtracting the observed detection fraction from one does not automatically give an absence fraction. The complement includes missed presence. The arithmetic is easy once the two routes to zero are visible; the conceptual repair is recognising that zero has more than one possible cause.
CHAPTER 3 OF 14 · Work through repeated visits
3. See why one visit cannot resolve both probabilities
Imagine an enormous, perfectly recorded single-visit dataset showing detections at 30% of sites. Under the simple model, that observation concerns the product psi × p. Several pairs can produce the same product: occupancy 0.30 with detection 1.00; occupancy 0.60 with detection 0.50; or occupancy 1.00 with detection 0.30.
Those models have very different biological meanings. In the first, the method finds every occupied site but only 30% are occupied. In the last, every site is occupied but the method misses the species on most visits. More sites measured once can estimate the product more precisely without separating its factors.
This is an identification problem. It is not solved merely by increasing spreadsheet size or adding decimal places. The data need information that distinguishes the unknown quantities, or the analysis needs justified additional assumptions or independent evidence.
Repeated observations at the same defined sites provide one route. If a species is detected on one visit and missed on another within an appropriately stable occupancy period, the history contains information about imperfect detection. A set of such histories can inform occupancy and detection together under an appropriate model.
MacKenzie and colleagues’ 2002 occupancy paper, described by the US Geological Survey, develops a likelihood-based method for this problem. Its central distinction is that non-detection need not mean absence when detection probability is below one. The paper is a primary methodological reference; the numerical cases in this article are our own constructions.
Do not turn that reference into a promise that repeated visits automatically identify every real population parameter. The design, number of detections, parameter structure and model assumptions matter. If nearly every record is zero, there may be little information to distinguish very rare occupancy from very poor detection.
For learners, a useful paper exercise is to list three pairs with the same product and explain their different meanings. Only then introduce repeated histories. The sequence reveals why a new kind of observation is required, rather than presenting another survey visit as a ritual that makes any conclusion more trustworthy.
CHAPTER 4 OF 14 · Work through repeated visits
4. Calculate the value of repeated visits under a stated model
Suppose the site remains occupied or unoccupied throughout three visits. Conditional on occupancy, detection has probability p = 0.50 on each visit and detections are independent across visits in this simplified model. Independence here concerns the observation outcomes after conditioning on the occupied state.
At an occupied site, the chance of missing the species on all three visits is (1 – p)³ = 0.5³ = 0.125. Therefore the chance of at least one detection is 1 – 0.125 = 0.875, or 87.5%. Repetition improves the chance of recording the occupied site under these assumptions.
With occupancy psi = 0.60, the probability that a random site is detected on at least one visit is 0.60 × 0.875 = 0.525. The expected ever-detected fraction is 52.5%, still below the model’s 60% occupancy. Three visits do not make detection perfect.
Compare one, two and three visits. Conditional ever-detection is 50%, 75% and 87.5%. The additional gains are twenty-five percentage points from the second visit and 12.5 points from the third. This diminishing increment follows from the assumed repeated independent chances; it is not a universal empirical schedule for wildlife work.
If p were 0.10, three visits would give 1 – 0.9³ = 0.271, or only 27.1% conditional ever-detection. Repetition with a poorly matched method may remain weak evidence about absence. Biology, timing and method need attention alongside visit count.
The general expression is 1 – (1 – p)^K for K visits under constant p and conditional independence. Write the assumptions with the formula. Without them, inserting a visit count can create numerical confidence that the design does not support.
For a field project, an expert would consider information needs, disturbance, resources and appropriate design. A learner can understand the mathematical relationship through invented histories. There is no need to imitate animal calls, enter restricted sites or alter a habitat to make the equation feel practical. Responsible scientific understanding includes knowing which parts can be learned safely on paper.
CHAPTER 5 OF 14 · Work through repeated visits
5. Interpret an all-zero history without declaring absence
Return to psi = 0.60, p = 0.50 and three conditionally independent visits with stable occupancy and no false positives. A site produces the history 000: no detection on any visit. We want the probability it is occupied given that history, under this model.
The probability of being occupied and missed three times is 0.60 × 0.125 = 0.075. The probability of being unoccupied and producing three zeros is 0.40. The total probability of 000 is therefore 0.475. Dividing the occupied-and-missed route by the total gives 0.075 / 0.475, approximately 15.8%.
The three zeros reduced the model-based probability of occupancy from 60% to about 15.8%. They did not reduce it to zero. That is a useful example of negative evidence being informative without being conclusive.
| Route to history 000 | Probability under the fictional model |
|---|---|
| Occupied, missed three times | 0.60 × 0.50³ = 0.075 |
| Unoccupied | 0.40 |
| Total probability of 000 | 0.475 |
| Occupancy conditional on 000 | 0.075 / 0.475 ≈ 15.8% |
Now change only p to 0.10. The occupied-and-missed route becomes 0.60 × 0.9³ = 0.4374. Dividing by 0.4374 + 0.40 gives approximately 52.2%. When the method often misses the species, three zeros provide much less evidence against occupancy.
These calculations assume psi and p are known inputs. In real work they may be estimated and uncertain. Plugging in estimated values does not make the resulting site probability exact. A professional analysis must account for the model and relevant uncertainty rather than publish our classroom calculation as a verified diagnosis of an actual pond.
The learner’s task is to explain the denominator. It includes both ways to obtain the observed history. If you divide only by 0.40, you compare two different routes instead of conditioning on all-zero evidence. Return to the event tree in words before trying to memorise the conditional-probability formula.
CHAPTER 6 OF 14 · Inspect histories and assumptions
6. Keep the visit history instead of only its total
A repeated-visit dataset should preserve which site produced which sequence. Histories such as 100, 010 and 001 each contain one detection, but they place it on different visits. Those distinctions can matter when observation conditions or detection probabilities differ by visit.
In the simple constant-p model, the probability of the ordered history 101 at a random site is psi × p × (1 – p) × p. With psi = 0.60 and p = 0.50, it is 0.075. The positive entries establish occupancy within the no-false-positive model, while the zero between them demonstrates a missed detection at an occupied site.
If you ask for exactly two detections in three visits without caring about order, there are three histories: 110, 101 and 011. Under constant p and the stated independence, their total probability is 3 × psi × p² × (1 – p). Do not apply the factor of three to one specified ordered history.
A fictional four-site sheet might contain 101, 010, 000 and 011. Three sites were ever detected, so naive observed occupancy is 3 / 4 = 75%. This is a description of the sheet. Four sites are far too little information for the broad certainty a reader might attach to a polished “corrected” percentage, and we do not estimate a real ecological parameter from this toy dataset.
| Site code | Visit 1 | Visit 2 | Visit 3 | Ever detected |
|---|---|---|---|---|
| A | 1 | 0 | 1 | Yes |
| B | 0 | 1 | 0 | Yes |
| C | 0 | 0 | 0 | No |
| D | 0 | 1 | 1 | Yes |
Preserve missing visits separately. If the observer could not attend Site C on Visit 2, the entry is missing, not zero. Zero says a defined survey occurred without detection. Missing says that observation is unavailable. Replacing the latter with zero invents a survey result and can alter inference.
Keep a record of method deviations too. A short visit, equipment failure or uncertain identification should be handled under the study’s agreed rules. The cleanest-looking table is not necessarily the most informative one. Scientific quality includes preserving what the observation process actually did.
CHAPTER 7 OF 14 · Inspect histories and assumptions
7. Allow detection conditions to differ
Constant p is convenient for teaching, but visits can differ in visibility, observer experience, weather, recording equipment and animal activity. A model can sometimes represent relevant differences through covariates or structured detection probabilities. The point is to connect those inputs with a biological and observational explanation.
Suppose the conditional detection probabilities for three independent visits are 0.20, 0.50 and 0.80. The probability of missing an occupied site throughout is 0.80 × 0.50 × 0.20 = 0.08. Ever-detection is therefore 92%. We multiply the separate miss probabilities rather than automatically cubing one number.
Taking the average p = 0.50 and using 1 – 0.5³ gives 87.5%, a different result. The average does not preserve this product. That is a mathematical reason to retain visit conditions rather than assume every useful summary can be reduced to a mean.
Now consider site differences. Dense vegetation may affect both an animal’s use of a pond and the observer’s ability to detect it. A lower observed detection rate in dense sites could reflect occupancy, detection or both. Putting vegetation into a model requires deciding which process it may affect and having data capable of informing that structure.
More variables do not automatically produce better inference. A small dataset with many flexible effects may have little information for each parameter. Model checking, study design and appropriate expertise remain important. Avoid treating software output as a biological explanation simply because it includes a coefficient beside a habitat label.
For a student exercise, state the probabilities as hypothetical inputs and vary one at a time. Ask which change affects the hidden occupancy state and which affects observation. The goal is to separate mechanisms before combining them in a complex model.
Do not “improve visibility” by damaging habitat or disturbing animals. Observation conditions are part of the scientific and ethical design. Established programmes provide protocols for good reasons, and any proposed changes need the responsible review. A mathematical preference for higher p does not override welfare or access requirements.
CHAPTER 8 OF 14 · Inspect histories and assumptions
8. Check independence and the meaning of a repeat
Three entries in a spreadsheet do not necessarily represent three independent chances of detection. Repeated photographs from one brief encounter can share almost all their information. Calling them three visits can make the evidence appear stronger than the observation process supports.
Imagine a species hidden behind a fixed obstruction during an observation period. Taking three photographs seconds apart from the same position may repeat the same blind spot. Under perfect dependence, a 50% chance of detecting it in that encounter remains 50% after three identical observations. It does not become 87.5% merely because there are three files.
This does not mean all repeated observations are useless unless perfectly independent. It means the dependence structure needs appropriate treatment. Conditional independence in a model may be plausible after accounting for relevant state and covariates, or it may require another design or model. The scientific task is to justify the relationship rather than assume the spreadsheet layout guarantees it.
Different observers can also share conditions. Three people listening to the same silent pond at the same moment do not necessarily supply independent evidence about whether an occupied pond can produce a detectable call. Their individual identification skills matter, while the animal’s availability to be detected can be shared.
Distinguish technical repetition from biological replication. Several recordings of one encounter, several visits to one site and observations across several sites answer different parts of the question. A large file count cannot replace a missing range of sites or times.
The existing Zoologists article examines the difference between camera triggers, events and individual animals. Connect that distinction here: a trigger is neither automatically a new individual nor automatically a new independent occupancy survey. Name the observational unit appropriate to the model.
For learners, offer two invented datasets with identical totals but different dependence stories. Ask what changed in the meaning of the evidence. A good answer explains why the repeated chance calculation may no longer apply, rather than merely announcing that the second dataset is “unreliable”. Precision about the failure produces a more useful next question.
The simple repeated-visit model assumes occupancy status remains stable across the survey window. This is often called closure at the level relevant to the model. It does not necessarily mean each individual animal remains motionless; the biological interpretation depends on the site, species and defined occupancy state.
If a species colonises a pond between visits, the history 001 might represent genuine arrival rather than two missed detections followed by success. If the species leaves, 100 might involve departure. A model that assumes one stable state must not silently absorb every real change into detection probability.
Choose the survey period and model with the biology in mind. Shortening a window can support one closure interpretation while reducing opportunities to observe. Longer-term studies may use models that represent colonisation and local extinction. Those are extensions, not reasons to force an unstable situation into the simplest classroom formula.
False positives add another route to a detection. An uncertain sound label or look-alike species can produce a positive record at an unoccupied site. Our earlier inference that any positive history establishes occupancy depends on having ruled out that possibility within the model.
One positive plus two zeros therefore deserves review when identification is uncertain. Preserve the original recording or evidence under the programme’s rules, seek qualified verification and keep the uncertain status visible. Do not convert a model’s simplifying assumption into permission to ignore an ambiguous biological record.
Misidentification and non-detection can coexist. A procedure that improves sensitivity may also change false-positive risk. A responsible analysis explains how detections were verified and which model accommodates the actual observation process. A confident species name generated by software is not independent proof that the target was present.
For a classroom check, ask which assumption is challenged by each scenario: animals arriving between visits, observers repeating one recording, a missed visit entered as zero and a mistaken species label. The answers are closure, dependence, missing-data handling and false positives respectively. Naming the issue guides a specific repair.
CHAPTER 10 OF 14 · Compare and practise
10. Compare habitats without equating sightings with occupancy
Use a fresh hypothetical comparison with many comparable sites. Habitat A has occupancy 0.80 and conditional detection 0.25. Habitat B has occupancy 0.40 and conditional detection 0.75. A single visit detects the species with probability 0.20 in A and 0.30 in B.
An observer using raw detected-site fractions might conclude that B is more widely occupied. The assumed occupancy values show the reverse: A has twice the occupancy, but a much less effective detection process. This example isolates one reason an observed comparison can reverse after accounting for detection.
With three independent visits at constant habitat-specific p, A’s ever-detection probability is 0.80 × (1 – 0.75³) = 0.4625. B’s is 0.40 × (1 – 0.25³) = 0.39375. Repetition changes the expected observed ordering under these particular inputs. It does not guarantee that three visits are sufficient for every habitat comparison.
| Habitat | Assumed occupancy | Detection if occupied | One-visit detected-site probability | Three-visit ever-detection probability |
|---|---|---|---|---|
| A | 80% | 25% | 20% | 46.25% |
| B | 40% | 75% | 30% | 39.375% |
The numbers are probabilities, not an actual dataset. A finite set of sites can differ from these expectations. A real comparison needs uncertainty estimates, appropriate sampling of sites and an observation model. Detectability correction cannot repair a site sample that excludes important parts of the target landscape.
The existing case about a bird census whose observation sites changed owns another comparison problem. Changing the sites can alter what population is represented. Here, even with a fixed and appropriate site set, different observation processes can change apparent occupancy. Both issues deserve attention when present.
Do not translate the occupancy contrast directly into a conservation ranking. Habitat suitability, breeding, survival and connectivity may require further evidence. A species can use a site without thriving there, and a single target species does not summarise all biodiversity.
A defensible report separates observed ever-detection, model-estimated occupancy, uncertainty and biological interpretation. That lets readers understand what was seen, what was inferred and which further evidence is needed for a decision about habitat management.
Try an original paper exercise. Assume occupancy psi = 0.40, conditional detection p = 0.60, four independent visits given occupancy, stable site state and no false positives. First calculate the chance an occupied site is missed throughout. Then calculate the chance that a random site is ever detected and the occupancy probability conditional on four zeros.
At an occupied site, the all-miss probability is 0.4⁴ = 0.0256. Conditional ever-detection is 0.9744. Multiplying by occupancy gives 0.40 × 0.9744 = 0.38976, or 38.976%, for ever-detection at a randomly selected site.
The occupied-and-missed route to 0000 has probability 0.40 × 0.0256 = 0.01024. The unoccupied route has probability 0.60. Conditional occupancy is 0.01024 / 0.61024, approximately 1.68%. The zeros are strong negative evidence under this specified model while leaving a nonzero possibility.
Now remove two visits, keeping all other assumptions. The occupied-and-missed probability becomes 0.40 × 0.4² = 0.064. Dividing by 0.064 + 0.60 gives approximately 9.64%. Fewer observations provide less negative evidence under the same detection process.
Finally change the story: all four records are copies of one recording from one encounter. You cannot justify the fourth power merely by counting four entries. Under a model of perfectly duplicated evidence, the single-visit calculation would be relevant instead: 0.40 × 0.40 divided by 0.60 + 0.16, approximately 21.1%.
Explain the differences before trying another formula. What stayed constant? What changed in the evidence? Which assumption allowed multiplication across visits? If the learner can answer those questions, the arithmetic is connected to the observation process.
A practical teaching sequence begins with the two routes to zero, adds two independent visits, then introduces changing p and dependence. Keep one new difficulty visible at a time. The purpose is understanding why a conclusion changes, not accumulating increasingly complicated numbers about fictional frogs.
CHAPTER 12 OF 14 · Report and continue
12. Report an occupancy estimate at the right scale
A useful report separates the sampled-site description from an inference about a larger landscape. If twelve of twenty sampled ponds had at least one verified detection, the observed ever-detected fraction is 60%. Extending a model estimate to all ponds in a region also requires a defensible relationship between the selected ponds and that region.
Suppose the twenty ponds were chosen because they were easy to reach from a road. Even an excellent detection model does not automatically make them representative of remote ponds. The selection process and the detection process are different links in the inference chain. A correction at one link cannot silently repair the other.
Keep estimates, uncertainty and management interpretation separate. A point estimate is a summary under a model. Its uncertainty describes what the analysis can quantify under its assumptions. A habitat decision can require additional evidence about ecological function, disturbance and the effects of the proposed action.
For students, write a three-part conclusion: what the records show, what the model suggests and what remains outside the evidence. A concise answer can preserve all three. That makes a modest project more scientifically useful than a much longer report that calls every observed zero an absence and every adjusted percentage a confirmed biological fact.
CHAPTER 13 OF 14 · Report and continue
13. Answer common questions and plan responsible learning
Does no detection mean no animals?
It means the method did not record the species under the stated conditions. A claim about absence needs the relevant detection evidence and assumptions. Also distinguish absence of a species from a claim that no animals of any kind were present.
Is occupancy an estimate of the number of animals?
No. It concerns the proportion or probability of defined sites being occupied under the model. Animal abundance requires additional information and an appropriate method. One occupied pond can contain a very different number of individuals from another.
Can I divide the detected fraction by p?
With a known common detection probability and a specified simple expectation model, that relationship can illustrate the quantities. Treating an arbitrary guessed p as a correction is not a defensible analysis. Repeated-history models estimate parameters through an explicit framework and require suitable data and checks.
How many visits are enough?
There is no universal count in this article. Information depends on occupancy, detection, dependence, site sample, biological timing and the purpose of the study. Work through an established programme or qualified research design for actual fieldwork.
What if the species is identified incorrectly?
That challenges the no-false-positive assumption used in our simple examples. Preserve uncertainty and seek the programme’s verification route. Repeating a mistaken label does not turn it into stronger evidence.
What can a student do next without conducting a wildlife study?
Use invented detection histories, approved recordings or published educational datasets. Write the target question, calculate a conditional example and identify which assumption would change the conclusion. The resulting explanation can demonstrate substantial scientific reasoning without handling animals.
For public participation, follow the current rules of an established citizen-science programme. For research, check the actual institution and relevant authority’s current requirements before starting. Protect sensitive locations and respect the distinction between learning about a method and being authorised to carry it out.
The gold standard is a conclusion whose biological meaning and observation conditions remain connected. Curiosity starts the question; clear quantities, appropriate methods and honest limits make the answer useful.
Use the routes below for the specific question you want to pursue. The subject root keeps the wider map; the specialist guides develop different evidence jobs. A connected reading sequence is most useful when those responsibilities remain clear.
Biological records and professional research
Zoologists: Ethical Field Studies and Traceable Evidence. Continue into camera records, observation units and accountable research. A file count is not automatically a count of animals or independent survey opportunities.
Biologists: Testable Questions and Reproducible Evidence. Use the wider scientific route for connecting a question with its method and traceable observations. Occupancy is one specialised example of that discipline.
Different causes of misleading comparisons
School Scientific Detection Bias in Observations. Begin with this accessible qualitative explanation if detection probability is unfamiliar. The present guide adds conditional probabilities and repeated-history reasoning.
The Bird Survey Reported a Population Decline After Observation Sites Changed. Compare a changing site sample with imperfect detection at fixed sites. They are distinct problems and can occur together in a real monitoring project.
Responsible observation
Sensitive Nest Locations in Citizen Science. Keep evidence review compatible with protection of vulnerable wildlife locations. A reproducible explanation does not require indiscriminate public release of every coordinate.
Authoritative sources and scope
The following primary sources support the identified method or institutional context. Source routes were reviewed on 21 October 2026. All fictional counts, probability cases, timelines and learner exercises in this guide are original teaching constructions. They are not findings about an actual institution, service or wildlife site.
MacKenzie and colleagues: Estimating Site Occupancy Rates When Detection Probabilities Are Less Than One. USGS primary publication record for the 2002 Ecology paper. It supports the distinction between occupancy and imperfect detection; the numerical exercises here are original.
NParks: Research permits. Official starting point for checking requirements for a proposed Singapore biodiversity research activity. A classroom explanation does not grant fieldwork permission.
NParks: Citizen science programmes. Use current programme instructions for participation and record submission. Activity availability and requirements should be checked for the chosen programme.
For the wider learning purpose, continue with Learning That Transfers into Life. For related systems and subjects, use How X Works. Choose one new example and explain which relationship carries over, which assumptions change and what evidence you would need before applying the conclusion.