TWO SURVEYS PER SPRING ARE ENOUGH TO OBTAIN ROBUST POPULATION TRENDS OF COMMON AND WIDESPREAD BIRDS IN YEARLY MONITORING PROGRAMMES - RESEARCHGATE
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Ardeola 68(1), 2021, 33-51 DOI: 10.13157/arla.68.1.2021.ra3
TwO SUrvEyS pEr SprING ArE ENOUGh
TO OBTAIN rOBUST pOpULATION TrENDS
Of COMMON AND wIDESprEAD BIrDS IN yEArLy
MONITOrING prOGrAMMES
DOS CENSOS pOr prIMAvErA SON SUfICIENTES
pArA OBTENEr TENDENCIAS pOBLACIONALES rOBUSTAS
EN prOGrAMAS DE SEGUIMIENTO
DE AvES COMUNES
Luis M. CArrASCAL 1 * and Juan Carlos DEL MOrAL 2
SUMMAry.—Extensive bird monitoring programmes are fundamental for estimating inter-annual
population trends using data provided by thousands of observers through standardised fieldwork. Gordo
(2018) has proposed that abundance data recorded by common bird monitoring schemes (e.g. SACrE
programme) should be used cautiously due to its potential inaccuracy, because two surveys per spring
are not enough to record the actual maximum number of individual birds at a sampling location. we
carried out numerical simulations and analysed the interspecific pattern of statistical significance of
the published population trends of the Spanish common birds census, the SACrE programme (1998-
2011), in order to test how the number of repetitions of censuses per year affects the power of tests:
(i.e. the probability of detecting significant trends that are in fact true), and the probability of obtaining
low false discovery rates: i.e. identifying significant changes that are actually false, when estimating
yearly population changes. we agree with Gordo (2018) that two surveys of the same sampling stations
per year are unable to detect the maximum number of birds throughout a breeding season. Nevertheless,
the goal of monitoring programmes is not to obtain the maximum number of birds at each sampling
unit over a long time span but to measure reliable population trends. Our results demonstrate that the
average number of birds recorded in two surveys per season provides a highly reliable indication
of population trends for abundant and widely distributed bird species, the focal taxa in common birds
monitoring schemes, especially of long-term average trends > ±2.5% change annually. The actual
population trends for very rare species, such as those with data from fewer than 50 UTM squares and
< 5 individual birds per census and UTM cell, are hard to detect unless they show yearly percentage
population changes greater than ±5%.—Carrascal, L.M. & del Moral, J.C. (2021). Two surveys per
spring are enough to obtain robust population trends of common and widespread birds in yearly moni-
toring programmes. Ardeola, 68: 33-51.
Key words: abundance, inter-annual changes, power of the tests, SACrE, sample size.
1
Department of Evolutionary Ecology, Museo Nacional de Ciencias Naturales, CSIC,
C/ José Gutiérrez Abascal 2, 28006 Madrid, Spain.
2
Unidad de Ciencia Ciudadana, SEO/BirdLife, C/ Melquiades Biencinto 34, 28053 Madrid.
* Corresponding author: lmcarrascal@mncn.csic.es34 CArrASCAL, L.M. and DEL MOrAL, J.C.
rESUMEN.—para obtener las tendencias de población son fundamentales los datos proporcionados
por miles de ornitólogos voluntarios mediante el trabajo de campo estandarizado. Gordo (2018) ha
propuesto recientemente que los datos de abundancia registrados en estos programas (p. ej., SACrE)
se usen con precaución debido a su posible inexactitud, ya que dos censos por primavera y año no son
suficientes para registrar el número máximo real de aves en un lugar de muestreo. para probar cómo el
número de repeticiones de censos por año afecta el poder de los tests (i.e., la probabilidad de detectar
tendencias significativas cuando de hecho son verdaderas), y la probabilidad de obtener bajas tasas de
error al identificar cambios significativos cuando que en realidad son falsos, se han realizado simula-
ciones numéricas y analizado el patrón de variación interespecífica de la significación de las tendencias
de población publicadas en programa SACrE (1998-2011). Estamos de acuerdo con Gordo (2018) en
que dos censos de las mismas estaciones de muestreo por año no pueden alcanzar el número máximo
de aves durante una temporada de reproducción. Sin embargo, el objetivo de los programas de monito-
reo no es obtener el número máximo de aves en cada unidad de muestreo a lo largo de un período de
tiempo prolongado, sino cuantificar índices fiables de tendencias de población. Nuestros resultados
demuestran que el promedio del número de aves registradas en dos censos por temporada proporciona
altas tasas de descubrimiento de tendencias de población para especies de aves abundantes y amplia-
mente distribuidas, especialmente bajo tendencias promedio a largo plazo > ±2.5%. Sin embargo,
la veracidad de las tendencias es muy limitada para especies muy raras (e.g., < 50 cuadrados UTM y
< 5 aves por censo y celda UTM), a menos que muestren porcentajes anuales de cambio de población
superiores al ±5%. —Carrascal, L.M. y del Moral, J.C. (2021). Dos censos por primavera son sufi-
cientes para obtener tendencias poblacionales robustas en programas de seguimiento de aves comunes.
Ardeola, 68: 33-51.
Palabras clave: abundancia, cambios interanuales, potencia de los tests, SACrE, tamaño muestral.
INTrODUCTION scale and in four large regions (van Strien,
2001). forty-three countries currently work
The rate of population decline is one of within this pan-European programme, pro-
the five quantitative criteria used by IUCN viding information annually, but population
to assess the extinction risk of species, with indices are currently built with data from only
clearly defined thresholds to assign taxa to 28 countries. The data provided by these
one of several categories of conservation countries have been used to build the com-
status (Colyvan et al., 1999; Mace et al., mon European index, covering 37 years
2008; IUCN, 2019). Numerous countries (1980-2016) and summarising the popula-
worldwide carry out common bird moni- tion temporal trends of 168 species.
toring programmes for estimating inter- The utility of these monitoring pro-
annual population change rates by using data grammes has been explained and demon-
provided by thousands of observers through strated convincingly (Gregory et al., 2003;
standardised sampling methods, although Gregory et al., 2005; Gregory et al., 2008;
with different methodologies (e.g. point Collen et al., 2009). The raw information
counts, line transects or territory mapping). available has also allowed the publication of
At the European level, the European Bird many scientific papers, for example, on global
Census Council (EBCC) gathers information patterns of bird population trends (e.g.,
periodically, through the pan-European Com- voříšek et al., 2008; Klvaňová et al., 2009;
mon Bird Monitoring Scheme (pECBMS, Butchart et al., 2010; voříšek et al., 2010),
https://pecbms.info/), to calculate rates of changes in different environments (e.g.,
population change at the whole continental Gregory et al., 2007; Butler et al., 2010;
Ardeola 68(1), 2021, 33-51pOwEr Of yEArLy MONITOrING prOGrAMMES 35
Ivits et al., 2011; Scholefield et al., 2011), pECBMS, and the current European index is
or regarding the relationships with climate now based on 168 species from 28 countries.
change, variation in the distribution area or Sample replication of the same spatial
in the conservation status of species (e.g., units is somewhat desirable in order to in-
Möller, 2008; Gregory et al., 2009; Jilguet crease the power of the tests and to narrow
et al., 2009; Both et al., 2010; Mace et al., the confidence intervals of the estimates,
2010; popy et al., 2010). especially with data distributions that show
The participation of numerous observers very large dispersion of data values (e.g.
in a social endeavour, referred to as citi- poisson or negative binomial distributions).
zen science, raises certain doubts about the This is typical of bird counts carried out in
quality of the data collected, compared to extensive sampling programmes across very
data obtained by professional zoologists or large areas with a high variety of habitats,
ecologists, an aspect that has been examined considering the species-specific habitat
in several studies carried out with different preferences. Observers involved in citizen
taxa using a variety of field methods for science are not usually aware of technical
data collection (Kremen et al., 2011; Snäll aspects related to the stability of the statis-
et al., 2011; Mair & ruete, 2016; Brown & tical parameters that quantify the rates of
williams, 2019). In general, citizen science inter-annual population changes. precision,
observational data is in agreement with that statistical significance and the power of
provided by professional researchers re- those estimations involve the repetition of
garding patterns related to community-level the same sampling procedures a large num-
changes in abundance or richness over space ber of times during the same year, a sampling
and time. Nevertheless, citizen science ob- demand that can discourage volunteers and
servations may not reliably reflect the abun- reduce the number of participants in those
dance or frequency of occurrence of certain programmes.
rare species, that may therefore require par- In this study, we carried out numerical
ticular surveys dedicated to them. simulations and analysed the interspecific pat-
The rate of change of common bird popu- tern of significance of the published popu-
lations has been accepted by Eurostat as an lation trends of the SACrE programme, in
indicator of biodiversity change associated order to test (1) how the number of repeti-
with global change. The incorporation of this tions of censuses per year affects the power
indicator was subjected to numerous tests of tests (i.e. the probability of detecting sig-
before being accepted (e.g., EU farmland nificant trends that are in fact true), and (2)
Bird Indicator, Scholefield et al., 2011). The the probability of obtaining low false dis-
method takes into account the differences covery rates (i.e. identifying significant
in population sizes per country, as well as changes that are actually false) when esti-
differences in field methods and the num- mating yearly population trends. we suggest
bers of sites and years covered by the na- an increase in the power of the tests with
tional schemes. In order to test the method, increased sampling effort but, due to the
van Strien et al. (2001) collected data for probable asymptotic nature of this relation-
five farmland species in seven countries ship, we test whether the total or the average
over a 20-year period (1978-1997). The test of the number of birds recorded in two sur-
demonstrated that it was possible to combine veys per season provide high true discovery
national indices to provide supra-national rates of population trends for abundant and
yearly totals and their standard errors. Since widely distributed bird species.
then, there have been relevant shifts in the
Ardeola 68(1), 2021, 33-5136 CArrASCAL, L.M. and DEL MOrAL, J.C.
MATErIAL AND METhODS of the squares with non-null counts were di-
vided by 20 in order to obtain the average
The Spanish SACrE programme (moni- number of birds per census plot in each UTM
toring common breeding birds in Spain) be- cell. That figure was considered the new mu
gan in 1996. It surveys a random selection for a negative binomial distribution to gen-
of 600-750 10 ×10km Universal Transverse erate random numbers in the 20 census plots
Mercator (UTM) squares for monitoring within each UTM square (the size-k parame-
population changes of common bird species ter was maintained in each virtual species).
during the breeding season (SEO/BirdLife, This second procedure was repeated ten times,
2012). A minimum of twenty five-minute simulating a sampling protocol that carried
morning point count stations are established out ten surveys of the same 20 census plots in
in each UTM square to cover all habitats in each UTM square per breeding season. Thus,
proportion to their extents. Stations are visited it was possible to consider one, two and ten
twice (once in April-May and again in May- surveys for each occupied UTM square per
June) to allow for detection of early breeders breeding season. The data coming from these
and late migrants. Data for virtual species two steps define the simulated bird count data
(see below) have been obtained from data in time t. The third simulation step applied a
available for the occurrence and average fixed yearly inter-annual change to the data
abundance of species in the SACrE pro- simulated in the first step (negative binomial
gramme (see Supplementary Material, Ap- random data in 750 UTM squares), in order
pendix 1, Table A1). The data for the number to generate the bird counts in time t + 1 con-
of UTM squares where 117 species were sidering a certain level of population change.
present and their average linear population The total counts per UTM square in time t
trends refer to the period 1998-2011 (SEO/ were increased or decreased a percentage
BirdLife, 2012). for the maximum and aver- change according to five different yearly
age number of individuals per UTM square percentages: ±1%, ±2.5%, ±5%, ±10% and
where species were present (after sampling ±15%. The new increased, or decreased,
20 circular census plots for five minutes), we counts for each occupied UTM square were
used the data for 2004-2006 (Carrascal & divided by 20 to estimate the average bird
palomino, 2008), a period centred within the count per census plot in each UTM square,
1998-2011 range. and those figures were used to generate new
we simulated ten virtual species to mirror negative binomial distributions for individual
the actual patterns of distribution and local bird counts in the 20 census plots per UTM
abundance of birds in the SACrE monitoring cell (as above). Again, we simulated one,
programme, from very abundant and wide- two and ten surveys of the 20 census plots.
spread, to very scarce and locally distributed. we estimated the actual percentage of
In a first step, we employed a negative bino- change between time t and time t + 1 con-
mial distribution to generate random numbers sidering the total number of birds per UTM
in 750 virtual UTM squares, using different square with the occurrence of the virtual
combinations of the parameters mu (mean) species. we also calculated the pearson’s
and size-k (variance = mu + [mu2] / k). The correlation (COr) between the true origi-
second step was to generate a random dis- nally simulated number of birds per UTM
tribution of bird counts in 20 census plots square in time t (negative binomial random
within each of the UTM squares where the simulation) and the number of birds obtained
virtual species was present (i.e. the total after two (COr2) surveys of the 20 census
count in the UTM square > 0). The numbers plots per UTM cell. These correlations
Ardeola 68(1), 2021, 33-51pOwEr Of yEArLy MONITOrING prOGrAMMES 37
measure how well two surveys per breeding The previous simulations have been carried
season mirror the actual pattern of distribu- out analysing the power of ascertaining true
tion and abundance of each virtual species. population changes in virtual species between
These analytical procedures were repeated two consecutive years. This very restrictive
300 times per virtual species and yearly popu- analysis does not take into account that long-
lation change (ten species with five positive term trends under small inter-annual popu-
population changes and five negative popu- lation changes could establish significant
lation changes). The average percentage positive or negative linear trends. To over-
population change between time t and time come this limitation we have analysed the
t + 1, and its 95% confidence interval, was probability of obtaining a significant linear
calculated considering the data for the simu- trend within a relatively broad time span of
lated UTM squares with the occurrence of 13 years, using the published SACrE in-
the species. The estimation was considered formation from 1998 to 2011. Species’ popu-
significant at p = 0.05 if the confidence inter- lation trends were obtained using TrIM
val did not include the null value of change (Trends and Indices for Monitoring data;
(i.e., zero). Considering the 300 simulations http://www.ebcc.info/art-13/). This allows for
carried out per species and population change missing counts using estimation and yields
rate, we estimated the power of the tests as yearly indices and standard errors using
the proportion of times, out of 300 simula- poisson regression. The analysis of the proba-
tions, when the changes between time t and bility of obtaining significant long-term linear
time t + 1 were significant, being in fact true patterns of population changes over the time
at the specified percentage of population span 1998-2011 was carried out with the ob-
change. The r script for the simulations is served data for 117 bird species (see Supple-
presented in the Supplementary Material, mentary Material, Appendix 1, Table A1). The
Appendix 2. binomial response variable “yes v. no” was
The results of the ten virtual species for the significant trend at p ≤ 0.05 v. p > 0.05. It
each positive and negative inter-annual was related to predictors using a generalised
change were virtually identical, denoting per- linear binomial model (family: binomial;
fect symmetry of patterns for the power of link function: logit). The predictors of this
the tests and the correlations COr2. There- second model were: number of occupied
fore, only the results for the positive inter- UTM squares, average number of birds per
annual population changes are presented. survey in the occupied UTM cells, and the
The interspecific variation in the power absolute value of the average inter-annual
of the tests for the ten virtual species, three percentage of change from 1998 to 2011.
sampling schemes (one, two and ten surveys The predictors were log-transformed
per breeding season) and five percentages of (natural logarithm) prior to data analyses to
inter-annual changes (totalling 150 simulated account for linearity with the responses. These
conditions) were analysed by means of beta- two generalised models took into account
binomial linear models (family: binomial; the over-dispersion and the heteroskedas-
link function: logit; weights: 300 simula- ticity of residuals using the hC4 estimator
tions), working with the logarithm of the pre- suggested by Cribari-Neto (2004) to further
dictors. predictors were: number of occupied improve the performance of significance
UTM squares, average number of birds per estimations. All analyses were carried out
survey in the occupied UTM cells, the num- under r (r Core Team, 2016) version 3.5.0,
ber of surveys, and the percentage change using the car, MASS, MuMIn, sandwich and
between the two consecutive years. rOCr packages.
Ardeola 68(1), 2021, 33-5138 CArrASCAL, L.M. and DEL MOrAL, J.C.
rESULTS for the least abundant species distributed over
the lowest number of UTM squares (present
There were extremely high correlations in less than 60 UTM squares). The interspe-
between the originally simulated number of cific variation in this correlation was mainly
birds per UTM and the number of birds regis- linked to the logarithm of the number of
tered in the 750 UTM squares in the simu- UTM squares where the species were present
lation of two sampling events considering (r = 0.889, n = 10 species), with a consider-
the average of both replicates. There was an ably lower relationship with the logarithm
average correlation of 0.879 for the ten vir- of the local abundance of the species (i.e.
tual species, and minimum correlations > 0.8 the number of birds registered in the 20 sam-
TABLE 1
variation in the correlation between the true originally simulated number of birds in 20 census plots
per UTM across 750 sampled UTM squares, and the number of birds obtained with two repetitions
(r two-times) of the 20 census plots. See the Methods section for more details. #UTM: number of UTM
cells where the species were present. birds/UTM: average number of birds recorded per UTM square
considering only those squares where the species occurred. Maximum: maximum number of birds
recorded per UTM square. mu and size are the parameters of the negative binomial distributions used
to generate random numbers in 750 virtual UTM squares.
[Variación de la correlación entre el número de aves simulado originalmente en 20 puntos de censo
por UTM en 750 UTM de 10 × 10 km2 muestreadas, y el número de aves obtenido con dos repeticiones
(r two-times) de esos 20 puntos de censo. Consúltese la sección Métodos para más detalles. #UTM: nú-
mero de cuadrículas UTM con presencia de las especies. birds/UTM: número promedio de aves regis-
tradas por cuadrícula UTM, considerando solo aquellas donde la especie estaba presente. Maximum:
número máximo de aves registrado por cuadrícula UTM. mu y size son los parámetros de las distri-
buciones binomiales negativas utilizadas para generar números aleatorios en 750 cuadrículas UTM
virtuales.]
virtual species mu size # UTM birds/UTM Maximum r two-times
Spp1 12.00 1.00 657 13.7 158 0.962
Spp2 39.00 0.42 602 46.6 879 0.960
Spp3 3.00 4.00 562 3.9 22 0.876
Spp4 2.75 0.40 327 5.9 70 0.936
Spp5 12.00 0.20 359 23.0 484 0.933
Spp6 0.90 0.30 166 3.6 36 0.908
Spp7 3.17 0.12 182 12.1 197 0.900
Spp8 1.10 0.10 105 7.1 114 0.881
Spp9 0.70 0.17 104 3.8 36 0.890
Spp10 0.30 0.15 51 2.8 21 0.865
Ardeola 68(1), 2021, 33-51pOwEr Of yEArLy MONITOrING prOGrAMMES 39
pling plots per UTM; r = 0.397, n = 10 spe- Power of tests for inter-annual changes
cies). Therefore, two sampling visits per UTM between two consecutive years
and year provide a reliable spatial variation
pattern in bird abundance that closely mir- The probability of ascertaining a true popu-
rors the true pattern of distribution and abun- lation trend at p ≤ 0.05 (i.e. true positive
dance of the species, even in the cases of the rate, or test power = 1 – probability of error
scarcest and the least widely distributed ones. type II – to reject the alternative hypothesis
TABLE 2
power of the tests at p ≤ 0.05 measuring the probability of ascertaining a true population trend in ten
virtual species according to the variation in the number of UTM squares where the species were present,
the average and maximum number of birds per UTM square, five fixed true inter-annual population
changes (1%, 2.5%, 5%, 10% and 15%) and the number of times (one, two or ten) each UTM square
was sampled per study period. results for positive (e.g., +5%) and negative (e.g., –5%) percentage
changes in the second study year with respect to the previous one are conceptually and numerically
identical, so only the results of simulations working with positive population changes are shown for
brevity. power figures higher than 0.70 are marked in bold type. for more details see Table 1.
[Potencia de los tests a P ≤ 0,05 que mide la probabilidad de obtener la verdadera tendencia de po-
blación en 10 especies virtuales de acuerdo con la variación en el número de cuadrículas UTM de
10 × 10 km2 donde estaban presentes, el número promedio y máximo de aves por cuadrícula UTM, cinco
cambios simulados de variación interanual de la población (1%, 2.5%, 5%, 10% y 15%) y el número
de veces que cada cuadrícula UTM se muestreó por año (uno, dos o diez). Los resultados para los
cambios porcentuales positivos (e.g.., +5%) y negativos (e.g., –5%) en el segundo año de estudio con
respecto al anterior son conceptualmente y numéricamente idénticos, por lo que solo se muestran los
resultados de las simulaciones con cambios de población positivos. Los valores de potencia superiores
a 0,70 están señalados en negrita. Para más detalles véase la Tabla 1.]
ONE CENSUS
virtual species # UTM birds/UTM Maximum 1% 2.5% 5% 10% 15%
Spp1 657 13.7 158 0.09 0.20 0.63 0.99 1.00
Spp2 602 46.6 879 0.12 0.26 0.47 0.92 0.99
Spp3 562 3.9 22 0.02 0.05 0.19 0.74 0.98
Spp4 327 5.9 70 0.04 0.07 0.15 0.46 0.81
Spp5 359 23.0 484 0.08 0.12 0.22 0.49 0.69
Spp6 166 3.6 36 0.04 0.05 0.06 0.15 0.35
Spp7 182 12.1 197 0.03 0.03 0.09 0.16 0.27
Spp8 105 7.1 114 0.01 0.03 0.03 0.06 0.13
Spp9 104 3.8 36 0.02 0.03 0.04 0.07 0.13
Spp10 51 2.8 21 0.02 0.01 0.03 0.03 0.06
Ardeola 68(1), 2021, 33-5140 CArrASCAL, L.M. and DEL MOrAL, J.C.
TABLE 2 (cont.)
TWO CENSUSES
virtual species # UTM birds/UTM Maximum 1% 2.5% 5% 10% 15%
Spp1 657 13.7 158 0.10 0.46 0.92 1.00 1.00
Spp2 602 46.6 879 0.17 0.42 0.76 1.00 1.00
Spp3 562 3.9 22 0.03 0.15 0.54 0.99 1.00
Spp4 327 5.9 70 0.07 0.12 0.30 0.78 0.98
Spp5 359 23.0 484 0.13 0.17 0.38 0.76 0.94
Spp6 166 3.6 36 0.04 0.06 0.13 0.36 0.65
Spp7 182 12.1 197 0.08 0.12 0.19 0.36 0.58
Spp8 105 7.1 114 0.04 0.05 0.09 0.20 0.34
Spp9 104 3.8 36 0.03 0.03 0.08 0.19 0.31
Spp10 51 2.8 21 0.02 0.03 0.04 0.07 0.14
TEN CENSUSES
virtual species # UTM birds/UTM Maximum 1% 2.5% 5% 10% 15%
Spp1 657 13.7 158 0.38 0.96 1.00 1.00 1.00
Spp2 602 46.6 879 0.35 0.83 1.00 1.00 1.00
Spp3 562 3.9 22 0.14 0.64 1.00 1.00 1.00
Spp4 327 5.9 70 0.11 0.46 0.93 1.00 1.00
Spp5 359 23.0 484 0.24 0.49 0.88 1.00 1.00
Spp6 166 3.6 36 0.08 0.18 0.53 0.96 1.00
Spp7 182 12.1 197 0.14 0.24 0.54 0.93 0.99
Spp8 105 7.1 114 0.11 0.17 0.34 0.73 0.95
Spp9 104 3.8 36 0.07 0.12 0.34 0.83 0.98
Spp10 51 2.8 21 0.04 0.07 0.18 0.42 0.72
when in fact it is true –) is shown in Table 2 the predictors, accounting for 91.9% of the
according to the variation in the number of variation in the true positive rates (corrected
UTM squares where the species were present, Akaike information criterion, AICc = 3249;
the average and maximum number of birds AICc for the null model = 32607). Table 3
per UTM square, the true inter-annual popu- shows the regression coefficients of the beta-
lation change and the number of times each binomial linear regression model analysing
UTM square was sampled in the same year. the data in Table 2. The four predictors were
The power of the tests was closely related to highly significant, positively influencing
Ardeola 68(1), 2021, 33-51pOwEr Of yEArLy MONITOrING prOGrAMMES 41
the variation in the power of the tests. The The probability of detection of a very
most important predictor according to the small true population change (±1%) between
standardised partial regression coefficient two consecutive study periods is very low
was the percentage of inter-annual popula- under any circumstance of sampling effort
tion change, followed by the number of UTM or distribution-abundance of species. recall
squares where the species were present and that a steady increase / decrease in popula-
the number of repetitions, while the average tion numbers at an additive rate of ±1% per
abundance per UTM square was the predic- year generates an accumulated change of
tor with the lowest magnitude effect. +22% / –18% in 20 years. Subtle population
TABLE 3
results of the beta-binomial linear model analysing the variation of the power of the tests at p ≤ 0.05
when estimating population trends between two consecutive time periods (e.g., years) in ten virtual
species (broadly differing in the number of UTM squares where they were present and the average
number of individuals recorded in 20 census plots per occupied UTM), in five simulated percentages
of population increases, and three levels of repetition of the sampling of each UTM cell in the two con-
secutive study periods. coeff: regression coefficients; se: standard errors of the regression coefficients
working with the original values of the predictors in logarithm form; beta: standardised regression
coefficients. #UTM: number of UTM cells where the species were present. birds/UTM: average
number of birds recorded per UTM square considering only those squares where the species occurred.
# repetitions: times each UTM square was censused per study period. % change: percentage of change
between the two consecutive study periods.
[Resultados del modelo generalizado lineal beta-binomial que analiza la variación de la potencia de
los tests a P ≤ 0,05 cuando se estiman las tendencias de la población entre dos períodos de tiem-
po consecutivos (por ejemplo, años) en diez especies virtuales bajo cinco porcentajes simulados de
aumentos de población, y tres niveles de repetición del muestreo de cada celda UTM en dos períodos
de estudio consecutivos. Las diez especies virtuales difieren ampliamente en el número de cuadrículas
UTM 10 × 10 km2 donde estaban presentes y el número promedio de individuos registrado en 20 pun-
tos de censo por UTM ocupada. coeff: coeficientes de regresión; se: errores estándar de los coeficientes
de regresión estimados con los valores de las variables predictoras en logaritmo; beta: coeficientes de
regresión estandarizados. #UTM: número de cuadrículas UTM donde estaban presentes las especies.
birds/UTM: número promedio de aves registrado por cuadrícula UTM, considerando solo aquellas
UTM donde las especies estaban presentes. # repetitions: número de veces que cada cuadrícula UTM
se censó por año de estudio. % change: porcentaje de cambio entre los dos períodos de estudio con-
secutivos.]
beta coeff se P
Intercept — –15.872 0.67042 CArrASCAL, L.M. and DEL MOrAL, J.C. changes of ±2.5% between two consecutive doubles the power estimations under inter- years are detectable under a sampling scheme annual changes of 5%. A similar increase of all UTM squares of ten times per study in power is attained if a five-fold increase in period only if species are very broadly dis- sampling effort is addressed, repeating the tributed and abundant (e.g., occurring in censuses ten times instead of twice. This di- more than 600 UTM squares with an average minishing return is more obvious when true of more than ten birds per UTM); a steady inter-annual population changes decrease: change at this inter-annual rate promotes an under very small inter-annual population accumulated population increase of +64% or changes of c. ±1%, a five-fold increase in decrease of –40%. Important between-year sampling effort from two to ten repetitions of population changes with a magnitude of the censuses is accompanied by a two-fold ±10%, accounting for accumulated variations increase in the power of tests. however this of +673% or –88% over 20 years, are dis- is under a bleak panorama regarding the cernible with a high power for broadly dis- statistical results: all species attain low to tributed and relatively abundant species (e.g., very low or negligible probabilities of ascer- again, present in 300 UTM squares with an taining true ±1% changes, rendering futile average of more than four birds per 20 cen- the investment of the enormous effort asso- sus plots) if each UTM cell is sampled twice. ciated with carrying out ten repetitions at all high probabilities of detection of true popu- sampling locations. lation changes between two consecutive years for scarce species distributed over a medium number of UTM squares (e.g., 4-12 Probability of attaining significant results birds per UTM square in 100-200 occupied with long-term data UTM cells) are only possible under a heavily replicated sampling scheme (e.g. ten repeti- The results of the binomial linear model tions), even for large population changes analysing the significance of linear trends at of ±10%. figure 1 illustrates the pattern of p ≤ 0.05 for 117 Spanish bird species ob- covariation of the probability of detection tained by SEO/BirdLife (2012) during 1998- of true population changes (i.e., power of 2011 are shown in Table 4. The response the tests) for six different virtual species variable is related to the false positive rate, working with a sampling protocol of two and or the probability of error type I (to reject four censuses per year. the null hypothesis when in fact it is true). In spite of the increase of power with the The binomial model was highly significant number of times the UTM squares were cen- (likelihood ratio test: χ 2 = 107.5, df = 3, sused per year, there is a clear diminishing p < 0.001), accounting for 71.5% of the de- return when repeating the censuses ten times viance (Mcfadden pseudo-r2), and with a instead of twice. for example, when actual high classification power (AUC = 0.976; population change between two consecutive 89.7% of the species correctly classified years is ±5%, the summation of the power according to significance or not at p ≤ 0.05 figures for the ten simulated species increases of their TrIM results in the SACrE pro- from 1.92 for one census per year, to 3.44 gramme; positive predictive value = 0.945, for two censuses, and 6.72 for ten censuses. negative predictive value = 0.818). The three That is to say, doubling the sampling effort predictors attained high levels of positive as- for a broad spectrum of species according to sociations with the significance of the long- their distribution-abundance patterns from term linear trends of the species, with con- one to two censuses per year approximately siderable variation of the magnitude effect, Ardeola 68(1), 2021, 33-51
pOwEr Of yEArLy MONITOrING prOGrAMMES 43
two censuses four censuses
1.0 1.0
50 birds
0.9 0.9 50 birds
0.8 10 birds 0.8
0.7 0.7 10 birds
0.6 0.6
power
power
0.5 0.5
0.4 0.4
0.3 0.3
0.2 0.2
0.1 # UTM = 600 0.1 # UTM = 600
0.0 0.0
0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11
% change % change
1.0 1.0
0.9 0.9 25 birds
0.8 0.8
0.7 25 birds 0.7 5 birds
0.6 0.6
power
power
0.5 5 birds 0.5
0.4 0.4
0.3 0.3
0.2 0.2
0.1 # UTM = 300 0.1 # UTM = 300
0.0 0.0
0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11
% change % change
1.0 1.0
0.9 # UTM = 150 0.9 # UTM = 150
0.8 0.8
0.7 0.7 10 birds
0.6 0.6
power
power
0.5 10 birds 0.5 2 birds
0.4 0.4
0.3 0.3
2 birds
0.2 0.2
0.1 0.1
0.0 0.0
0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11
% change % change
fIG. 1.—pattern of covariation between the power of the tests of the change in bird counts between two
consecutive study periods and the actual percentages of change for six virtual species, considering the num-
ber of UTM squares occupied and the average number of birds per UTM, when the sampling was repeated
on two or four occasions. power refers to the probability of detecting a percentage change of that magni-
tude when in fact it is true (one minus the probability of error type II at p ≤ 0.05). The patterns have been
built with the regression coefficients in Table 3 considering that power = exp(model) / (1 + exp(model)).
[Patrón de covariación entre la potencia de los tests del cambio en el conteo de aves entre dos períodos
de estudio consecutivos, y los porcentajes de cambio interanual simulados para seis especies virtuales,
considerando el número de cuadrículas UTM de 10 × 10 km2 ocupado y el número promedio de aves por
UTM cuando el muestreo fue repetido en dos o cuatro ocasiones por año. La potencia se refiere a la
probabilidad de detectar un cambio porcentual interanual de esa magnitud cuando de hecho es cierto
(uno menos la probabilidad de error tipo II a P ≤ 0,05). Los patrones se han construido con los coefi-
cientes de regresión en la Tabla 3 considerando que Potencia = exp(modelo) / (1 + exp(modelo)).]
Ardeola 68(1), 2021, 33-5144 CArrASCAL, L.M. and DEL MOrAL, J.C.
decreasing according to the following se- term result increases as the species are more
quence: average percentage of inter-annual broadly distributed, are locally more abun-
change, number of occupied UTM squares dant and the average long-term percentage
and average number of birds detected per change in bird numbers between consecutive
UTM where the species were present. There- years increases. figure 2 depicts the proba-
fore, the chance of having a significant long- bility of obtaining significant results for 13-
1.0 1.0
probability of obtaining a significant result
probability of obtaining a significant result
50 birds
0.9 0.9
20 birds
0.8 0.8
25 birds
0.7 0.7
0.6 0.6
0.5 0.5
0.4 0.4
0.3 0.3
0.2 0.2 5 birds
0.1 0.1
0.0
# UTM = 600 0.0
# UTM = 300
0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11
% change % change
1.0 1.0
probability of obtaining a significant result
probability of obtaining a significant result
0.9 10 birds 0.9
0.8 0.8 5 birds
0.7 0.7
0.6 0.6
0.5 2 birds 0.5
0.4 0.4 1 bird
0.3 0.3
0.2 0.2
0.1 0.1
0.0
# UTM = 150 0.0
# UTM = 50
0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11
% change % change
fIG. 2.—pattern of covariation between the probability of obtaining a significant result (at error type
I ≤ 0.05) for a 13-year long-term linear trend and the average percentages of change for eight virtual
species, considering the number of UTM squares occupied and the average number of birds per UTM,
when the sampling was repeated on two occasions every year. The patterns have been built with the
regression coefficients in Table 4 obtained for 117 species in the SACrE programme from 1998 to
2011, considering that the probability of obtaining a significant result = exp(model) / (1 + exp(model)).
[Patrón de covariación entre la probabilidad de obtener un resultado significativo (con un error de
tipo I ≤ 0,05) para una tendencia lineal a lo largo de 13 años, y los porcentajes promedio de cambio
interanual para ocho especies virtuales considerando el número de cuadrículas UTM de 10 × 10 km2
ocupadas y el número promedio de aves por UTM, cuando el muestreo se repitió en dos ocasiones cada
año. Los patrones se han construido con los coeficientes de regresión en la Tabla 4 obtenidos para
117 especies del programa SACRE para el periodo 1998-2011, considerando que la probabilidad de
obtener un resultado significativo = exp(modelo) / (1 + exp(modelo)).]
Ardeola 68(1), 2021, 33-51pOwEr Of yEArLy MONITOrING prOGrAMMES 45
year study periods when there are consistent birds per UTM cell and one sampling event,
linear patterns towards increases or decreases in a census scheme with only two repetitions.
in bird counts, working with a sampling pro- This is the logical consequence of the con-
tocol of two censuses per year of all plots sistency of small changes throughout time,
and UTM cells. despite the fact that each of them between
The patterns in figures 1 and 2 show that two consecutive years has a low power. Thus,
although it is difficult to attain high levels of modest power figures of population changes
power between two consecutive years (i.e. between two consecutive years may emerge
high true discovery rates, figure 1) where as robust long-term patterns, with very low
population changes are below 5%, in nearly probabilities of false discovery rates, even
all species, the probability of obtaining sig- with only two repetitions of the census plots
nificant results for long-term trends of 13 per year in relatively scarce species. Never-
years (i.e. low false discovery rates) is very theless, there are extremely low powers for
high at average population changes > 3%. detecting true changes between consecutive
This is the case even for species occurring in years, and very low probabilities of obtaining
150 UTM squares and with more than two long-term significant patterns, under popu-
50 50
45 45 B
maximum number of counts
average number of counts
40 40
35 35
30 30
25 25
20 20
15 15
10
A 10
5 10 15 20 25 30 5 10 15 20 25 30
number of replicates number of replicates
fIG. 3.—Numerical simulation relating the maximum and average values of a sample of 2, 3, 4, … 30
replicates to the golden standard of a negative binomial distribution with a mean and variance equal to
20 that it is intended to represent (horizontal arrows). The maximum value obtained in a simulated dis-
tribution with N = 5 * 10 7 was 48. The 99% confidence interval of the maximum number of counts never
included that figure and was considerable lower for sample sizes ranging between 2 and 30 (grey area
in panel A), with maximum values of 36-38 after 1,000 trials (thick continuous line). Conversely, the
99% confidence interval of the means were always centred around the true mean (panel B).
[Simulación numérica que relaciona los valores máximo y promedio de una muestra de 2, 3, 4, … 30
réplicas con el patrón de referencia de una distribución binomial negativa con una media y una
varianza iguales a 20 (flechas horizontales). El valor máximo obtenido en una distribución simulada
con N = 5 * 10 7 fue 48. El intervalo de confianza al 99% del número máximo de conteos nunca incluyó
esa cifra, y fue considerablemente menor para tamaños de muestra que oscilan entre 2 y 30 réplicas
(área gris en el panel A), con valores máximos de 36-38 después de 1.000 procesos de simulación (línea
gruesa contínua). Por el contrario, el intervalo de confianza del 99% de las medias siempre estuvo
centrado en la media verdadera (panel B).]
Ardeola 68(1), 2021, 33-5146 CArrASCAL, L.M. and DEL MOrAL, J.C.
TABLE 4
results of the binomial linear model analysing the significance results at p ≤ 0.05 of the SACrE pro-
gramme during 1998-2011 (yes vs. no) related to the number of UTM squares where 117 bird species
were present (#UTM), the average number of individuals recorded in 20 census plots per occupied
UTM obtained after two censuses per year (birds/UTM), and the absolute value of the estimated aver-
age inter-annual rates of change (in percentage computed with TrIM software; % change). for original
data see the Supplementary Material, Appendix 1, Table A1. The three predictors are in logarithmic
scale. coeff: regression coefficients; se: standard errors of the regression coefficients working with the
original values of the predictors in logarithm; beta: standardised regression coefficients informing on
magnitude effects.
[Resultados del modelo generalizado lineal binomial que analiza los resultados de significación a
P ≤ 0,05 del programa SACRE entre 1998-2011 (sí vs. no) en relación con el número de cuadrículas
UTM de 10 × 10 km2 donde estaban presentes 117 especies de aves (#UTM), el número promedio de
individuos registrado en 20 puntos de censo por UTM ocupada obtenido con dos censos por año
(aves/UTM), y el valor absoluto de las tasas promedio de cambio interanuales (en porcentaje, calculado
con el software TRIM; % change). Para los datos originales de las especies, consúltese el Material
Suplementario, Apéndice 1, Tabla A1. Los tres predictores se incluyeron en el modelo generalizado
lineal binomial en escala logarítmica. coeff: coeficientes de regresión; se: errores estándar de los coefi-
cientes de regresión; beta: coeficientes de regresión estandarizados que informan sobre la magnitud de
los efectos.]
beta coeff se P
Intercept — –25.680 4.195pOwEr Of yEArLy MONITOrING prOGrAMMES 47
bility of attaining significant long-term linear two surveys during the same breeding season.
trends were highly predictable considering Gordo’s study (2018), carried out during one
the number of UTM squares where the spe- breeding season at one locality using a 2km
cies were recorded, the average number of line transect and computer simulations, sug-
birds per UTM cell when present and the gests that “the protocols of the monitoring
inter-annual rates of change. Although true schemes of common bird populations should
discovery rates for small population changes consider a greater number of surveys for some
between two consecutive years may be low species because this is the best option when
for many species that are neither widely dis- occupancy and detectability rates are uncer-
tributed nor very abundant, those small rates tain”. This result is the logical consequence
generate significant linear trends with a very associated with the repeated sampling of any
high probability if they are consistently main- poisson or negative binomial distribution of
tained for long periods of time (> 10 years). bird numbers: the maximum value of a data
Nevertheless, long-term linear trends are not series increases with the increase in sample
reliable for very rare species detected in only size, although the average remains very sta-
50 UTM squares, or scarce species with data ble around the true average (see figure 3).
for 150 UTM squares if average inter-annual Nevertheless, this obvious mathematical re-
rates are lower than ±2.5%. Conversely, for sult, linked to the repeated sampling of any
broadly distributed and abundant bird species continuous data distribution, does not invali-
(e.g. found in over 300 UTM squares with, date survey protocols using two sampling
on average, more than five birds per census days per year in common bird-monitoring
of UTM cells), the target species in common schemes. There are logical, mathematical and
bird monitoring programmes such as SACrE, natural history aspects that support the va-
it is highly probable to attain robust long- lidity of census programmes such as SACrE.
term significant trends with average inter- first, as figure 3 shows, it is considerably
annual change rates as low as 1%. finally, more convenient to work with the average
the spatial variation among a large number of than with the maximum value of a sample, in
study UTM squares of the average number order to represent the true parameters of a
of birds registered in two annual repetitions poisson distribution (a similar pattern is ob-
mirrors in great detail the actual pattern of tained for a negative binomial distribution,
distribution and abundance. with more marked results for the maximum
In a recent study, Gordo (2018) has pro- number of counts). Any number of repli-
posed that abundance data for the Common cates of an unknown distribution produces
Swift Apus apus and house Martin Delichon an average estimate that is very well centred
urbicum, two very conspicuous, common around the true figure, with a confidence in-
and widely distributed small birds, should terval that is considerably narrower than that
be used cautiously due to its potential inac- obtained for the maximum number attainable
curacy, because two surveys per spring are that never includes the true maximum of that
insufficient to record the actual maximum distribution (compare the broadness of the
number of individual birds in a locality, due grey areas in figure 3, and note that the true
to the huge between-day variability of records maximum figure is not included in the 99%
for highly mobile and/or gregarious species. confidence interval). A maximum may be a
In fact, he convincingly demonstrates that misleading parameter because it may be in-
the probability of recording an accurate fluenced by events not directly related to the
count of the maximum local abundance of target true local abundance. for example,
the species is very low by conducting only maximum counts may be linked with mas-
Ardeola 68(1), 2021, 33-5148 CArrASCAL, L.M. and DEL MOrAL, J.C. sive passage of migratory birds that are not UTM cells twice a year? (devoting the same resident in the study area, or with random amount of effort in both situations; see field movements of very mobile species that nest et al., 2005; Carrascal et al., 2007). Both nearby and that the researcher detects in things matter, but if the representativeness of her/his study area, or with the inclusion of the monitoring scheme is the goal, it would juveniles born in the ongoing breeding season be advisable to opt for surveying more dif- that cannot easily be distinguished during ferent UTM squares instead of having more censuses. If only two censuses are possi- visits per UTM square, because the increase ble within the most appropriate dates, the of sampling units increases both the power average or the sum of those two replicates is and representativeness if the sampling pro- better than the maximum, since that average tocol is well-designed. To increase the total will better represent the real average of the number of UTM squares sampled where the distribution. species are present is especially important Second, the mathematical simulations for locally scarce species and where the per- show that the data from two census repli- centage changes in inter-annual population cates conveniently illustrate the spatial pat- rates are low (see power figures in Table 2). tern of variation in species abundance and Also, on statistical grounds, very low false their average inter-annual change rates be- discovery rates (associated with probabilities tween two consecutive years. Although the of obtaining significant results at p ≤ 0.05 number of censuses per year has an impor- higher than 90%; figure 2) are attained for tant influence on the power of the tests (num- long-term population changes with only two ber of repetitions in Table 3), there are other censuses per year. This pattern is observed similar or more important factors: the mag- even for relatively scarce species with data nitude of the inter-annual rate of change and for 150 UTM cells and with an average count the number of UTM squares where the spe- of two birds per census, and inter-annual cies occur. Thus, the concern is not about ob- percentage changes as low as ±2.5% (a 64% taining the most precise and true maximum increase or 60% decrease over 20 consecu- number of birds in a particular sampling area, tive years). but to manage a high true discovery rate (i.e. All other things being equal, the critical power), while attaining a low false discovery aspect with the number of replicates per year rate with high significance levels, when esti- of the same census plots is the level of reso- mating population trends. In that endeavour lution of the “significance” of population the number of censuses is only one variable changes when in fact they are true. The co- of interest that has to be considered by moni- nundrum for organisers of long-term moni- toring organisers. Moreover, the goal is not toring schemes is to find a sensible balance only to determine exactly, and with very among the precision of population trend esti- narrow confidence intervals, the percentage mates (i.e. narrow intervals), the generalisa- inter-annual change in a small number of tion degree of those estimates (i.e. more sam- repeatedly monitored locations, but to ob- ple units over larger spatial scales) and the tain a more general and robust pattern over probability that participants in citizen-science the largest possible area and number of lo- persevere with monitoring programmes. par- cations. If time and well-trained observers ticipating in a collective activity that involves are limited in monitoring schemes, what is observing and recording a wide variety of more convenient: to sample a low number birds following standardised sampling pro- of UTM squares many times every year, or tocols is acceptable if it does not end up be- to sample a considerably larger number of coming monotonous. But the requirement to Ardeola 68(1), 2021, 33-51
pOwEr Of yEArLy MONITOrING prOGrAMMES 49
repeat the same sampling procedures a great with important benefits for bird conservation and
number of times during the same year can environmental management. Claire Jasinski im-
discourage volunteers, reduce the number proved the English of the manuscript.
of participants and thus the number of loca-
tions that are sampled. An increase in the
number of visits per UTM square would be AUThOr CONTrIBUTIONS.—L.M.C. and J.C.d.M.
conceived the ideas. L.M.C. designed methodolo-
desirable for monitoring very rare species
gy. L.M.C. analysed the data and wrote the paper.
of special conservation concern (e.g. endan- All authors contributed critically to the drafts and
gered on a national or continental basis) but gave final approval for publication.
after prioritising study areas that account for
a large proportion of the entire population of
those species. rEfErENCES
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ACKNOwLEDGEMENTS.—This paper is a con- vironment, 137: 348-357.
tribution to project CGL2011-28177, funded by Carrascal, L.M., Seoane, J., palomino, D. &
MINECO / fEDEr-EU. we are most grateful to Alonso, C.L. (2007). El corredor sahariano en
all the volunteers whose hard work in the field España. I Censo Nacional (2005-2006). Mono-
provides valuable information on biodiversity, grafía nº 14. SEO/BirdLife. Madrid.
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