Biology · Organisms, Environments & Ecological Niches
Field observations, natural experiments and ecological uncertainty
An imagined site has no detection on three visits. Another site's recorded count falls after a regional event. The first record concerns observation as well as occupancy; the second concerns a change with possible alternative causes. Neither record explains itself.
Life, Evidence & Biological Scale introduces observations, models and biological organisation. Energy, Enzymes & Metabolism introduces energy use and material requirements. Evolutionary Processes & Adaptation supplies the distinction between individual change and inherited population change. The numerical examples here need only counting, fractions and ordinary graph reading; the next chapter develops population accounts in more detail.
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Interpret nondetection, nested observations and before–after comparisons without confusing conditional calculations or descriptive contrasts with causal proof.
Not recorded is different from not present
An organism can be present without being detected. A presence record and an absence claim therefore need different treatment. Detection-aware occupancy reasoning explicitly relates the state of a site to the chance of observing it.
The original calculation assumes the site is occupied throughout the visits, each visit independently has detection probability 0.4, and there are no false-positive detections. Under those assumptions the chance of missing it on one visit is 0.6.
Multiplying the independent miss probabilities gives 0.6³ = 0.216 for three misses conditional on presence. Subtracting from one gives 0.784 for at least one detection. These are probabilities of records under a supplied occupied state, not the probability of absence after seeing a record.
Missed records conditional on an occupied site
Read the diagram in words
With per-visit detection 0.4, all-miss probabilities for one, two and three visits are 0.6, 0.36 and 0.216; at-least-one detection is 0.4, 0.64 and 0.784. With per-visit detection 0.7, all misses are 0.3, 0.09 and 0.027; detection is 0.7, 0.91 and 0.973. Every probability is conditional on a present organism under the stated assumptions.
| Number of visits | Assigned per-visit detection probability | Probability of all misses given presence | Probability of at least one detection given presence |
|---|---|---|---|
| 1 | 0.4 | 0.6 | 0.4 |
| 2 | 0.4 | 0.36 | 0.64 |
| 3 | 0.4 | 0.216 | 0.784 |
| Number of visits | Assigned per-visit detection probability | Probability of all misses given presence | Probability of at least one detection given presence |
|---|---|---|---|
| 1 | 0.7 | 0.3 | 0.7 |
| 2 | 0.7 | 0.09 | 0.91 |
| 3 | 0.7 | 0.027 | 0.973 |
P(all misses | occupied) = (1 − p)^k
The site is stipulated occupied throughout
This is not absence probability after nondetection
Conditional on fixed occupancy, constant assigned per-visit detection, independent visits and no false positives. Original theoretical probability accounts, without a fitted occupancy model, posterior absence probability, actual survey design or operational monitoring schedule.
Changing a conditional question changes the evidence needed
To ask how likely a site is absent after three nondetections, one would need information about occupancy before the record as well as the observation process. The displayed 0.216 cannot simply be relabelled as an absence probability.
Repeated visits can also share conditions that make their detections dependent. Occupancy can change during a record, and detection probabilities can differ among visits or sites. A calculation assuming constancy and independence does not establish those assumptions in an actual field record.
The model's second series assigns detection probability 0.7. Under its same assumptions, three misses have probability 0.027 and at least one detection 0.973. Comparing these series explains why observation quality matters; it recommends no monitoring schedule or field procedure.
Repeated observations keep their shared site identity
The comparison record contains three sites, each with three assigned observations before and three after a stipulated event. Eighteen recorded values therefore belong to three site identities. The first site is event-associated; the other two are references.
Additional observations within a site can describe its variability, but they do not create additional independently exposed sites. Treating all eighteen as independent event replicates would discard the structure relevant to an event-effect claim.
Random selection from a target set concerns which units are represented. Random assignment concerns how conditions are allocated to units. Neither is supplied here. The sites and numbers are assigned teaching data, so there is no sampling-based regional estimate or randomised causal comparison.
Several readings retain their shared site identity
Read the diagram in words
The focal means are twelve and seven, change minus five; reference A means ten and eight, change minus two; reference B means fourteen and thirteen, change minus one. Focal-minus-reference contrasts are minus three and minus four; subtracting the mean reference change gives minus 3.5. Eighteen readings retain three site identities, with one event-associated site.
| Shared site identity | Before observations | After observations | Before mean | After mean | After minus before mean |
|---|---|---|---|---|---|
| Event-associated focal site | 10, 12, 14 | 5, 7, 9 | 12 | 7 | -5 |
| Reference site A | 8, 10, 12 | 6, 8, 10 | 10 | 8 | -2 |
| Reference site B | 12, 14, 16 | 11, 13, 15 | 14 | 13 | -1 |
| Reference site A | -5 − (-2) = -3 |
|---|---|
| Reference site B | -5 − (-1) = -4 |
After minus before mean: (-2 + -1)/2 = -1.5
Focal change minus reference change: -5 − (-1.5) = -3.5
Eighteen readings belong to three sites: 18; Shared site identity: 3; Only one site is event-associated: 1
The descriptive contrast does not identify a cause
Original assigned records at two periods, three site identities and three observations per site-period. One site is event-associated and two are references; no random sampling, random assignment, independent event replication, causal identification, uncertainty estimate or statistical significance is supplied.
A reference contrast improves the question without answering every cause
The focal mean changes from twelve to seven, a decline of five. Reference A changes from ten to eight and reference B from fourteen to thirteen. Comparing changes acknowledges that places other than the focal site also changed.
Subtracting reference A's change gives a focal contrast of minus three; using reference B gives minus four. The average reference change gives minus 3.5. These descriptive comparisons differ because the references differ, not because one arithmetic operation proves a cause.
A natural experiment concerns a contrast created by events outside the researcher's assignment. Its interpretation still depends on comparability, timing, exposure and other possible influences. An event-associated difference could reflect the event, a separate local change, observation changes or several processes. The supplied record has no model eliminating those alternatives.
Reporting uncertainty means stating which claim the evidence leaves unresolved. Here the counts and arithmetic are completely specified, while wider representativeness and the cause of the focal change remain open. Adding a confident causal label would not add evidence.
Worked example
A decline, two references and a shared-site denominator
The focal observations are 10, 12, 14 before and 5, 7, 9 after; their means are twelve and seven. Reference A's means are ten and eight, and B's fourteen and thirteen. Their mean changes are −5, −2 and −1.
The focal change minus the mean reference change is −5 − ((−2 + −1)/2) = −3.5. Relative to A alone it is −3; relative to B alone it is −4. These are differences in supplied mean counts, not estimated causal effects or statistical-significance results.
The ledger contains eighteen observations, three site identities and one event-associated site. Six observations of that one site do not turn it into six independent event sites. Likewise, three nondetections in the separate probability model remain an observation record conditional on assumptions rather than proof of absence.
Check your understanding
With fixed presence, independent visits and detection probability 0.4, what is the chance of no detection on three visits?
Show reasoning
Each miss has probability 0.6, so three misses have probability 0.6 × 0.6 × 0.6 = 0.216 conditional on presence. This is not the probability that a site is absent after nondetection.
Do the eighteen supplied before–after observations constitute eighteen independent event-associated sites?
Show reasoning
No. They belong to three sites, only one of which is event-associated. Repeated measurements preserve their shared unit identity and do not replicate event exposure across new sites.
Does the contrast of −3.5 identify the event as the cause of the focal change?
Show reasoning
No. It describes a change relative to the supplied reference average. The record does not establish comparable counterfactual trends, random assignment, unchanged detection or exclusion of other local influences.
What to carry forward
Keep the ecological state, observation process, sampling units and causal comparison distinct when reading a field record.
References
Resources supporting this lesson’s explanations and examples.
- Estimating site occupancy rates when detection probabilities are less than one (Ecology 83(8):2248–2255, 2002; doi: 10.1890/0012-9658(2002)083[2248:ESORWD]2.0.CO;2)D. I. MacKenzie, J. D. Nichols, G. B. Lachman, S. Droege, J. A. Royle and C. A. LangtimmPrimary methodological research
- Pseudoreplication and the Design of Ecological Field Experiments (Ecological Monographs 54(2):187–211, 1984; doi: 10.2307/1942661)Stuart H. HurlbertPrimary methodological analysis
- On Beyond BACI: Sampling Designs that Might Reliably Detect Environmental Disturbances (Ecological Applications 4(1):3–15, 1994; doi: 10.2307/1942110)A. J. UnderwoodPrimary methodological analysis