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\begin{document}

\title{\emph{}DECODING COLONY SIZE OF AMAZONIAN STINGLESS BEES THROUGH
INTRINSIC PARAMETERS}



\author[1]{Kamila Leão  LEÃO}%
\author[2]{Alistair  Campbell}%
\author[1]{Jamille  Veiga}%
\author[2]{Cristiano  Menezes}%
\author[1]{Felipe Andrés León CONTRERA}%
\affil[1]{Universidade Federal do Para}%
\affil[2]{Embrapa Amazonia Oriental}%


\vspace{-1em}



  
  \date{May 22, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
1. Stingless bees live in populous colonies that vary in size from a few
hundred individuals to tens of thousands, although information on actual
colony size is limited. Determining colony sizes using easily measurable
biological parameters are important steps to understanding their life
histories and ease their utilization and keeping. The objectives of this
study were to determine the colony size of five Amazonian stingless bee
species (\emph{Melipona flavolineat}a, \emph{Melipona fasciculata},
\emph{Scaptotrigona} aff. \emph{postica}, \emph{Frieseomelitta longipes}
and \emph{Plebeia minima}), and to identify biological parameters that
covary with colony size. 2. The number of brood cells, adult bees, and
food stocks were counted under laboratory conditions, alongside field
assessments of egg-laying rate and external activity of adult workers.
To identify covariates of colony size, the number of adult bees was
regressed against the number of brood cells, egg-laying rate, external
activity of adult workers, and food stocks, and the best Candidate
models were ranked using the Akaike Information Criterion. 3. Mean (\selectlanguage{ngerman}±
s.d.) adult population sizes were: 1,046 ± 185 in \emph{M.
flavolineata}; 593 ± 300 in \emph{M. fasciculata}; 7,404 ± 1,391 in
\emph{S.} aff. \emph{postica}; 2,425 ± 1,000 in \emph{F. longipes}; and
405 ± 254 in \emph{P. minima}. We showed that the external activity is
the biological parameter, after the number of brood cells, that presents
the best relationship with the number of adult bees, which can be easily
evaluated in the field.%
\end{abstract}\selectlanguage{ngerman}%



\sloppy


\textbf{DECODING COLONY SIZE OF AMAZONIAN STINGLESS BEES THROUGH
INTRINSIC PARAMETERS}

Kamila Le\selectlanguage{ngerman}ão Leão\textsuperscript{1}

Alistair John Campbell\textsuperscript{2}

Jamille Costa Veiga\textsuperscript{1,3}

Cristiano Menezes\textsuperscript{2,4}

Felipe Andrés León Contrera\textsuperscript{1,*}

1 - Laboratório de Biologia e Ecologia de Abelhas - Universidade Federal
do Pará, Belém/PA, Brazil

2 -- Embrapa Amazônia Oriental - CPATU, Belém/PA, Brazil

3 -- Instituto Tecnológico Vale - ITV, Belém/PA, Brazil

4 -- Embrapa Meio Ambiente -- Jaguariúna/SP, Brazil

ORCID: K.L. Leão: https://orcid.org/0000-0001-9099-0850 email:
kamilabelha@gmail.com

ORCID: A.J. Campbell: https://orcid.org/0000-0001-8163-6737 Email:
alistaircampbell87@gmail.com

ORCID: J.C. Veiga: https://orcid.org/0000-0001-7554-2785 Email:
jal.cveiga@gmail.com

ORCID: C. Menezes: https://orcid.org/0000-0002-8473-6298 Email:
cristiano.menezes@embrapa.br

ORCID: F.A.L. Contrera: https://orcid.org/0000-0002-7078-5048 email:
felipe@ufpa.br

\textbf{*Correspondence}

Felipe Andrés León Contrera

Laboratório de Biologia e Ecologia de Abelhas, Universidade Federal do
Pará. Rua Augusto Corrêa 01. Instituto de Ciências Biológicas,
66075-110, Belém, Brazil

E-mail: felipe@ufpa.br

\textbf{Funding information}

This study was funded by CNPQ (project PVE 400435/2014-4) and by
CNPQ/MCTIC/IBAMA/ASSOCIAÇÃO A.B.E.L.H.A (process 400585/2018-9). KLL and
JCV received a Ph.D. grant from CAPES/EMBRAPA (15/2014) and AJC a
post-doc grant from CNPQ/MCTIC/IBAMA/ASSOCIAÇÃO A.B.E.L.H.A (process
400568/2018-7).

\textbf{Data availability statement}

The data that support the findings of this study are openly available in
Open Science Foundation - OSF at~https://osf.io/, reference number

https://osf.io/s32gm/\textbf{.}

\textbf{Conflict of interest}

All authors declare no conflict of interest.

\textbf{DECODING COLONY SIZE OF AMAZONIAN STINGLESS BEES THROUGH
INTRINSIC PARAMETERS}

\textbf{NUMBERED ABSTRACT}

1. Stingless bees live in populous colonies that vary in size from a few
hundred individuals to tens of thousands, although information on actual
colony size is limited. Determining colony sizes using easily measurable
biological parameters are important steps to understanding their life
histories and ease their utilization and keeping. The objectives of this
study were to determine the colony size of five Amazonian stingless bee
species (\emph{Melipona flavolineata} , \emph{Melipona fasciculata}
,\emph{Scaptotrigona} aff. \emph{postica} , \emph{Frieseomelitta
longipes}and \emph{Plebeia minima} ), and to identify biological
parameters that covary with colony size.

2. The number of brood cells, adult bees, and food stocks were counted
under laboratory conditions, alongside field assessments of egg-laying
rate and external activity of adult workers. To identify covariates of
colony size, the number of adult bees was regressed against the number
of brood cells, egg-laying rate, external activity of adult workers, and
food stocks, and the best Candidate models were ranked using the Akaike
Information Criterion.

3. Mean (± s.d.) adult population sizes were: 1,046 ± 185 in \emph{M.
flavolineata} ; 593 ± 300 in \emph{M. fasciculata} ; 7,404 ± 1,391
in\emph{S.} aff. \emph{postica} ; 2,425 ± 1,000 in \emph{F. longipes} ;
and 405 ± 254 in \emph{P. minima} . We showed that the external activity
is the biological parameter, after the number of brood cells, that
presents the best relationship with the number of adult bees, which can
be easily evaluated in the field.

\textbf{Keywords} : Meliponini, Population size, External activity,
Egg-laying rate, Food stocks.

\textbf{INTRODUCTION}

Colony size is related to several aspects of life history strategies in
social insects, such as colony efficiency, division of labor, social
interactions, task partitioning and reproduction (Oster and Wilson 1978;
Anderson \& Ratnieks 1999; Bourke 1999; Strohm and Bordon-Hauser 2003;
Dornhaus et al. 2006; Hou et al. 2010; Fewell \& Harrison 2016).
Eusocial hymenopterans (bees, ants, wasps) live in colonies of variable
size that are considered as ``superorganisms'' (Holldobler and Wilson
2009), in which each individual (i.e., unit, ``cell'') cooperates for
the survival and reproductive success of the major unit (i.e., colony,
the ``organism''). Therefore, colony size is linked to their life
history and influences several aspects of collective organization
(Gillooly et al. 2010; Dornhaus et al. 2012).

Alongside with honeybees (Apini), stingless bees (Meliponini) are
advanced eusocial bees, which live in perennial colonies and possess a
great diversity of nesting habits and life-history traits (Roubik 2006;
Grüter 2020). They have a pantropical distribution (Michener 2013), and
their colonies are generally composed of a single queen, hundreds to
thousands of workers, and dozens to hundreds of males (Roubik 2006),
with populations ranging from a few hundred to over a hundred thousand
individuals (Wille and Michener 1973; Wille 1983; Grüter 2020). However,
for most stingless bee species (417 species in the Neotropical region
and 244 in Brazil; Pedro 2014), empirical data on colony size is scarce
or absent, with the notable exception of \emph{Trigona
spinipes}(Fabricius, 1793), for which a recent study (Valadares et al.
2021) provided robust measurements and estimates and for \emph{Melipona
rufiventris} and \emph{M. seminigra} (Roubik \& Peralta, 1983). Where
authors have provided estimates, in most cases, there is often no
mention about the methods used (Lindauer and Kerr 1960; Wille and
Michener 1973; Michener 1974; Wille 1983; Kerr et al. 2001), and in the
handful of studies that present formulae for estimating colony size,
there is no attempt to validate estimates using empirical data (i.e.
counting number of individuals in studied colonies) (Ihering 1930; Aidar
1996). Moreover, these formulae are often based on single species,
leaving uncertainty over their applicability to other species.

Several biological parameters (e.g., the number of immature bees,
external activity, life expectancy of individuals, egg laying rate, size
of brood combs, colony weight) are related to the number of individuals
present in a colony. Therefore, they can be used as proxies to estimate
the size of the colonies (DeGrandi-Hoffman et al. 1989; Malham et al.
2013; Duarte et al. 2016; Roldão -Bordoni et al. 2018). However, some of
these parameters involve highly invasive sampling methods, in some cases
provoking the death of sampled colonies (Delaplane et al. 2013). For
this reason, the main aim of this study was to understand how some of
these parameters relate to colony size and their viability as proxy
measures of colony size.

Stingless bees are essential pollinators of many crops (Giannini et al.
2020). Therefore, knowledge on colony size is important for their use in
crop pollination and for better management practices in meliponiculture
(Jaffé et al. 2015). Thus, the main objectives of this study were: (i)
to measure the colony size (number of adult bees) of five Amazonian
stingless bee species and (ii) to determine biological parameters of
colonies (number of immature bees, egg laying rate, external activity,
food stocks) that covary with colony size.

\textbf{MATERIAL AND METHODS}

\emph{Study site and species}

This study was performed in the meliponary housed at the Botany
Department of Embrapa Amazônia Oriental (1º26\selectlanguage{english}'11.52\selectlanguage{english}"S, 48deg26\selectlanguage{english}'35.50\selectlanguage{english}"W),
Belem, Para, Brazil, during the dry season of 2016 (September and
October), and the rainy seasons of 2017 and 2018 (May). Five species of
stingless bees were studied (Fig. S1): \emph{Melipona
flavolineata}Friese, 1900, \emph{Melipona fasciculata} Smith,
1854,\emph{Scaptotrigona} aff. \emph{postica} Latreille,
1807,\emph{Frieseomelitta longipes} (Smith, 1854) and \emph{Plebeia
minima}(Gribodo, 1893). These species were chosen because they are well
adapted to housing in wooden hives, resistant to handling and
manipulation, and can be multiplied for use in crop pollination
(Contrera et al. 2011; Jaffe et al. 2015; Leao et al. 2016).
\emph{Melipona flavolineata}occurs in the Brazilian states of Ceara,
Maranhao, Para and Tocantins;\emph{M. fasciculata} occurs in the states
of Maranhao, Mato Grosso, Para, Piaui and Tocantins; \emph{S.} aff.
\emph{postica} and \emph{F. longipes} occurs in the state of Para; and
\emph{P. minima} in the states of Acre, Amapa, Amazonas, Maranhao, Mato
Grosso and Para, besides Peru, Bolivia, and Suriname (Pedro 2014).

For the experiment, eight colonies of \emph{M. flavolineata} , eight
colonies of \emph{M. fasciculata} , nine colonies of \emph{F. longipes}
, 12 colonies of \emph{P. minima} and 13 colonies of \emph{S.}
aff.\emph{postica} were used. These colonies were left undisturbed and
without supplemental feeding during the three months prior to the
experiment and were kept in individual wooden shelters (Contrera and
Venturieri 2008), distanced at least 2 meters from each other. To reduce
the possibility of drifting (i.e., foragers returning to wrong colonies;
see Oliveira et al. 2021), the entrances of neighboring colonies were
arranged in opposing directions.

\emph{Colony size}

We used the number of adult bees to represent the colony size, like
previous studies on other eusocial bees (Dornhaus et al. 2012). To count
the number of adult bees in individual colonies, hives were closed at
night on the day prior to the experiment using a fine metal gauze (5 x
10 cm) to cover hive entrances, which prevented adult bees from leaving
the colony while allowing adequate ventilation. The following day, hives
were transferred to a small laboratory and enclosed in a 1.5 x 1 m fine
mesh cage to aid collection of adult bees using a manual aspirator. For
the more populous species (\emph{F. longipes} and \emph{S. aff. postica}
), carbon dioxide (glass cylinder, 95\% concentration) was given to the
colony for up to two minutes to anesthetize the individuals (Tustain and
Faulke 1979) prior to their capture. Males and female workers were not
discriminated during counting, while the mated queen and the gynes were
counted and separated from other adult bees. At the end of the bee
counting, all brood combs, food pots and adult bees were carefully
returned to the hive and colonies received supplemental food (sugar
syrup and pollen) to aid their recovery post assessment. By following
these procedures, no colonies died due to our handling.

\emph{Biological parameters}

We investigated the relationships between colony size and four
biological parameters of stingless bee colonies: (i) external activity
(in the field, before lab counts - non-invasive), (ii) egg-laying rate
(in the field, before lab counts - moderately invasive --hives were
opened to paint the brood cells), (iii) food stores (in the lab --
invasive --all pollen/nectar pots were weighed), (iv) brood cells
(immature bees; in lab - extremely invasive --all brood cells were
removed and counted) (Figure S2 and S3). These parameters were chosen
since they reflect the intensity of resource gathering by colonies and
their reproductive rates, factors likely linked to population size.
Moreover, they are easily measurable, allowing their replication in
other species.

Measurement of external activity and egg-laying rates were done \emph{in
situ} , seven days before the counting of adult bees in the laboratory,
whereas measurement of brood cells and food stocks were obtained during
counts of adult bees (see previous section), to avoid excessive handling
of the colonies.

To estimate (i) external activity of colonies, we counted the number of
workers returning to the colony over 5 min per hour (Hilario et al.
2000). Data were collected during the peak activity period for all
species (0900 and 1100; two survey hours per day), for five consecutive
days, to obtain the average number of bees returning to the nest. On
rainy days, data were not collected. To evaluate (ii) the egg-laying
rate, the edge of the newest brood comb (in \emph{Melipona} and\emph{S.}
aff. \emph{postica} ) was marked with water-based acrylic paints, and
after 24 h the new cells were counted. For \emph{F. longipes} and
\emph{P. minima} , all constructed cells were painted and after 24 h,
all new cells were counted. This procedure was repeated for all species
during three consecutive days. From this data we calculated the average
number of new cells constructed over a three-day period.

For the evaluation of (iii) amount of food stocks, we weighed all the
food pots of the colonies (honey and pollen) using a precision balance
(Toledo\selectlanguage{english} Prix 3; minimal load: 5g) for all species, except \emph{P.
minima} , for which we used a precision balance Master\selectlanguage{english}; minimal load:
0.02g). To obtain the (iv) number of brood cells (i.e., immature bees)
in species that construct brood combs in horizontal layers
(\emph{Melipona} spp. and \emph{S.} aff\emph{, postica} ), brood combs
were individually measured and photographed for counting of cells.
In\emph{F. longipes} and \emph{P. minima} , in which brood cells are
built in loose bunches of cells (Roubik 2006), brood cells were marked
with water-based acrylic paints and manually counted (Figure S3).

\emph{Data analyses}

To analyze relationships between colony size and biological parameters
of the colonies we used linear mixed models (LMMs) using the R package
`nlme' (Bates et al. 2015). Prior to model construction, data from
individual species (adult bee counts and biological parameters) were
standardized by using z-scores, to allow meaningful comparisons among
the different bee species, and effect sizes. The response variable was
the number of adult bees per colony, with the external activity,
egg-laying rate, food stocks and number of brood cells, and included as
fixed effects, and species (five levels) held as random grouping factor.

We considered only simple models (single terms, four competing models).
Candidate models were ranked using the \emph{dredge} function in the R
package ``\emph{MuMIn} '' (AICc values -- Akaike Information Criterion
-- corrected for small sample sizes) (Barton, 2019). Models within 2
delta AICc of the model with the lowest AICc value were considered
statistically equivalent. Parameter estimates and confidence intervals
(95\%) of models were constructed using restricted maximum likelihood
(REML) and model fit was assessed using marginal
R\textsuperscript{2}values (Nakagawa and Schielzeth 2013). In addition
to analyses with standardized data (z-scores), simple regression models
of the raw data from individual species were used to test relationships
between colony size and predictors, using the \emph{lm} function in the
R ``\emph{car} '' package (Fox and Weisberg 2011). Residuals from
selected models were visually checked for assumptions of homogeneity of
variance and normality using plots.

For obtaining the equations for estimating the colonial sizes according
to the measured parameters, a simple regression was used. All analyses
were performed in the R software (R Core Team 2018).

\textbf{RESULTS}

\emph{Colony size}

Adult bee counts in 50 colonies of five Amazonian stingless bees
revealed those species with small (\textless{}1,000 adult bees: \emph{P.
minima} {[}12 colonies{]}, \emph{M. fasciculata} {[}8{]} \emph{and M.
flavolineata} {[}8{]}), medium (between 1,000 and 5,000 adult
bees;\emph{F. longipes} {[}9{]}), and large-sized colonies
(\textgreater{}5,000 adult bees; \emph{S.} aff. \emph{postica} {[}13{]})
(Table 1).

\emph{Relationships between colony size and biological parameters}

The number of brood cells was the biological parameter that best
explained colony size, followed by the external activity and egg-laying
rate (Table 2 and Figure 1). As brood counts involved highly invasive
sampling (complete removal of brood comb), which would likely lead to
eventual death of the colony, we also considered the second candidate
model as the most viable proxy for colony size.

The number of brood cells was the biological parameter that best
explained colony size, followed by the external activity and egg-laying
rate (Table 2 and Figure 1). The linear regression of each biological
parameter tested, and the number of adult bees showed a strong
relationship with the external activity for two of the species evaluated
(\emph{M. flavolineata} : R\textsuperscript{2} = 0.193; \emph{M.
fasciculata} : R\textsuperscript{2} = 0.752; \emph{S.}aff.
\emph{postica} : R\textsuperscript{2} = 0.313\emph{; F. longipes} :
R\textsuperscript{2} = 0.221; \emph{P. minima} : R\textsuperscript{2} =
0.559), while there was a strong relationship with the laying rate in
four species (\emph{M. flavolineata} : R\textsuperscript{2} =
0.654\emph{; M. fasciculata} : R\textsuperscript{2} = 0.879;
\emph{S.}aff\emph{. postica} : R\textsuperscript{2} = 0.055; \emph{F.
longipes} : R\textsuperscript{2} = 0.575; \emph{P. minima} :
R\textsuperscript{2} = 0.726). In only one species there was a strong
relationship with the food stocks (\emph{M. flavolineata} :
R\textsuperscript{2} = 0.0003;\emph{M. fasciculata} :
R\textsuperscript{2} = 0.872\emph{; S. aff. postica} :
R\textsuperscript{2} = 0.014; \emph{F. longipes} : R\textsuperscript{2}
= 0.109; \emph{P. minima} : R\textsuperscript{2} = 0.104), and there was
a strong relationship with the number of brood cells in all species
evaluated (\emph{M. flavolineata} : R\textsuperscript{2} = 0.596\emph{;
M. fasciculata} : R\textsuperscript{2} = 0.908\emph{; S.} aff\emph{.
postica} : R\textsuperscript{2} = 0.562; \emph{F. longipes} :
R\textsuperscript{2} = 0.784; \emph{P. minima} : R\textsuperscript{2} =
0.752) (Figure 2).

The formulae that provided an estimation of population size for all
species, by using a simple regression, are: (1) External activity:
Y=45.9*X + 448.9; p\textless{}0.001; R\textsuperscript{2}=0.913; (2)
Brood cells: Y=0.905*X - 21.6; p\textless{}0.001,
R\textsuperscript{2}=0.964; (3) Egg-laying rate: Y=25.9*X + 372.5;
p\textless{}0.001; R\textsuperscript{2}=0.906. The number of food stocks
was not significant in the simple regression (p\textless{}0.108;
R\textsuperscript{2}=0.052).

\textbf{DISCUSSION}

By studying 50 colonies from five species of stingless bees, we showed
that the number of brood cells and external activity are the biological
parameters that best relate to colony size, regardless of the striking
differences in their size and life history traits. To measure bee colony
size and relate it to biological parameters closes important knowledge
gaps in the life histories of several widely distributed Amazonian
stingless bees, but also identifies useful proxy measures of colony size
for colony management and multiplication.

The number of brood cells was the best predictor of colony size;
however, its measurement involves an intensive handling of colonies, and
it is impossible to obtain in natural nests. External activity was also
positively correlated with population size, and it is feasible to obtain
in managed or natural colonies; we hypothesize this relationship occurs
because it is linked with the number of foragers (the last task in the
life of workers; Michener 1974; Sakagami 1982; Wille 1983), which are
responsible for keeping the food stocks in optimal levels, and thus in
capacity to nourish the immatures and adult bees.

External activity is commonly used for measuring the ``strength'' of the
colony; together with the number of adult bees, the number of brood
cells and the number of food pots (Hilario et al. 2000; Gostinski et al.
2017). External activity is a metric that can be easily assessed even in
natural colonies, where the measurement of brood combs and food stocks
is impossible to obtain without destroying the colony (Hilario 2007).
The relationship of colony size with the other measured biological
parameters varied among the different species. The food stocks only
presented a positive relationship with the number of adult bees
in\emph{M. fasciculata} . For the other species, there was no
relationship, as shown in the general model, including all species.
Regarding the egg-laying rate, in \emph{S.} aff. \emph{postica} we
observed high levels of variation in the relationship with the adult
population, probably due to the high mortality of immature bees observed
in this species (Figure S4).

Among the five species studied, \emph{S.} aff. \emph{postica} had the
largest population, corroborating previous estimates made by Lindauer
and Kerr (1960; around 15,000 adult workers), while \emph{P.
minima}presented the smallest population (mean colony size around 400),
much higher than the estimate of 175 bees made by Wille and Michener
(1973). For \emph{M. fasciculata} , our measures presented a smaller
population than the estimate of 776 adult bees, which may be due to
methodological differences between studies (Kerr et al. 2001). Another
possibility is that the since the study of Kerr et al. (2001) was made
with other populations of \emph{M. fasciculata} , in a region
approximately 600 km from our study site and with different vegetation
physiognomies. Thus, differences in the estimates made for \emph{M.
fasciculata} (and for\emph{P. minima} ; Wille and Michener 1973) may be
due to populational variation and the resources available to colonies in
the different areas. For \emph{F. longipes} and \emph{M. flavolineata} ,
there were no previous estimates of their population size.

The size of a colony in social insects is linked with several aspects of
their life-history, such as foraging strategies and reproduction rates
(Oster and Wilson 1978; Planque et al. 2010). Species with large
populations, like we found in \emph{S.} aff\emph{. postica} and \emph{F.
longipes} potentially have large numbers of workers involved in defense
and resource gathering, and therefore the colony's consumption of
resources may increase proportionally. In contrast, small populations,
such as \emph{P. minima} , although potentially not able to collect
large amounts of resources, may have smaller resource demands, thus
compensating for the small number of available foragers. However,
relationships between consumption/gathering of resources are yet to be
studied in stingless bees, with one of the reasons being the perceived
difficulty in estimating colony size. As such, our results will help
future studies investigate this relationship.

From a practical perspective, knowledge on stingless bee colony sizes is
highly relevant for their use as crop pollinators (Giannini et al.,
2020). For example, in the Amazon region, \emph{Scaptotrigona}
aff.\emph{postica} visit crops of economic importance, such as Rambutan
(\emph{Nephelium lappaceum} L.) and pollinate others, such as Acai palm
(\emph{Euterpe oleracea} Mart) (Ricon-Rabanales 2015; Campbell et al.
2018). However, for crop pollination, clear recommendations on colony
stocking densities are necessary for the development of effective
managed pollinator programs, as already defined for \emph{Apis
mellifera} (Vaudo et al. 2012). This number depends on the foraging
range of the colonies, the number of foragers, and the number of flowers
that need to be pollinated within croplands (Kuhn-Neto et al. 2009;
Rands and Whitney 2011). Thus, our data can be combined with existing
information on species' foraging ranges to develop novel managed
pollinator protocols using native bee species for several important
regional crops (Campbell et al. 2019; Araujo et al. 2004).

Finding an efficient method for estimating population size is important
for commercial rearing of stingless bee colonies, for monitoring colony
health, and for future scientific studies. Our study is the first to
count the total number of bees (adult and immature) and correlate it
with intrinsic factors in meliponine colonies. Previous studies provided
formulae to estimate colony size but did not validate these formulae
with biological data (Ihering 1930; Aidar 1996), and a recent study
showed that colony size of stingless bees has been overestimated
(Valadares et al. 2021). Since the direct measure of the number of adult
bees involves invasive sampling methods (Valadares et al. 2021), our
study provided a reliable approach to estimate the number of adult bees
by using the external activity. On the other hand, our study shows that
estimating population size will not be possible with a general formula
that works for all Meliponini.

For building a reliable and feasible estimation method for population
size, future studies should focus on single species or genus. It is also
important to collect larger and broader samples to deal with
disturbances caused by natural variation and thus understand the error
range of the method. External activity is a good parameter to start
developing a formula, because it is a variable that is easy to obtain in
natural or managed colonies, and it is highly correlated with population
size in most species. Future studies also must focus on other bee genera
and verify possible variation in interspecific population size related
with different life-history traits, as well as with temporal
fluctuations.

\textbf{ACKNOWLEDGMENTS}

We thank Janete T. Gomes, Ana Carolina M. de Queiroz, Hayron K.
Cordeiro, Alex Sousa, Barbara S. C. Lopes, Thaliana Sousa, Alessandra do
Rosario Leite, Karina Leao, Ana Lucia T. Seabra, Denyse C. da Silva,
Janaina de Cassia B. Ferreira and Andre Gomes for assistance in data
collection. Christoph Gruter and Francisca Segers helped with useful
discussion on preliminary results. We also thank Embrapa Amazonia
Oriental and the staff from the Botany Laboratory for access, lab space,
and support during this study.

\textbf{AUTHOR'S CONTRIBUTIONS}

\textbf{Kamila Leao} : Conceptualization; Data Curation; Formal
Analysis, Investigation, Methodology, Validation, Visualization, Writing
-- Original Draft Preparation, Writing -- Review and
Editing.\textbf{Alistair Cambell} : Formal Analysis, Methodology,
Writing -- Review and Editing. \textbf{Jamille Veiga} : Formal Analysis,
Methodology, Validation. \textbf{Cristiano Menezes} : Conceptualization,
Funding Acquisition, Project Administration, Resources,
Supervision.\textbf{Felipe Contrera} : Conceptualization, Funding
Acquisition, Project Administration, Resources, Supervision, Writing --
Original Draft Preparation, Writing -- Review and Editing.

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\textbf{Table 1.} Mean and standard deviation of colony sizes in five
species of stingless bees (\emph{Melipona flavolineata} , \emph{Melipona
fasciculata} , \emph{Scaptotrigona} aff. \emph{postica}
,\emph{Frieseomelitta longipes} , \emph{Plebeia minima} ). n = Number of
colonies counted, Adult bees = Number of adult bees counted in each
colony (males + workers), Sample size = colony size considering (small
\textless{}1,000 adult bees; medium = between 1,000 and 5,000 adult bees
and large-sized colonies \textgreater{}5,000 adult bees), Total
population = Adult bees + Brood cells, Brood cells= Number of brood
cells (bees in the egg, larva or pupa phase) counted in each colony,
Range of adult bees = Minimum and maximum the number of adult bees for
each species studied.\selectlanguage{english}
\begin{longtable}[]{@{}lllllllll@{}}
\toprule
\begin{minipage}[t]{0.11\columnwidth}\raggedright\strut
\textbf{Species}\strut
\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright\strut
\textbf{n}\strut
\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright\strut
\textbf{Colony} \textbf{size}\strut
\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright\strut
\textbf{Total} \textbf{population}\strut
\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright\strut
\textbf{Brood cells}\strut
\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright\strut
\textbf{Brood cells}\strut
\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright\strut
\textbf{D Adult bees}\strut
\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright\strut
\textbf{Range of} \textbf{adult bees}\strut
\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright\strut
\textbf{Range of} \textbf{adult bees}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
\emph{M. flavolineata}\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
8\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
small\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
2,111.13 \emph{+} 404.71\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
2,111.13 \emph{+} 404.71\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
1,065.13 \emph{+} 244.25\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
1,046.00 \emph{+} 185.17\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
768 -- 1,353\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
\emph{M. fasciculata}\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
8\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
medium\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
1,340.38 + 730.39\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
1,340.38 + 730.39\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
747.63 \emph{+} 438.76\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
592.75 \emph{+} 300.06\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
294 -- 1,008\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
\emph{S.} aff. \emph{postica}\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
13\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
large\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
15,429.46 \emph{+} 2,781.99\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
15,429.46 \emph{+} 2,781.99\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
8,025.46 \emph{+} 1,582.63\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
7,404.00 \emph{+} 1,390.96\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
5,898 -- 10,036\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
\emph{F. longipes}\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
9\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
medium\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
5,415.77 \emph{+} 2,167.08\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
5,415.77 \emph{+} 2,167.08\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
2,990.44 \emph{+} 1,230.91\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
2,425.33 \emph{+} 1,000.16\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
1,051 -- 4,393\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
\emph{P. minima}\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
12\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
small\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
880.75 \emph{+} 471.74\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
880.75 \emph{+} 471.74\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
476.0 \emph{+} 233.49\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
404.75 \emph{+} 254.42\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
208 -981\strut
\end{minipage} & \begin{minipage}[t]{0.08\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 2.} Results from LMM analyses of standardized (z-scores)
colony sizes (number of adult bees) and four biological parameters
(fixed effects): number of external activity of workers, egg-laying
rate, food stocks (total weight) and brood cells (for details on
parameter estimation, see \emph{Materials and Methods} ). Parameter
estimates (coefficients) are presented with 95\% confidence intervals,
model AICc values, and delta AICc.\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
\textbf{Model} & \textbf{Intercept} & \textbf{External activity} &
\textbf{Egg-laying} & \textbf{Food stocks} & \textbf{Brood cells} &
\textbf{AICc} & \selectlanguage{greek}\textbf{Δ AICc}\selectlanguage{english}\tabularnewline
\midrule
\endhead
1 & 0.00 & & & & \textbf{0.84 (0.68 - 1.00)} & 84.99 &
0.00\tabularnewline
2 & 0.00 & \textbf{0.62 (0.39 - 0.85)} & & & & 121.17 &
36.18\tabularnewline
3 & 0.00 & & \textbf{0.58 (0.34 - 0.82)} & & & 124.95 &
39.95\tabularnewline
4 (NULL) & 0.00 & & & & & 143.15 & 58.15\tabularnewline
5 & 0.00 & & & 0.17 (-0.11 - 0.46) & & 144.00 & 59.01\tabularnewline
\bottomrule
\end{longtable}



\textbf{Figure 1}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1.} Effect of biological parameters (number of external
activity of workers, egg-laying rate, food stocks (total weight) and
brood cells (for details on parameter estimation, see \emph{Materials
and Methods} ) on colony size (number of adult bees) considering all
species. Points represent individual colonies, and the black line is the
general estimate of the model. The gray shaded area defines the 95\%
confidence intervals for the model. The predictor and response variables
for individual species were standardized using Z-scores. a) -
Relationship between brood cells and size of the adult population, b) -
Relationship between external activity and size of the adult population,
c) - Relationship between egg-laying rate and size of the adult
population, d) - Relationship between food stocks and size of the adult
population. Colors represent colonies of five stingless bee species:
pink = \emph{Melipona flavolineata} , gold = \emph{Melipona fasciculata}
, green = \emph{Frieseomelitta longipes} , lilac =
\emph{Scaptotrigona}aff. \emph{postica} , blue = \emph{Plebeia minima} .

\textbf{Figure 2}\selectlanguage{english}
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\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

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\textbf{Figure 2.} Linear regressions between biological parameters
(number of external activity of workers, egg-laying rate, food stocks
(total weight) and brood cells (for details on parameter estimation,
see\emph{Materials and Methods} ) and colony size (adult bees) of each
bee species studied (\emph{Melipona flavolineata} {[}8
colonies{]},\emph{Melipona fasciculata} {[}9{]}, S\emph{captotrigona}
aff.\emph{postica} {[}13{]}, \emph{Frieseomelitta longipes} {[}9{]}
and\emph{Plebeia minima} {[}12{]}).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figura-1/Figura-1}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figura-2-pop-ecology/Figura-2-pop-ecology}

\end{center}
\end{figure}

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