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Kéry, M.

Grundlagen der Bestandserfassung am Beispiel von Vorkommen und Verbreitung.

2008

105

353–386

Key words
(von 1994 bis 2006 vergeben)

Bestandeserfassung, Bestand, Monitoring, Zählungen, Revierkartierung, Höhenverbreitung, Antreffwahrscheinlichkeit, Schätzung, Binomialverteilung, Statistik, Site-Occupancy-Modell

Schlagwort_Vogelart
(wissenschaftlich)

Tetrao urogallus, Pernis apivorus, Accipiter gentilis, Accipiter nisus, Aquila chrysaetos, Falco peregrinus, Bubo bubo, Dryocopus martius, Dendrocopos medius, Dendrocopos minor, Troglodytes troglodytes, Erithacus rubecula, Luscinia megarhynchos, Turdus torquatus, Sylvia atricapilla, Phylloscopus sibilatrix, Phylloscopus collybita, Garrulus glandarius, Corvus corax, Passer hispaniolensis italiae, Fringilla coelebs

Schlagwort_Vogelart
(deutsch)

Auerhuhn, Wespenbussard, Habicht, Sperber, Steinadler, Wanderfalke, Uhu, Schwarzspecht, Mittelspecht, Kleinspecht, Zaunkönig, Rotkehlchen, Nachtigall, Ringdrossel, Mönchsgrasmücke, Waldlaubsänger, Zilpzalp, Eichelhäher, Kolkrabe, Italiensperling, Buchfink

Schweiz, Nordjura, Voralpen, Graubünden, Oberengadin

deutsch

Abhandlung

Foundations of bird surveys with examples from occurrence and distribution. – Occurrence and distribution are central topics in ornithology. However, every ornithologist knows very well that birds can be overlooked, that is, that detection probability (p) is usually less than 1 (p < 1). Typically therefore, our observations map the true population sizes and true occurrence of birds only in an incomplete and potentially distorted, that is, biased, way. Mathematically, all our bird observations are random variables. Whenever p < 1, our observations aren’t fixed numbers anymore. Instead, by pure chance replicate observations will typically differ even under identical conditions and will be predictable only on average. The binomial distribution of statistics represents the theoretical basis for a bird survey where N units (such as occupied quadrats) all independently have the same chance p of being recognized as occupied by a species of interest; the resulting count of occupied quadrats is binomially distributed. The flip of a loaded coin is a perfect analogy to the observation process involved in any bird distribution study: all the birds in each of N occupied quadrats flip the coin, and only when any of the inhabitants of a quadrat tosses heads is that quadrat recognized as occupied and therefore appears in the count of occupied quadrats. Loaded means that a coin’s probability of heads can be any number between 0 and 1 in principle, not only 0.5. The binomial model of bird surveys perfectly illustrates three key features of bird observations: (1) The observed number of occupied quadrats (n) will almost always differ in repeated surveys, even under identical conditions, and varies between zero and the true number of occupied quadrats (N). (2) We can’t say much about any individual count n, but the mean count, i.e., averaged over many replicate counts, will be equal to N * p, the expected value of a binomial random variable. In addition, counts will automatically vary one from another and the magnitude of that variation is known to be sqrt (N * p * (1–p)), the standard deviation of a binomial random variable. Furthermore, since p <= 1, we will almost always underestimate true distributions. (3) Changes in counts of occupied quadrats over time or differences between sites or habitats in the number of occupied quadrats can be due to differences in the true number N of occupied quadrats, differences in the probability to detect an occupied quadrat (p), a combination of both or even just due to (binomial) chance variation. Therefore, trends in detection probability p can mask genuine distributional trends or feign changes in a distribution that is in fact static. Whenever we need to know the absolute distribution (N) of a species or when we fear the presence of «dangerous patterns» in p (by which term is meant that p and N depend on the same factor of interest) we must estimate N directly. This involves estimation of p and therefore correction of our observations for imperfect detection (p < 1). Key to this in the context of distribution studies are observations that are replicated in the short-term, so that the true occupancy state (occupied or not) does not change. Under this condition, the pattern of detection and nondetection of a species contains the information required to estimate p separately from the true distribution. Using such replicate observations, a new class of statistical models that goes by the peculiar name «site-occupancy model» (MacKenzie et al. 2002) enables one to estimate true distribution and its relationship with external (e.g., habitat or climatic) variables corrected for imperfect detection probability. Conceptionally, site-occupancy models are based directly on the binomial model of bird surveys and represent two coupled logistic regression models: the first describes the imperfectly observed true pattern of presence and absence, and the second describes the pattern of detection/nondetection, given the true pattern of occurrence. Covariates can be introduced into both regressions, that is, both distribution and detection probability can be made a function of the values of measured factors of interest. In this essay, I describe site-occupancy models and in a simulation study show how they are much better able to estimate the true distribution of a species than conventional ways of interpreting distributional data. In a second simulation study I show that, unlike conventional methods, estimates under a site-occupancy model can correct estimates of species distributions for the presence of «dangerous patterns» in detection probability, for instance, when elevation affects occurrence probability and detection probability of a species alike. It is argued that many species distribution studies conducted by professional or amateur ornithologists alike would benefit from more conceptual rigour. The binomial distribution of statistics represents the theoretical underpinning for the design, conduct, analysis and interpretation of all empirical studies on distribution and occurrence of species. I hope that this essay fosters a deeper understanding of the fundamentals of bird distribution surveys and that increased application of site-occupancy models for estimation of species distributions will enhance the quality and interpretability of such studies.