Introduction

Many bird species complete seasonal migration movements between their breeding range and non-breeding areas, such as stopover and wintering range, which allows them to exploit different environments with contrasting importance for survival and reproduction (^{Newton, 2010}; ^{Rappole, 2013}). A number of migratory birds depend on wetlands and can be considered as waterbirds (^{van der Valk, 2012}). There is abundant evidence that during the 20^th Century, in many parts of the world, wetlands have been strongly degraded (^{Millenium Ecosystem Assessment, 2005}). In fact, the conservation status of wetland wildlife, waterbirds included, is deteriorating faster than that of terrestrial species (^{Millenium Ecosystem Assessment, 2005}; ^{Rosenberg et al., 2019}, for a recent survey in North America; ^{Shuter et al., 2011}). Therefore, it is important to track temporal changes in the abundance of migratory waterbirds (^{Gray et al., 2013}; ^{Wetlands International, 2010}).

Many migratory waterbirds congregate their populations in a small number of sites during certain periods of the year, which could render their counting easier to perform (^{Henderson, 2003}; ^{Weller, 2004}). By correctly undertaking repeated counts at the same study site at different points through time, one can study temporal changes in bird numbers (^{Greenwood & Gibbons, 2008}; ^{Gregory et al., 2004}). The study of temporal trends in populations can be applied to assess the carrying capacity at a given environment (^{Alonso et al., 1994}), or to evaluate progress toward a management goal (^{Elzinga et al., 2001}), which is usually part of a larger monitoring program (^{Greenwood & Robinson, 2006}). Although monitoring wetland wildlife is difficult, and diverse techniques are usually needed to obtain robust population estimates (^{Gray et al., 2013}), waterbirds are among the best monitored animals throughout the world (^{van der Valk, 2012}; ^{Wetlands International, 2010}), and many authors have studied seasonal and/or inter-annual changes in the abundance of waterbirds. For instance, ^{Russell et al. (2014)} examined how the distribution and abundance of 54 waterbird species changed between 1992 and 2010 in a rare wetland type in South Africa. To update our knowledge of a critically endangered species, the Spoon-billed Sandpiper (Calidris pygmaea), ^{Zöckler et al. (2016)} described field surveys undertaken between 2005 and 2013 in several countries along the East Asian-Australasian flyway. And ^{Molina et al. (2018)} documented how the distribution, density and population structure of American Avocets (Recurvirostra americana) wintering in a biosphere reserve in Mexico changed between 2010 and 2013.

In ecology, a census is the result of counting all the individuals within a group of interest in a well-defined area and time interval (^{Southwood & Henderson, 2016}; ^{Thompson et al., 1998}). Without correcting for detectability (^{Buckland et al., 2008}; ^{MacKenzie et al., 2018}), field-based census methods can work for relatively few bird species, and only at small spatial or temporal scales, where all individuals could be counted. Nevertheless, the complete enumeration of all the individuals in a given population can be costly, time-consuming and inefficient (^{Greenwood & Robinson, 2006}; ^{McComb et al., 2010}). More likely, total counts result unattainable, and samples must be taken to statistically estimate the size of the population (^{Fasham & Mustoe, 2005}; ^{Jones, 2000}). Actually, a large number of factors can lead to estimates of population size that are unacceptably above or below the true value, including a poor sampling strategy, an inappropriate field method, or the unintentional double counting of the same birds during a given census or sampling (^{Buckland et al., 2008}; ^{Gibbons & Gregory, 2006}; ^{Gregory et al., 2004}; ^{Thompson et al., 1998}). Under these circumstances, replicated surveys can not be considered independent, true replicates, and the researcher could incur in a problem of temporal pseudoreplication (for instance, ^{Hurlbert, 1984}).

Numbers of birds recorded during fieldwork are often used to infer change over time in waterbird abundance, or to monitor differences in bird numbers amongst habitats or regions (^{Buckland et al., 2008}). After conducting replicated counts of waterbirds at different time intervals, some authors choose to summarize obtained data by computing one of the following simple statistics (^{Nur et al., 1999}): the total (cumulative) abundance of the studied species throughout the study period; the mean (average) value, or the maximum (peak) one. This should be decided in advance, and only after taking into account the goals of the study (^{Greenwood & Robinson, 2006}). In this paper, we 1) analyze some procedures researchers usually apply in summarizing their studies of temporal changes in the abundance of waterbird populations or assemblages; 2) illustrate how these practices can inadvertently lead to distorted conclusions if obtained results are applied in ecological studies, or to rank wetlands for waterbird conservation purposes, and 3) suggest a simple solution to standardize approaches and avoid these problems.

Materials and methods

To illustrate some of the problems researchers face when using mean (average) abundance values to document the importance of a given wetland for waterbirds, we will use a fictitious scenario. Let us assume that the total world population of an endangered migratory waterbird ―from now on, Rarita rarita― is estimated at 1,000 individuals (Table 1). Let us assume, also, that the entire population of this species can be found at a given wetland 1 for only 1 month, whereas half the population, always the same 500 individuals, inhabit wetland 2 during the rest of the year. Then, following ^{Greenwood & Robinson (2006)}, wetland 1 might be considered more important for our focal species than wetland 2. For this result, we simply computed the mean abundance of the species at both wetlands. An observant reader could realize that our fictitious values were highly skewed (Table 1). When distributions are strongly skewed, the median is often preferred over the mean because it summarizes best what is typical in the data (^{Agresti & Franklin, 2013}). In fact, several authors used median abundances in their waterbird studies (for instance, ^{Martínez-Curci et al., 2015}; ^{Wilson et al., 2014}). Therefore, we also computed the median abundance of R. rarita at both wetlands.

We also use an ecological, real dataset to illustrate the same point. For this end, we used our own dataset describing seasonal changes in the waterbird assemblage at “Presa de Valsequillo,” a Ramsar site in Puebla, Mexico (^{Berumen-Solórzano et al., 2017}). From February 2014 to January 2015, monthly surveys were completed, except for April and July, and 30 waterbird species were retained for study. For all the waterbird species in the Valsequillo dataset (Table 1), we used PAST vers. 3.22 to compute the sample skewness (G ₁); G ₁ = 0 for normally distributed data, G ₁ > 0 for a long tail to the right, and G ₁ < 0 for a tail to the left (^{Hammer, 2018}). Computer intensive methods could be used to obtain confidence intervals for skewness measures; yet, even the “best,” bias-corrected and accelerated bootstrap confidence intervals give “suspect” results for samples under size 30 (^{Good, 2005}); then, we report here only point estimates for G ₁.

Instead of reporting the mean (average) or the maximum (peak) abundance, researchers can also compute the total (cumulative) abundance of the species throughout the study period (^{Nur et al., 1999}). Although, this practice can also yield ecologically misleading results. We illustrate some problems researchers can face when using total (cumulative) abundance values to document the ornithological importance of a given wetland by using our fictitious example previously explained.

Results

Regarding our fictitious scenario, if 10 censuses were regularly taken throughout the year at both wetlands 1 and 2, the mean abundance of R. rarita at wetland 1 would be 100 individuals (Table 1). However, this value was never observed in the field, and can hardly be deemed a valid measure of the central tendency of the abundance of the species at wetland 1. Moreover, the median abundance of R. rarita at wetland 1 also results ecologically irrelevant since it is zero (Table 1).

Regarding our real dataset from “presa de Valsequillo,” some waterbird species were registered only twice, like the Franklin’s Gull (Leucophaeus pipixcan: 1 bird was observed in October, and 3 in November), or even once, like the Black-bellied Whistling-duck (Dendrocygna autumnalis: 33 birds were observed in December). Indeed, for exceedingly rare species inhabiting wetlands, detection can be near zero (^{Gray et al., 2013}). Had we computed mean abundances from those 10 samples, the average values for Franklin’s Gulls (0.4 birds/survey) and Black-bellied Whistling-ducks (3.3 birds/survey) would have been ecologically irrelevant. Our analyses with the Valsequillo dataset reveal that skewness values in abundance data suggested asymmetric, positively skewed distributions for 13 out of the 30 species retained for study (Table 1). Therefore, the median (but not the mean) should theoretically be used as a measure of the central tendency of the corresponding distributions. Nevertheless, the median was 0 for 12 out of the 30 species in our dataset, and the frequency of this result increased with the measure of skewness (Table 1). This suggests that, at least for species with a low frequency of occurrence, the median is not a good measure summarizing abundance values.

Remember the world population of our fictitious endangered waterbird, R. rarita, was estimated at 1,000 individuals. If one computes the total, cumulative abundance of this species for both wetlands in our example (Table 1), this value is 1,000 for wetland 1, which is ecologically correct, but it is 4,500 (i.e., 9 months × 500 birds/month) for wetland 2. An inattentive reader could interpret the last value as if 4,500 “different birds” were registered in the study area, all at the same time; however, the peak, maximum abundance per survey was only 500, and the whole population was only 1,000. On the other hand, 4,500 “different birds” could have also been observed if their identity completely changed over time, i.e., if the turnover among individual waterbirds was complete. However, this was not the case in our fabricated example, since the individuals in wetland 2 were always the same and, again, the whole population was only 1,000. Finally, it should be noted that, if wetland 2 were regularly surveyed throughout the year once-a-month, the total, cumulative abundance of R. rarita would be 5,500 (i.e., 11 months × 500 birds/month).

Discussion

As our fictitional and real data expose, both mean abundances and total, cumulative values through time can be ecologically misleading. On the one hand, mean abundances can be markedly skewed, and median values should be used; but median values can also be ecologically meaningless, if never registered in the field. Therefore, reporting the maximum (peak) abundance could be the best option for our data, and this might also be true for real datasets, since biological variables frequently are positively skewed (^{Quinn & Keough, 2002}). On the other hand, total, cumulative values can inadvertently count the same individuals multiple times. In fact, the total, cumulative abundance of a given species at a given site unavoidably increases with the actual number of samples/surveys taken.

Actually, we have found this procedure of reporting the total, cumulative abundance of a population, or a whole assemblage, several times in the recent literature on temporal changes of migratory waterbirds in Mexico. The following references should only be taken as a small (n = 15) and surely biased sample, included here just to illustrate our point: ^{Guzmán et al. (1994)}; ^{Cupul-Magaña (1997}, ²⁰⁰⁰⁾; ^{Hernández-Vázquez (2000}, ²⁰⁰⁵⁾; ^{Mellink and De la Riva (2005)}; ^{Munguía et al. (2005)}; ^{Amador et al. (2006)}; ^{Zárate-Ovando et al. (2006)}; ^{Gerardo-Tercero et al. (2010)}; ^{Sánchez-Bon et al. (2010)}; ^{Fonseca et al. (2012)}; ^{Mera-Ortiz et al. (2016)}; ^{Hernández-Colina et al. (2018)}, and ^{Molina et al. (2018)}. The interested reader can also see this procedure in ^{Arizaga et al. (2014)} or ^{Isotti et al. (2015)}, for instance. Interestingly, several of these authors reported the total, cumulative abundance but also other measures of the central tendency in the abundance of their study species or assemblages.

Because of their contrasting objectives and survey protocols during field work, the number of samples/surveys also varied dramatically amongst the abovementioned studies reporting total, cumulative abundance. For example, to document spatio-temporal changes in the distribution and abundance of waterbirds wintering in “ciénega de Tláhuac,” a lacustrine wetland in Mexico, ^{Ayala-Pérez et al. (2013)} completed only 4 surveys, 1 per month. On the other hand, to study if the formation of an artificial lagoon affected waterbird diversity in Urdaibai, a biosphere reserve in Spain, ^{Arizaga et al. (2014)} surveyed waterbirds 24 times, 1 survey per 15-d interval. Without doubt, total, cumulative abundance data for species or assemblages obtained from studies with so dissimilar sampling efforts cannot be directly compared.

Furthermore, 86.7% of the studies in our abovementioned sample of references reported the total, cumulative abundance of the studied waterbirds in the corresponding ‘Abstract/Summary’ sections of their publications. In this way, those numbers received a wider audience, since this is the most read part of a published article (^{Gladon et al., 2011}), and it can be freely available via abstracting services and/or search engines (^{British Ecological Society, 2015}). Therefore, after reading the ‘Abstract/Summary’ section of the abovementioned papers, an unobservant reader might obtain an ecologically misleading idea about the abundance of waterbirds in the study wetlands.

Among the potential confusions that could be caused by reporting the total (cumulative) abundance of waterbirds is the fact that it allows for improper comparisons between study sites. For instance, ^{Mera-Ortiz et al. (2016)} studied temporal changes in the composition and abundance of waterbirds at “mar Muerto,” a coastal lagoon in Oaxaca-Chiapas, Mexico. After visiting, once per month, 3 different landscapes in this lagoon during March, April, May and September 2011, they registered 40 species of aquatic and semi-aquatic birds and reported a total, cumulative abundance of 1,577 individuals. Then, ^{Mera-Ortiz et al. (2016)} compared these values with those previously reported for similar wetlands along the tropical, Mexican Pacific coast, and concluded that waterbird assemblages inhabiting “mar Muerto” exhibited low richness and abundance (^{Gerardo-Tercero et al., 2010}; ^{Hernández-Vázquez, 2005}; ^{Sánchez-Bon et al., 2010}). Moreover, authors proposed putative ecological explanations to support their conclusion, taking into account vegetation differences among the study sites.

And yet, the conclusion by ^{Mera-Ortiz et al. (2016)} might be biased, since the studies they used in their comparisons had followed the same procedure we are criticizing here. First, from December 1997 to November 1998, ^{Hernández-Vázquez (2005)} completed monthly surveys in 2 natural water pools in Jalisco, Mexico, and reported a total, cumulative abundance of 66,976 individuals (78 species) for one site, and 112,832 individuals (73 species) for the other site. Also, from October 1996 to May 1997, ^{Gerardo-Tercero et al. (2010)} completed 8 surveys in total at 3 different environmental units in a coastal lagoon in Chiapas, Mexico, and reported a total, cumulative abundance of 89,413 individuals (39 species). Finally, after completing 1 census per month from July 2006 to June 2007 at several sampling sites in a coastal lagoon complex in Sinaloa, Mexico, ^{Sánchez-Bon et al. (2010)} reported a total, cumulative abundance of 55,849 individuals (71 species). It is impossible for us to know the real survey effort employed in these studies, but undoubtedly it was heterogeneous enough to make direct comparisons of abundance values not feasible. Many authors have observed that, when sampling effort varies between study sites, direct comparisons of richness values are not possible (^{Gotelli & Colwell, 2011}; ^{Gotelli & Ellison, 2013}; and references therein).

We think the same is true for total, cumulative abundance values, but it seems to us that this significant point has been frequently forgotten. Fortunately, several authors have developed standardized protocols for surveying waterbirds of conservation concern, like marsh-dependent birds in North America or marine birds in Alaska, which allow researchers to obtain consistent results among locations and gain a better knowledge of the status, distribution and population trends of selected species (^{Conway, 2011}; ^{Smith et al., 2014}).

At least 2 global biodiversity conservation schemes consider data on waterbird abundance to ascribe conservation status to wetlands all through the world: the Convention on Wetlands of International Importance, also known as the Ramsar Convention (https://www.ramsar.org/), and the BirdLife International, Important Bird Areas (IBA) program (https://www.birdlife.org/). In summary, a given site could be included onto the List of Wetlands of International Importance (at the time of the writing, 2,341 Ramsar sites), or considered as IBA (at the time of the writing, more than 12,000 IBAs; sic), if it is known or thought to support, on a regular basis, at least 20,000 waterbirds of 1 or more species (Ramsar Criterion 5, IBA Criterion A4iii), or at least 1% of the individuals in a biogeographic population of a congregatory species or subspecies (Ramsar Criterion 6, IBA Criterion A4i).

Note that, as previously stated, these criteria do not clarify what type of abundance values should be considered when applying both thresholds to infer the conservation importance of wetlands for waterbirds (^{Ramsar Convention Secretariat, 2010}). And this is significant since, otherwise, resources for conservation might be misapplied if the inferences about trends or differences in waterbird abundance are inaccurate (^{Buckland et al., 2008}). For instance, ^{Valle et al. (2014)} studied seasonal changes in the abundance of waterbirds at a key stopover site on the West Asian-East African flyway, and used peak counts to assess the importance of the Sabaki River Mouth, Kenya, for a number of migratory waterbirds, including the Saunders’s Tern (Sterna saundersi). The maximum abundance of this species (750 individuals) exceeded 1% threshold of its global population, which confirmed the international rank of that estuary. However, we could not determine if other considered total, mean, or peak abundances when evaluating the importance of the studied wetlands for waterbirds researchers (^{Eiserman & Avendaño, 2009}; ^{Vega et al., 2006}). This lack of a common approach in assessing the degree of compliance with standard criteria might help to recognize, or to exclude, a given wetland as a Ramsar site or IBA. By ignoring the abovementioned, positive relationship between sampling effort and cumulative abundance, a researcher could complete a large number of surveys at a given study site and unconsciously inflate abundance data, which might exceed the threshold values in the corresponding criteria, and artificially increase the conservation importance of the studied wetland for waterbirds.

Since birds are highly-mobile organisms, determining how many individual birds use a site from counts alone is not an easy task, and many authors advise those who count birds of the importance of not registering multiple times the same individuals (^{Frost et al., 2019}; ^{Lloyd et al., 2000}; ^{McComb et al., 2010}; ^{Mustoe et al., 2005}). To avoid double-counting the same birds at a given time, ^{Gregory et al. (2004)} simply recommended using careful observation and common sense, and similar measures have been considered by some researchers studying waterbirds (^{Cui et al., 2014}; ^{Prosser et al., 2017}). Nevertheless, when replicated samples/surveys are spread out over time, these simple measures are difficult to apply, if not impossible. In this paper we maintain that, if a simple measure summarizing the abundance of waterbirds is needed, then computing the mean (average) abundance over time of a given species or assemblage, or the total (cumulative) abundance throughout a long study period, could both be ecologically misleading. In the former case, because abundance values could be skewed; in the latter case, because of the non-zero probability of counting the same individual birds multiple times. Therefore, how can we capture with a single number the importance over time of a waterbird species or assemblage?

Following ^{Johnson (2008)}, we propose to use the maximum, peak abundance of a given species during the course of the study as a simple but ecologically relevant measure of its numerical importance. Actually, this approach has been previously applied by ^{Ayala-Pérez et al. (2013)} to study spatio-temporal changes in the distribution of wintering waterbirds in “ciénega de Tláhuac”, a lacustrine plain in Mexico; by ^{Valle et al. (2014)} to highlight the importance of the Sabaki River Mouth for a number of waterbirds on the West Asian-East African flyway, and (partially) by ^{Zöckler et al. (2016)} to study the world winter distribution of the critically endangered Spoon-billed Sandpiper. For example, using the Valsequillo dataset (Table 1), the total, cumulative abundance of American Coots (Fulica americana) was ca. 12,150; however, the maximum, peak abundance was registered in December, when ca. 3,000 birds were counted. Also, the cumulative abundance of the endemic Mexican Duck (Anas platyrhynchos diazi) was ca. 650, but the peak was only ca. 100 ducks. These peak abundance values likely underestimate the real number of individuals throughout the study period, since the identity of the birds inhabiting the study site might have changed with time; therefore, we think they ought to be regarded as lower bounds for their corresponding total abundance (^{Ayala-Pérez et al., 2013}).

Moreover, to obtain a reasonable measure of the total number of individuals for whole assemblages, we propose to sum the peak abundance values across all the species during the course of the study. This approach has been successfully applied by the British Trust for Ornithology in their Wetland Bird Survey (^{Frost et al., 2019}; https://app.bto.org/webs-reporting/), which reports site totals for many wetlands in the United Kingdom as the sum of each species maxima from the appropriate time period. Note that, if this time period is short enough (e.g., only 1 year), then the peak abundance could also be misleading, since it could be unrepresentative of the general trend of the population in time. For reasons like this, organizations as the British Trust for Ornithology are using a 5-year mean of peaks to infer site importance (^{Ramsar Convention Secretariat, 2010}). For the Valsequillo dataset (Table 1), the total, cumulative abundance of the 30 studied waterbird species was ca. 20,800 individuals; nevertheless, after adding the peak values across all the species, we obtained an estimate of ca. 6,400 individuals. Note that this number of “different birds” was never registered at the same point in time in our study area, since the highest monthly abundance was ca. 4,450, registered in November (Table 1). Note, finally, that additional, replicated information is required to account for inconsistencies in data and to properly judge the regular basis of peak abundance values in a given wetland; otherwise, we could be confusing sites that regularly hold wintering waterbird populations of national or international importance with those which might happen to exceed the abovementioned thresholds only in occasional winters.

Total, cumulative abundance might offer the most credible (i.e., exact) results for those sites over which migratory birds produce spectacular concentrations and must pass, like well-known narrow migration bottlenecks, where temporal turnover is very high; or for irruptive species (^{Devenish et al., 2009}; ^{Newton, 2010}). For the rest of sites and species, common sense tells us that the probability of counting multiple times the same bird increases as individuals repeatedly use the same sites on successive journeys and the turnover rate decreases. By systematically reporting cumulative counts as a reliable measure of waterbird abundance, ecological studies and conservation efforts might be misguided. We think that these problems could be prevented, or at least alleviated, by using species/assemblage maximum (peak) abundance data for the appropriate time periods.