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Keywords:

  • biological monitoring;
  • capture–recapture models;
  • detectability;
  • extinction probability;
  • metapopulation biology;
  • plant census;
  • revisitation study

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  • 1
    Extinction is a fundamental topic for population ecology and especially for conservation and metapopulation biology. Most empirical studies on extinction resurvey historically occupied sites and estimate extinction probability as the proportion of sites where a species is no longer detected. Possible non-detection of surviving populations is usually not accounted for, which may result in extinction probabilities that are overestimated.
  • 2
    As part of a large revisitation study in north-east Switzerland, 376 sites with historically known occurrences of a total of 11 plant species 80–100 years ago were visited by two independent observers. Based on typical population size, ramet size and plant architecture, we judged six species as easy to find and five species as hard to find. Using capture–recapture methods to separate non-detection from true extinction, we gauged the bias of extinction probability estimates that do not account for non-detection.
  • 3
    When non-detection was not accounted for, a single visit resulted in an average estimate of population extinction probability of 0.49 (range 0.27–0.67). However, the mean detection probability of a surviving population during a single visit had an estimated average of only 0.81 (range 0.57–1). Consequently, accounting for non-detection resulted in extinction probability estimates ranging between 0.09 and 0.61 (mean 0.36). Based on a single survey, our revisitation study would have overestimated the extinction rate on average by 11 percentage points (range 5–22%) or by 59% (range 0–250%) relative to the estimated true value.
  • 4
    A simple binomial argument enables the calculation of the minimum required number of visits to detect a surviving population with high probability (e.g. 95%). For the easy to find species, approximately two visits would be required to find most of the surviving populations, whereas up to four visits would be required for the hard to find species.
  • 5
    In revisitation studies, only repeated revisits allow the separation of extinction from simple non-detection. Unless corrected for possible non-detection, extinction probability may be strongly overestimated, and hence some control for non-detection is desirable at least in a subset of species/sites in revisitation studies. These issues are also relevant to the estimation of extinction in metapopulation studies and to the collection of quality data for habitat and distribution models.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

The empirical measurement of plant population extinction probabilities and the identification of those factors that cause the local disappearance of a species are fundamental to conservation biology. They are usually accomplished by comparing historical and current records of the occurrence of plants (Nilsson & Nilsson 1982; Ouborg 1993; Drayton & Primack 1996; Leach & Givnish 1996; Turner et al. 1996; Landergott et al. 2000; Endels et al. 2002; Lienert et al. 2002). Assuming the absence of any colonizations, extinction probability in such studies is estimated as the proportion of historical sites where a species is no longer detected. Resulting estimates can then be related to factors such as habitat type, population size, plant size or life history to test whether these factors might have caused extinction (Turner et al. 1996; Fischer & Stöcklin 1997; Stöcklin & Fischer 1999; Duncan & Young 2000). Related problems are in the field of metapopulation biology, where occupancy of patches is assessed by searching for the species of interest in a large number of possible sites, and in the assessment of the conservation status of species, where the number of occupied sites is an important criterion for vulnerability (García et al. 2002).

Formally, the probability of observing a surviving population during one revisit is φ × p, i.e. the product of population survival probability φ and population detection probability p. The widely used estimator of population extinction probability of one minus the proportion of populations no longer detected, thus gives estimates of 1 − φ × p and not 1 − φ as desired. From this, it is clear that this extinction probability estimator will overestimate true extinction probability whenever p < 1. If this is the case, then the vulnerability of such a plant species will be exaggerated (García et al. 2002) and estimates based on metapopulation models may be biased (Moilanen 2002). In a metapopulation study, some of the overlooked populations will be ‘rediscovered’ at later surveys, and hence p < 1 will obviously also bias estimates of colonization probability.

Furthermore, when the population detection probability p varies as a function of some covariate such as habitat or population size, this covariate may be spuriously ‘identified’ as being related to extinction probability (Kéry 2004). Despite this disturbing fact, possible non-detection of surviving plant populations has not been addressed formally in any of the above cited studies and, to our knowledge, has never been dealt with in any study to date. Instead, all the cited studies implicitly assumed that detection probability p equals 1 and there is no way to gauge the possible bias of most or all extinction probability estimates reported in the literature so far.

Here, we show that the imperfect detection of surviving populations can be of real concern for revisitation studies. As part of a much larger revisitation study in north-east Switzerland based on 80- to 100-year-old records (J. H. Spillmann & R. Holderegger, unpublished data), we selected 11 plant species occurring historically at a total of 367 sites, each of which was visited by two independent observers, and we used a capture–recapture approach to separate extinction probability from non-detection probability. We then show how knowledge of detection probability can be used to answer the question of how many times a site must be visited to detect a species with high probability if the species is still present.

Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

study area

The main study (J. H. Spillmann & R. Holderegger, unpublished data) aimed at revisiting all c. 2000 sites with records of occurrence of at least one of a total of 100 species 80–100 years ago (Hegi 1902; Kägi 1920). The total area covered 174 km2 of montane uplands (700–1300 m a.s.l.) around Schnebelhorn peak (1292 m a.s.l.; 8°59′ W, 47°20′ N) in the Tössbergland foothills of the north-east Swiss Alps. It consisted of a variety of habitat types ranging from rocky outcrops and ravines to beech and spruce woodlands and montane grassland.

study species

We selected six species thought to be easy and five species thought to be hard to find (Table 1). This choice was based on the typical size of populations/patches, ramet size and the degree of conspicuousness in terms of growth form or colour when flowering. The easy to find species were Cardamine kitaibelii (Brassicaceae, 30–50 cm, large pale yellow flowers), Crepis aurea (Asteraceae, basal rosette, 5–30 cm, single orange–red flower head), Senecio alpinus (Asteraceae, 30–100 cm, multiple branches and large leaves, yellow flowers), Homogyne alpina (Asteraceae, 10–30 cm, pink flowers), Alchemilla conjuncta aggr. (Rosaceae, 10–30 cm, small green–yellow flowers) and Vaccinium vitis-idaea (Ericaceae, 5–30 cm, dwarf shrub, white–reddish flowers). The hard to find species were Selaginella selaginoides (Selaginellaceae, 5–10 cm, delicate, moss-like and creeping pteridophyte), Salix retusa (Salicaceae, 5 cm, creeping shrub), Veronica fruticans (Scrophulariaceae, 5–20 cm, blue flowers), Poa alpina (Poaceae, 10–40 cm, grass) and Epilobium alpestre (Onagraceae, 20–60 cm, pink flowers).

Table 1.  Extinction probability estimates from a revisitation study with 11 species in north-east Switzerland. C gives the average number of populations found by one observer. Ê′: naïve extinction probability estimate (for one observer); , 95% CI() and p: estimated number of surviving populations (with 95% CI), and per-visit detection probability of a surviving population under the Jackknife estimator; Ê and CI(Ê): estimated true extinction probability and its 95% CI. Bias% is (Ê′ − Ê)/Ê expressed as a percentage. Easy species: assumed to be easily detected; hard species: assumed to be hard to detect
 Historical sitesTotal populations detectedCÊCI()pÊCI(Ê)Bias%
Easy species
 Cardamine kitaibelii342823.50.313129–410.760.090.00–0.15250
 Crepis aurea3519170.511919–300.890.460.14–0.46 13
 Senecio alpinus4434320.273434–450.940.230.00–0.23 20
 Homogyne alpina341411.50.661515–250.770.560.26–0.56 18
 Alchemilla conjuncta aggr.453129.50.343634–390.820.200.13–0.24 72
 Vaccinium vitis-idaea3313110.671313–240.850.610.27–0.61 10
Hard species
 Selaginella selaginoides13 9 90.31 91.000.31  0
 Salix retusa2311 8.50.631212–220.710.480.04–0.48 32
 Veronica fruticans14 7 60.57 8 8–130.750.430.07–0.43 33
 Poa alpina513727.50.464038–500.800.220.02–0.25114
 Epilobium alpestre412215.50.622724–370.570.340.10–0.41 82

field work

During the growing seasons of 2002 and 2003, C.T. and J.H.S. independently visited each of the 367 historical sites to search thoroughly for the 11 selected plant species. Site diameter was on average 100 m (range 10–1000 m). Visits lasted up to 2 h for each site and were conducted preferentially during the height of the flowering season of each species. When sites had to be revisited more than once, because the flowering season of several species did not overlap, only results from the two visits aimed at a particular species were counted. The observers never met in the field nor did they share any information until field work was completed.

statistical analysis

Capture–recapture estimation of population size N consists of adequately modelling the factors that affect detection probability (Williams et al. 2002). Note that we are estimating the ‘population size’ of surviving populations. We assumed that each surviving population had its own constant probability of detection and estimated N using the Jackknife estimator (Burnham & Overton 1978, 1979). The data required are the capture frequencies, fh, i.e. the numbers of populations detected exactly h = 1, 2, … , K times, where K = 2 in the present study. The Jackknife estimator for the number of surviving populations has the following form:

  • image(eqn 1)

Here, R is the number of extant populations detected and the αhk are constants corresponding to Jackknife estimators of order k (for more details see Burnham & Overton 1978, 1979).

This estimator is widely used and has performed well in animal population ecology (Otis et al. 1978; Palmer 1990, 1991; Baker 2004). With two visits, it has been found to be hardly biased even with small sample sizes unless true detection probability is < 0.6 (Wintle et al. 2004; also see Discussion), and is robust against moderate variation in the detection probability between observers (Boulinier et al. 1998). For each species i, we used the Jackknife estimator as implemented in the program CAPTURE (Otis et al. 1978) within the program MARK (White & Burnham 1999) to obtain an estimate of the number of surviving populations &#x004e;̂i and of the imprecision (SEi) of that estimate.

We obtained a detectability-corrected estimate of the extinction probability Êi as

  • Êi = 1 − i/Si(eqn 2)

where Si was the total number of historical sites for species i that were revisited and &#x004e;̂i was the estimated number of surviving populations. Because the uncertainty about population size point estimates is asymmetric, we report confidence intervals rather than standard errors to convey the imprecision in these estimates. Estimating the number of surviving populations Ni, rather than directly observing it, introduces an imprecision into Êi. We use a ‘plugin’ estimator, i.e. insert the 95% confidence bounds for &#x004e;̂i into eqn 2. This correctly propagates the estimation error in &#x004e;̂i into Êi. For comparison, we also calculated the naïve (uncorrected) estimate of the extinction probability &#x004e;̂i as:

  • image(eqn 3)

where Si was as in eqn 2 and Ci was the mean (over both observers) number of sites where species i was detected.

For n independent visits, the probability Pn to detect a surviving population at least once is given by

  • Pn = 1 − (1 − p)n(eqn 4)

where p is the per-visit probability of detection of a surviving population (Kéry 2002). Setting this at 0.95 and solving for n yields the minimum sampling effort required to detect a population with at least 95% probability (McArdle 1990).

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

extinction and detection probability

For the easy to find species there were 33–45 historically known sites per species and 13–51 for the hard to find species (Table 1). A single visit resulted in an average naïve estimate of the population extinction probability of 0.49, ranging from 0.27 for Senecio alpinus to 0.67 for Vaccinium vitis-idaea. However, use of a Jackknife estimator for the number of surviving populations showed that the mean detection probability of a surviving population only ranged between 0.76 and 0.94 (mean 0.84) for easy to find species and between 0.57 and 0.80 (mean 0.71) for four hard to find species. For a fifth species thought to be hard to detect, Selaginella selaginoides, the mean detection probability estimate was equal to 1, and hence overall mean detection probability was estimated at 0.77 for all five hard to find species.

Correcting for non-detection resulted in extinction probability estimates ranging between 0.09 and 0.61 (mean 0.36) for easy to find species and between 0.22 and 0.48 (mean 0.35) for hard to find species. Consequently, estimates of extinction probability that did not account for possible non-detection of surviving populations were overestimated by 5–22 (mean 11) percentage points for the easy to find species and by 0–28 (mean 16) percentage points for the hard to find species. The bias of the uncorrected estimates relative to the estimated true extinction probability was on average 59% when based on a single visit, as is often the case in revisitation studies. For some species with a high detection probability, such as Selaginella selaginoides, there was no bias, whereas for the species with lowest detectability, Cardamine kitaibelii, bias was as high as 250%.

minimum required sampling effort

Using the above estimates of detection probability and a simple binomial argument, we computed that for species thought to be easy to detect, at least 1.65 visits to a site without seeing it are required before a historical population can be concluded to be extinct or a presumed site assumed to be unoccupied. Similarly, 2.20 visits for hard to find species (with Selaginella; see above) or 2.50 visits (without Selaginella) would be required to draw a well-founded statistical conclusion regarding the absence of an extant population at a site.

Power curves such as that in Fig. 1 plot the combined probability of detection Pn over n visits and are important tools for survey planning and interpretation. Prospectively, they serve to determine the minimal number of visits required to detect a species with a chosen probability. Retrospectively, they serve to estimate the sensitivity of an inventory, given the number of times each site was visited. This means that following one visit, only approximately 80% of the populations of Poa alpina would be expected to be found, whereas over 95% would be found following two visits (Fig. 1b).

image

Figure 1. ‘Power curves’ for surveys of 11 plant species based on a revisitation study in north-east Switzerland. For each species, Pn = 1 − (1 − p)n is plotted for a number of surveys n, given the per-visit estimate of the detection probability of a surviving population (for explanation see eqn 4 and text). (a) Species easy to detect, (b) species hard to detect. The horizontal line indicates a probability of 0.95.

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

the empirical estimation of extinction probability

Extinction is a topic central to ecology, metapopulation and conservation biology. Using historical records, extinction probability has frequently been estimated as the proportion of sites where a species is no longer found during revisitations (Nilsson & Nilsson 1982; Ouborg 1993; Drayton & Primack 1996; Leach & Givnish 1996; Turner et al. 1996; Fischer & Stöcklin 1997; Stöcklin & Fischer 1999; Duncan & Young 2000; Landergott et al. 2000; Endels et al. 2002; Lienert et al. 2002). Apart from ignoring recolonizations, these studies have failed to appreciate that extinction probability is confounded with non-detection probability. The same issue applies for metapopulation studies, where essentially the same study design is used: patches are visited to try and find an extant population. Moilanen (2002) has shown that not accounting for imperfect detection of populations may be the most serious biasing factor in metapopulation studies. In this paper, we show that the non-detection problem can be addressed fairly easily by repeating the revisits. This allows extinction probability to be teased apart from (non-)detection probability.

In our study of 11 species, detection probability of a surviving population during a single visit was estimated at only 0.81 (range 0.57–1). Consequently, our revisitation study would have overestimated extinction rates on average by 11 (range 5–22) percentage points or by 59% (range 0–250%) relative to the estimated true value had we not corrected for imperfect detection. If this result can be generalized to other studies, then extinction probabilities and hence the vulnerability of many species may sometimes have been greatly exaggerated.

The problem of imperfect detectability of surviving populations was not uniform in our study. For some species with high detection probability, the uncorrected extinction probability estimator (eqn 3) was not strongly biased. It may not be known in advance whether a species is easy or hard to detect. For instance, we had a priori selected a sample of species thought to be hard and another sample thought to be easy to detect. Our choice was based on an intimate knowledge of both these species and the area in which our revisitation study was carried out. However, our results do not show a great difference between the two groups. This indicates that there may be problems with imperfect detection even in species that one might consider unlikely to be problematical.

For instance, we had thought a priori that Cardamine was an easy to find species and Selaginella was a hard to find species. However, Cardamine was the fourth most difficult species to detect, whereas all populations of Selaginella, a tiny and ‘unspectacular’ pteridophyte, were found by both observers. Selaginella often grows at nutrient-poor, rocky pasture sites with very low vegetation cover. Furthermore, its gestalt is fairly distinct from that of angiosperm meadow species. Clear habitat requirements of a species, distinct morphology and a good search image can thus greatly improve detection probability.

In future studies it will be important to analyse the factors affecting detection probability of plant populations, e.g. habitat type, patch size, plant architecture and growth form, or identity of surveyor among many others. This will help in interpreting the results of previous studies and improve the design of future studies.

minimal sampling effort

Given an estimate of the detection probability of an extant population, one can estimate the minimal required number of revisits to an average site in order to achieve a high probability to detect a surviving population (McArdle 1990). For our plant populations, the required number of visits (2–4) was an order of magnitude smaller than what was required for the detection of small populations of snakes (Kéry 2002). Thus, reliable measurement of extinction by repeating revisits for some or all species or sites may indeed be feasible. However, a 5% false extinction probability may be rather large in some applications and for instance might seriously bias estimates in population viability analyses for groups of populations. The minimum number of required visits in eqn 4 may then have to be determined by setting Pn at, for example, 0.99.

Of course, our results depend on several model assumptions and on survey specificities. For instance, we assumed in our analysis that all sites were comparable with each other. This can be questioned in view of the variance in the area of the surveyed sites and most likely also of surviving populations. In other studies, habitats may be more or less impenetrable, study species more or less elusive and the surveyors more or less experienced. Hence, it would be unwise to extrapolate our results directly to other cases. Regardless, there is an almost total absence of empirical estimates in plant ecology regarding factors such as the detection probability of populations or the minimum number of visits required. We believe that even crude estimates that average over all possible effects are valuable.

study design and analysis

In our opinion, this study is the first published attempt to account formally for imperfect detection in plant revisitation studies. We used the simplest possible design that allows the separation of detection from extinction probability, namely minimal replication of two. Consequently, our analysis needs to assume that all populations are comparable and independent in terms of extinction probability. However, this may not be true, as a critic has pointed out; for instance, there may be spatial correlation in extinction probabilities (González-Megías et al. 2005), which should ideally be taken into account in the analysis. However, it is likely that the bias in the uncorrected estimates of extinction probability is far greater than any bias in our corrected estimates, as bias caused by spatial autocorrelation is also shared by uncorrected estimates.

Estimation of the detection probability p, number of surviving populations N and extinction probability E can be accomplished in many different ways. In earlier work, we had used a constrained version of the Cormack–Jolly–Seber (CJS) model (Kéry 2004), and the model developed by MacKenzie et al. (2002, 2003) is equally well applicable (Bailey et al. 2004; Pellet & Schmidt 2005).

Here, we used an indirect estimator of extinction probability by first estimating the number of surviving populations, because neither the CJS model nor, with just two visits, that of MacKenzie et al. (2002) allows for unmodelled heterogeneity in detection probability. However, it is well known that unmodelled heterogeneity results in an underestimate of N and hence in an overestimate of the extinction probability (Williams et al. 2002). Plant populations are likely to differ greatly in terms of the area they occupy, the number of ramets they comprise and many other factors that affect p. It would be interesting to investigate such factors and correlate them with detection probability. This would be valuable both for the design of future studies and for the precision of estimates. However, the Jackknife estimator explicitly accounts for all such heterogeneity by assuming that the site-specific detection probabilities come from a particular distribution, and furthermore, is fairly robust as to how this distribution looks (Burnham & Overton 1978, 1979). Hence, by using the Jackknife estimator of N, we correct for heterogeneity in p without having to specify it or to know the reasons for it.

Our use of the Jackknife estimator with just two sampling occasions has been critisized: these contained little information regarding the level of heterogeneity in detection probability among surviving populations and consequently the resulting estimates may be poor. However, we feel justified in our use of this estimator by the simulation results of Wintle et al. (2004). They show that the Jackknife estimator is fairly unbiased for our design provided that detection probability is high, for example greater than 0.6. However, it is true that in the same study, maximum likelihood estimates (MLEs) for a model that does not account for heterogeneity (MacKenzie et al. 2002) also produced fairly unbiased estimates, even though MLEs are known to be biased in this situation. Hence, it may be that our estimates are also less satisfactory than the simulation study suggests.

Nevertheless, accounting for heterogeneous detection probability in capture–recapture models is an active area of research (e.g. Royle 2006). We suggest that our analysis is the best that can currently be done with just two visits using readily available software such as MARK (White & Burnham 1999). It is clear that more visits will be beneficial in terms of the quality of the estimates and that in the near future, other models may be available that yield better estimates.

the no-colonization assumption

All the cited revisitation studies above, as well as our own, assume that there are no site (re)colonizations. That is, we condition on a number of populations that are known to have existed at some time in the past and estimate how many of them have disappeared. For species that have a metapopulation structure with frequent colonizations and extinctions, this procedure may give a too gloomy picture of the state of that metapopulation. In addition, if there are cycles in the development of the habitat of a species, such as successional gradients, that are set back from time to time, for example by fires, a fairly constant number of populations may move around among patches. An estimate of extinction probability over a short time period may then yield dramatically high extinction probability estimates, even though in the long term the number of extinctions may be at equilibrium with that of recolonizations.

Hence, to gain an overall view about the current state of a species (e.g. current distribution or extent of occurrence), which is important in metapopulation studies and conservation assessments, it is important to focus on both extinctions and colonizations of the species under consideration. Therefore, the important message is that imperfect detection biases estimates of colonization rates in exactly the same way as it does for extinction and that designs and analysis methods need to be chosen that allow one separately to estimate true colonization probability from the probability to ‘rediscover’ a previously overlooked population.

Conclusions

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

Our study stresses the importance of estimating separately the probabilities of extinction and non-detection in revisitation studies by means of replicated visits; otherwise, extinction probability may be greatly overestimated. This need not be overly expensive: an intensive, replicated sampling may only be applied to a subsample of all studied species or sites, to which resulting correction factors may then be applied (Pollock et al. 2002), or sites may only be re-visited until a species is detected (MacKenzie & Royle 2005).

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References

We thank B. R. Schmidt, L. Jenni, N. Yoccoz and two anonymous referees for valuable comments on the paper, M. Broggi from the Bristol Foundation (Schaan, FL) for financial support and the Swiss Federal Research Institute WSL for logistical support. M.K. thanks B. Schmid (Institute of Environmental Sciences, University of Zürich) for continuing support for his research.

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  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
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