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Demography is the key to understanding spatial and temporal variation in abundance of plants. Longitudinal studies yield the most detailed knowledge. Most often, the plant life cycle is divided into discrete states, and marked or mapped plants in permanent plots are followed through time (e.g. Tamm 1972; Hutchings 1987; Oostermeijer et al. 1996; Pascarella & Horvitz 1998). The sample of marked plants in a plot is assumed to be representative of the entire population studied. Once a year or at some other appropriate time interval all individuals in the plots are ‘censused’. The presence or absence of each individual, and attributes such as life-state, size, and number of fruits are then recorded. This permits estimation of survival and recruitment rates, and transition rates between life-states, which may be integrated into matrix population models to project the asymptotic population dynamics (Caswell 2001).
Cross-sectional studies may compare several populations at one point in time. Population structure is often sampled in plots thought to be representative of the entire population. A snap-shot of population structure (e.g. the numbers of seedling, vegetative, and flowering plants), may contain useful information on population dynamics. For instance, Oostermeijer et al. (1994) surveyed population structure of the rare Gentiana pneumonanthe in the Netherlands and distinguished three types of populations. ‘Dynamic’ populations had a large proportion of young life-states (seedlings and juveniles), ‘senile’ populations contained only adult states, while ‘stable’ populations contained members of all life-states. There was a strong positive relationship between the percent of bare soil surface and litter cover and the density of seedlings and juveniles. This finding indicated that the status of a population could be assessed by one quick visit to a site.
Plant demographic plots are often small (0.1–100 m2); so most studies implicitly assume that every individual is indeed found, i.e. that detectability equals 1. However, detectability even in small plots could be affected by various factors. Possible sources of variation in detectability are the size of a plant, its life-state, and phenologic state in the reproductive cycle (e.g. individuals with flower buds, flowers in anthesis, and fruits). Furthermore, its previous ‘detection history’ may affect its detectability. An individual recorded in earlier surveys may be less likely to be overlooked than a new recruit, of whose location the demographer has no prior knowledge. There may be temporal variation in detectability associated with varying light conditions or with changes in the vegetation matrix. Often there is small-scale heterogeneity in cover, structure and size of the vegetation matrix in a plot, and this could influence detectability. Detectability is likely to be different for different observers and is likely to be a function of experience for a particular observer. Finally, biotic interactions such as herbivory may decrease or increase detectability, e.g. by reducing the size of a plant or causing it to wilt and turn brown so that it becomes more conspicuous in surrounding green vegetation.
Detection probabilities < 1 introduce a bias into most estimates of population parameters such as abundance, recruitment, mortality rates, and transition rates between life-states. If they are not accounted for they can produce misleading conclusions from a plot-based demographic study. We believe that the assumption that every plant within a plot is found is an important one that should be tested. If it is found to be false, then estimation of demographic parameters must account for detection probabilities, as in multistate capture–recapture models (Nichols & Kendall 1995).
The aim of this study is twofold: (1) to provide one counterexample to the widespread implicit assumption in virtually all plant demographic studies that every plant is always found, and (2) to show that detectability can readily be estimated within the rigorous statistical framework of capture–recapture models. We illustrate this by an example using a double-observer approach. We identify the factors that affect detectability in the medium-sized terrestrial orchid Cleistes bifaria, and draw attention to the potential biases incurred when one wrongly assumes that detectability equals 1. We believe that we point out a widespread issue for plant demography and show how it can be addressed. We further believe that our approach, results, and conclusions are relevant to plant demographic studies in which parameters such as survival and recruitment rates or population growth rates are estimated from a sample of marked individuals or from simple counts of detected plants. We emphasize that capture–recapture models are useful not only for detecting variable detection probabilities but also for developing models to properly estimate demographic parameters in the face of such variation.
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The most parsimonious model for detectability of C. bifaria in our study plot was model 12 (Table 3). It had a different set of detectabilities for each life-state for previously tagged vs. previously untagged plants. A comparison of model 12 with the less well fitting model 11 indicated that the tagging history effect was mainly due to the presence of tags and not to prior knowledge of the locations of the plants. Support for model 12 was almost twice as strong as that for the next best model (model 9), as shown by the ratio of the Akaike weights. However, model 9 was within two AICc units and hence, it provided a good approximation to the data as well (Burnham & Anderson 1998). This model suggests that detectability was indeed similar between the two vegetative states.
To test whether the effect of life-state in the most parsimonious model was mainly due to the different size of the life-states, we set detectability as a function of the average size of each life-state. This model fitted almost as well as our best model 12 (ΔAICc = 1.16). Therefore, the life-state effect appears to be largely a size-effect.
Based on the low-AICc model, detectability (followed by SE, where available) for previously tagged C. bifaria plants in the one-leaf, two-leaf vegetative, and flowering/fruiting state was estimated at 0.76 (0.05), 0.92 (0.06), and 1, respectively, for both observers (Fig. 1). For previously untagged plants in the same states, detectability was 0.84 (0.08), 0.75 (0.22), and 0, respectively. The unexpectedly low estimate for untagged flowering plants was due to a single plant that was overlooked. Judging from standard errors, sampling error is the most likely explanation for detectability change in opposite directions for plants that were, and were not, previously tagged.
Figure 1. Estimated detectability (95% CI) of Cleistes bifaria plants based on the most parsimonious model in Table 3 (model 12), which had life-state specific effects for previously tagged vs. untagged plants and no differences between observers. Tag1, tag2, and tagF denote previously tagged plants in the one-leaf, two-leaf, and flowering/fruiting state. Untag1, untag2, and untagF denote the same for previously untagged plants. The estimate for both kinds of flowering plants (asterisks) was at the boundary of parameter space, so no CI is available.
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To incorporate the uncertainty in model selection into the estimate of detectability, we also obtained the unconditional estimates (Table 4). They support the result from the analysis of the most parsimonious model, which shows that we did not have sufficient information to reliably estimate detectability for untagged flowering plants (estimate for observer 1: 95% CI 0.010–0.947).
Table 4. Model-averaged estimates of the detectability on a study plot of Cleistes bifaria. Estimates and their standard errors are obtained as weighted average of the estimates of each model with the weighting scheme based on Akaike weights in Table 3 (Burnham & Anderson 1998). Also shown are lower and upper 95% confidence limits
|Life-state||Tagging status||Observer||Detectability||SE||Lower 95% CL||Upper 95% CL|
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Detectability for individuals of the orchid C. bifaria in a permanent plot used for a long-term demographic study was life-state dependent, and averaged only 0.82 for vegetative plants. As expected, detectability was almost 1 for the more conspicuous flowering plants, but even they were sometimes overlooked.
Only two studies have previously estimated detectability in plants. They did so at much larger spatial scales and for different demographic units. Detectability for patches of the milkweed Asclepias meadii in a 4.5-ha prairie patch averaged only 0.25 (Alexander et al. 1997). For clumps of the relatively conspicuous orchid Cypripedium calceolus var. parviflorum in an area of 0.044 ha, detectability was 0.91 (Shefferson et al. 2001).
Our study shows that even under excellent survey conditions (moderately large herbaceous plant, small, flat plot with relatively open vegetation), not all plants may be found. This may be typical for plant demographic studies. The least conspicuous life-state of C. bifaria, one-leaf plants, averaged 16.2 cm in height and was thus reasonably tall. Many demographic studies include seedlings and other much smaller states that probably have a much smaller detectability. We believe that an implicit assumption made by plant demographers, that all plants in a plot are always found, may often be wrong.
This gives cause for concern, because in demographic estimation detectability < 1 leads to biased estimates of survival probabilities, state-transition probabilities, and state-specific numbers of organisms (Nichols & Pollock 1983; Williams et al. 2002). Perhaps more important than simple bias is the possibility that covariate relationships may be determined by relationships involving detectability rather than the estimated demographic parameter. For instance, part of the positive relationship between percentage of bare soil surface and recruitment in populations of Gentiana pneumonanthe (Oostermeijer et al. 1994) and Salvia pratensis (Hegland et al. 2001) may perhaps have been due to the fact that fewer seedlings could have been overlooked where there was more bare ground.
We illustrate the potential impact of ignoring detectability < 1 on the estimation of demographic parameters with the following hypothetical example. Consider a stable population of a theoretical plant species with three life-states, one- and two-leaf vegetative, and flowering plants. There is no seed bank. One-leaf plants become two-leaf plants the following year, flower, or die. Two-leaf plants either survive in that state, flower, or die. Flowering plants either survive in that state, become two-leaf plants, produce one-leaf plants via seed, or die. Recruitment can therefore be estimated by the ratio of the number of one-leaf plants in year 2 and the number of flowering plants in year 1. Survival and transition rates can be estimated by recording the fate of marked individuals in successive years. Matrix A describes the true dynamics of this population (Table 5a).
Table 5. Illustration of the potential impact on a matrix model of imperfect detectability for a stable population of a hypothetical plant species with three states and no seed bank. (a) True transition matrix A (λ = 1.00). (b) Apparent transition matrix A′ (λ = 0.92). See text for derivation of A′
We then simulated the effect of imperfect detectability on the inference from a matrix model based on a 2-year survey. Levels of detectability were set at similar values to those recorded for tagged plants in our C. bifaria plot (0.77, 0.89, and 0.95, respectively, for one-leaf, two-leaf, and flowering plants).
The effect of imperfect detection can be seen by comparing the true transition matrix A with the apparent transition matrix A′. The hypothetical population was chosen to be stable (λ = 1.00). However, from matrix A′, it would be inappropriately concluded that the population is in strong decline (λ = 0.92). Elasticity estimates were biased on average by 6.4%. Imperfect detection in plant demographic studies may thus be a factor leading to underestimation of the true population growth rates based on matrix models. This may have been a reason why matrix models of three populations of the biennial forb Gentianella germanica projected precipitous declines, when in fact the number of flowering plants over 3 and 4 years remained stable or even increased (Kéry 2000).
There is a further bias that we have not addressed in this study. The sample of detected plants is unlikely to be representative of all plants in a plot. Detectability of C. bifaria was lower for smaller plants. However, plant size is usually correlated with survival, fecundity, and transition probability between states. The plants detected in a plot will therefore be biased towards larger and more conspicuous life-states. The unseen fraction of plants in a plot will differ from the detected plants in fecundity and recruitment. Then even when the re-detectability is high (i.e. when most marked plants are found), estimates will be biased, because the marked plants constitute a size-biased sample from all the plants present in a plot. Imperfect detection always distorts estimates of demographic parameters to some degree. Conclusions from demographic models (e.g. matrix population models) built with multiple estimates, each of which suffers a bias due to detection probabilities < 1, may therefore be even more strongly biased.
Some might claim that it is sufficient to standardize the survey protocol across time and space and increase survey effort. They would then be prepared to make the untested assumption that detectability equals 1. We argue that this is not a valid solution. Rather, the onus should be on those that make the assumption that their detectability is essentially equal to 1 to produce evidence based on a study such as ours to support their claim. Capture–recapture models are designed to achieve this.
Although we used two observers, a richer set of hypotheses about sources of variation in detectability can be formulated and tested with more observers. Care, however, has to be taken not to disturb the vegetation, as this might change both the demography and presumably also the detectability of a study species (Cahill et al. 2002). Possible factors whose effects can be estimated include observers, survey methods, and spatial and temporal differences between surveys. Where demographic surveys are carried out by multiple observers, it will be desirable to estimate detectability for each of them. A priori hypotheses about how observers differ in detectability could be readily tested. For instance, observer differences might only be relevant for small life-states and vegetative plants and not for flowering plants. Constraints could be used to achieve more parsimony. For instance, detectability could be modelled as a linear function of plant height. Huggins’ model (1989; 1991) could also be used to directly model the relationship between detectability and plant height without taking account of plant life-states. However, most plant demographic work is based on models for discrete life-states rather than models for continuous size. Therefore, we retained the life-state distinction in all models. The animal ecology literature is rich in references to capture–recapture models, many of which are useful for plant ecologists (e.g. Otis et al. 1978; Nichols et al. 1986; Williams et al. 2002).
When nothing is known about possible factors related to detectability, models that allow for unspecified heterogeneity of detectability between individuals may be used, such as the estimators for model Mh implemented in program CAPTURE (Otis et al. 1978), or the finite mixture estimators of Pledger (2000) that can be fitted using program MARK (White & Burnham 1999).
In conclusion, although plants stand still and wait to be counted (Harper 1977), they may sometimes hide. The problem will be greater for smaller and less conspicuous species or life-states and for larger plots. However, even in small-scale plot studies of conspicuous plants, detectability should not be assumed to equal 1. If this assumption is not met, estimates of demographic rates are bound to be distorted. Capture–recapture models offer a flexible framework to estimate detectability and to test what factors affect it. We suggest that plant demographers should estimate detection probabilities at least once during their study. Then, if detection probabilities are indeed < 1 for some states, it is possible to adjust demographic models of survival and recruitment processes.