Vital Statistics of Genus species (Triatominae: Hemiptera

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Rabinovich and Nieves: Vital Statistics of
Rhodnius neglectus
Journal of Medical Entomology
Life History
J. E. Rabinovich
Centro de Estudios Parasitológicos y de Vectores
Universidad Nacional de La Plata
Calle 2 No. 584
1900 La Plata
Province of Buenos Aires, Argentina
Phone: 54-221-472-4694
Fax: 54-221-472-4694
E-mail: [email protected]
Vital Statistics of Triatominae (Hemiptera: Reduviidae) Under Laboratory Conditions
III. Rhodnius neglectus (Hemiptera: Reduviidae)
Jorge Eduardo Rabinovich* and Eliana L. Nieves
Centro de Estudios Parasitológicos y de Vectores, Universidad Nacional de La Plata, Calle 2 No.
584, 1900 La Plata, Prov. de Buenos Aires, Argentina
The experimental work was carried out while the first author was a researcher at the Instituto
Venezolano de Investigaciones Cientificas, Caracas, Venezuela.
*
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Abstract. Five cohorts of 100 eggs of R. neglectus were reared simultaneously in the laboratory
under constant conditions (temperature 27 ± 1 C, 80 ± 10% RH), with mortality and fecundity
data recorded weekly. We calculated stage-specific development times (total development time
was 15 weeks), vital statistics (age-specific mortality and fecundity, and stage-specific and total
pre-adult mortality), and population growth parameters (the intrinsic rate of natural increase (r0=
0.2), the finite population growth rate ( 1.2), the net reproductive rate (R0= 262)), and the
generation time (T= 39.8 weeks)). Elasticity analysis showed that the dominant life-history trait
determining  were the adult female survival, and the time nymphs V remain in that instar. Adult
females dominated the stage-specific reproductive value, and the egg stage dominated the stable
stage distribution (SSD). The damping ratio ( = 1.13) suggests a relatively rapid period of
recovery to a disturbed SSD. The vital statistics were compared with previous values from the
literature and they proved to conform relatively well, considering that environmental conditions
were not always the same. Compared with other five species of the same genus (R. domesticus, R.
neivai, R. nasutus, R. prolixus, and R. robustus) R. neglectus ranked higher in fecundity (total
eggs/♀/life) and in female longevity, ranked intermediate in the intrinsic rate of natural increase
(r0), and lower in development time and mortality. Using our laboratory r0 value and by fitting the
density field values we estimated the carrying capacity of the spontaneous colonization of two
field experimental chicken coops.
Keywords: Chagas, triatomines, population parameters, population growth, life-history traits
Resumen. Cinco cohortes de 100 huevos de R. neglectus se criaron de manera simultánea en el
laboratorio bajo las condiciones constantes (temperatura 27 ± 1 C, 80 ± 10% HR), registrándose
semanalmente la mortalidad y la fecundidad. Calculamos los tiempos de desarrollo por estadios
(tiempo de desarrollo total= 15 semanas), las estadísticas vitales (mortalidad y fecundidad
específica por edades, y mortalidad pre-adulta específica por estadios), y los parámetros de
crecimiento poblacional (la tasa intrínseca de crecimiento natural (r0 = 0,2), la tasa finita de
crecimiento poblacional (= 1,2), la tasa de reproducción (R0 = 262)), y el tiempo generacional (T
= 39,8 semanas)). El análisis de elasticidad indica que el rasgo dominante de la historia de vida
que determina  es el la supervivencia de la hembra adulta, y el tiempo en que las ninfas V
permanecen en ese estadio. Las hembras adultas dominaron el valor reproductor específico por
estadios, y la fase del huevo dominó la distribución estable de estadios (SSD). La tasa de
amortiguación ( = 1,13) sugiere un período relativamente rápido de recuperación a un SSD si la
misma es perturbada. Se compararon las estadísticas vitales con valores de la literatura y se
encontró una concordancia relativamente satisfactoria, tomando en consideración que las
condiciones ambientales no siempre eran las mismas. En una comparación con otras cinco
especies del mismo género (R. domesticus, R., neivai, R., nasutus, R., prolixus, y R. robustus) R.
neglectus evidencia valores más altos en la fecundidad (huevos totales /♀/vida) y en la longevidad
de la hembra, valores intermedios en la tasa intrínseca de crecimiento natural (r0), y valores más
bajos en el tiempo de desarrollo y en la mortalidad. Usando nuestro valor r0 de laboratorio y
haciendo un ajuste valores de densidad de el campo se pudo estimar la capacidad de carga luego
de una colonización espontánea de dos gallineros experimentales en condiciones de campo.
Palabras clave: Chagas, triatominos, parámetros poblacionales, crecimiento poblacional, hisotrias
de vida
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This paper continues the previous two articles of a series of publications with the demographic
features (life cycle, reproduction, and mortality) and population parameters (population growth
rates, age-specific reproductive values, stable age distribution) of triatomine species, and that
covered the species Triatoma infestans (Rabinovich 1972) and Triatoma maculata (Feliciangeli
and Rabinovich 1985). Here we will analyze Rhodnius neglectus Lent 1954, cited for Brazil (Lent
and Wygodzinsky 1979), and Venezuela (Gamboa 1973). Since the publication of the first two
articles of this series an abundant literature has been published on a variety of population
parameters of several triatomine species. Also since 1972 and 1985 new methods of analysis have
been developed in the area of animal and plant demography; in this paper we will continue that
series of articles to provide statistical information about the demography of another triatomine
species kept under controlled laboratory conditions using the most recent methodologies. We hope
to fill a gap in the existing literature, providing statistics of demographic parameters of triatomine
population, and knowledge about the absolute and relative variation of those parameters. These
results, when applied to parameters as development time, population growth rates, and mortality,
are particularly important to analyze the outcome of competition among different triatomine
species, and contribute to explain triatomine species coexistence and diversity in a given habitat.
The resulting information has also important applications in the laboratory (e.g., to optimize the
design of colony rearing of triatomines) and in the field (e.g., to design an optimal vector control
strategy). The quantitative analysis of life-history traits, and particularly the population growth
parameters, is also related to the geographic dispersal of triatomines, so it will find application in
the epidemiology of Chagas disease because it is directly linked to their potential geographic
ranges in the face of global climatic changes.
R. neglectus belongs to the prolixus group that includes a series of species (R. prolixus, R.
robustus, R. neglectus, and R. nasutus) that are particularly difficult to distinguish, a fact that has
led to misidentification on several occasions (Monteiro et al. 2000). Within this similarity, R.
nasutus and R. neglectus constitute a sister group (Chavez et al. 1999). R. neglectus ranges
between the latitudes of approximately 5 and 25 °S, and between 5 and 700 masl (Galíndez Girón
et al. 1996), although occasionally it can be found above 1000 masl. It has been cited for Northeast
Brazil in the States of Bahia, Goias, Mato Grosso, Minas Gerais, and Sao Paulo (Lent and
Wygodzinsky 1979) and the States of Paraná, Maranhao and Pernambuco (Carcavallo et al. 1999,
Galvão et al. 2003), and for Venezuela in the State of Amazonas, at least until 1965 (Gamboa
1973). This species is found in a region characterized by mean annual temperatures ranging
between a minimum of 19 and a maximum of 30 °C (average 23.3 °C). However, its distribution
range shows minimum monthly temperatures as low as 8.3 °C and maximum monthly
temperatures as high as 30.3 °C. The mean precipitation is 1,246 mm/year (std. dev. 429.39,
coefficient of variation 34.5%, N= 12). R. neglectus has been identified by Curto de Casas et al.
(1999) as occupying the Holdridge Dry Forest and Very Dry Forest or Savannah Life Zones.
R. neglectus is a predominantly sylvatic species: it has been found in hollow trees or in the crown
of palm trees (Orbignya maritime, O. oleifera, O. martiana, Acrocomia macrocarpa, A. speciosa,
A. phalerata, A. sclerocarpa, Mauritia vinifera, M. flexuosa, Arecastrum romanzoffianum,
Syagrus oleracea, and Scheelea phalerata) (Diotaiuti 1984, Abad-Franch et al. 2005), and it has
been encountered, although on rare occasions, in birds' nests belonging to the family Furnariidae
(Anumbius annumbi) (Lent and Wygodzinsky 1979). Rocha et al. (1999) found that 14% of
“Buriti” palms (Mauritia flexuosa) within 250 m of human dwellings were colonized by R.
neglectus and Psammolestes coreodes. Barreto and Carvalheiro (1966) collected R. neglectus
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associated with T. sordida and Panstrongylus megistus in various palm species which were
positive in various degrees to Trypanosoma cruzi (11.1% in Acrocomia sclerocarpa, 13.5% in
Mauritia vinifera, and 30.5% in Orbignya maritime). R. neglectus has not been found in reptile
refuges, bromeliad epiphytes, cacti, caves, insect nests or under stones, as many other Triatoma
and Rhodnius species (Carcavallo et al. 1998). R. neglectus has also been found in human
dwellings, chicken houses, pigeon coops, and in other peridomestic habitats (Pinto Dias 1968,
Dias-Lima et al. 2003); Lent and Wygodzinsky (1979) considered this species a recent colonizer
on the way to becoming a truly domestic species, and this was confirmed by the field triatomine
investigations of Forattini et al. (1984). Carcavallo et al. (1998) categorized R. neglectus as a
frequently or occasionally peridomiciliary species. Due to its dominant sylvatic condition R.
neglectus is not considered a critical vector species of Chagas disease transmission, although it has
been found naturally infected by T. cruzi (Forattini et al. 1977).
The main feeding sources of sylvatic R. neglectus are marsupials (Didelphis sp.), rodents, birds
and bats (Barretto 1967a, 1967b); occasionally they have been found to feed on amphibians and
reptiles such as the Brazilian cobra (Diotaiuti 1984). Minter (1975), compiling information from
precipitin tests, reports that birds invariably supply most feeds (46-80 %). In addition to humans
the main hosts associated to human dwellings are bovids, goats, cats and dogs (Forattini et al.
1971).
Analyses of the life cycle and reproduction of R. neglectus have been carried out under various
laboratory conditions of temperature, humidity and feeding by Freitas et al. (1967), Mello (1977),
Forattini et al. (1983b), Diotaiuti and Pinto Dias (1987), Lima et al. (1987), Garcia da Silva and da
Silva (1988), and Silva Rocha et al. (2001); however no population parameters’ estimates have
been provided. Here we present the results of a cohort study of R. neglectus and our estimates of
its population parameters, with their variability and sensitivity to life history traits.
Materials and Methods
Population origin. The population of R. neglectus used in this study was made available by Dr.
Rodolfo Carcavallo and came from the insectaria of the Instituto Oswaldo Cruz (Rio de Janeiro,
Brazil), although its exact geographical origin is not known.
Experimental procedures. The experiment was carried out in Caracas, Venezuela, in a climatic
room with constant conditions of temperature (27 ± 1 C) and humidity (80 ± 10% RH).
Photoperiod did not need to be controlled, for at the latitude of Caracas its seasonal variation is
very small (day length in December is 11:29 h, and in June is 12:42 h). The experimental design
involved the follow-up of five independent cohorts initiated simultaneously. Each cohort was
started with 100 recently laid (0-48-h-old) eggs, kept in 150 cc glass containers until all viable
eggs hatched. The 1st instar nymphs were transferred to 3.785-liter jars, covered with nylon mesh,
and with vertically placed strips of paper inside that served both as resting places and for climbing
to the top at feeding time.
Each cohort was fed weekly using hens placed on a wooden box with holes at the bottom, through
which the tops of the cohort jars could be tightly inserted. The hens were plucked on one side and
with the legs and part of the body tied up do reduce movements. The insects climbed to the top and
fed through the nylon mesh. Food was offered for 1 h, and during the following hour the jars were
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horizontally exposed to a fan, to avoid the accumulation of excessive moisture in the glass
containers common after the insects become engorged.
After being exposed to the fan, each jar was opened weekly in order to check the number of dead
individuals (identified by instar), and number of eggs laid; identification by sex was made only as
adults. In a few instances the strict weekly feeding and counting schedule could not be maintained
(although they were never out of phase for more than 3 days), and as the biodemographic methods
require a constant time unit for analysis, the recorded information was subjected to linear
interpolation to keep the week as the time unit for the calculation of population statistics.
Statistical analyses. The weekly death schedule of the cohorts’ follow-up provided the necessary
information to construct a life table (Deevey 1947). Calculations followed the method of Dublin et
al. (1949); definitions of the components of a life table, with the formulae used, are given in the
Appendix. As each member of the cohort was not followed individually, a frequency table of the
time in each instar was used to provide an estimate of the average and standard deviation of the
development time of each instar. The frequency tables were based on time and number of
individuals (a) entering a particular instar, (b) dying in that instar, and (c) molting to the following
instar. Adult longevity (also average and standard deviation) was calculated from the frequency
table of the number of weeks lived by groups of individuals, and it was evaluated for each sex
separately.
The weekly mortality data was used to calculate survival as a function of age (l(x)), which coupled
with the weekly female age-specific fecundity (m(x), also called the maternity curve), allowed the
calculation of such statistics as the intrinsic rate of natural increase (using the Euler equation), the
net reproductive rate, the instantaneous birth and death rate (Birch 1948), the age specific
reproductive value (Fisher 1930), and the stable age distribution. All definitions and formulae are
also given in the Appendix. Parameters were calculated based exclusively upon the female
population by multiplying all values by the sex-ratio (calculated as ♀/(♂+♀)), determined by the
total number of males and females emerged from instars V. Calculations were carried out by
means of a special computer program for PC computers developed by the authors for this purpose
in Delphi 2007 language.
Additionally an age population matrix system was constructed (Caswell 1989) based on the
development of the following projection (or transition or Leslie) matrix, called A:



A




F1
F2

Fs 1
P1
0

0
0
P2

0



0
0
0

Ps 1
Fs 

0 
0 

0 
0 
where, Pi is the probability that individuals of age i will survive from time t to time t+1, Fi is the
age-specific fertility (actual reproductive performance, sensu human demographers, i.e., Fi is the
number of age class 1 individuals at time t+1 per age class i individuals at time t) (Caswell 1989).
The relationships between the projection coefficients Pi and Fi and the survival and maternity
curves (l(x) and m(x), respectively), are given by Caswell (1989) as:
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Pi 
li  li 1
(l l )0.5
and Fi  0 1 (mi  Pi mi 1 ) ,
li 1 l i
2
where, i stands for age (in weekly units), and l0 and l1 are the initial and the last (non-zero) agespecific survival values of the cohort. Fig. 1a depicts graphically the relationships between the
projection coefficients Pi and Fi . The multiplication of matrix A by a vector at time t of the
population size by age classes (weeks), or age-specific population vector, (x(t)), produces a new
age-specific population vector at time t+1, (x(t+1)). That is, Ax(t)=x(t+1), where  is the finite
population growth rate once a stable age distribution has been achieved, A is the transition matrix,
and x are the age-specific population vectors at times t and t+1; the classical relationship ln()= r0
holds, where r0 is the intrinsic rate of natural increase. However, it is possible to determine  from
matrix A without having to project the population until a stable age distribution is achieved. The
procedure consists in obtaining the characteristic equation of matrix A, and then to find the roots
of the characteristic equation; the largest, positive root (eigenvalue) is the value of , the finite
population growth rate (Caswell 1989).
However, many organisms are characterized by a series of stages (eggs, five instars, and an adult
stage, in the case of triatomines), which may be very different from the point of view of their
physiology, behavior and demographic features. That is, the survival and reproductive rates are
more dependent on stage than on age. The Leslie matrix (A) presented above was extended by
Lefkovitch (1965) to represent organisms grouped by stages, and the stage-specific matrix A’
(called the Lefkovitch matrix) has the following structure:



A'  




s1
f2

f n1
g1
s2

0
0
g2

0



s n1
0
0

g n1
fn 

0 
0 

0 
s n 
Where now i refers to a given stage, si is the probability of staying (and remaining alive) in stage i,
and gi is the probability of transferring (alive) from stage i to the next stage i+1 (note that [1-si-gi]
represents the probability of dying in stage i). The symbol fi represents the fertility in female eggs
per female per unit time; in the case of the triatomines only the adults (fn) have non-zero values,
for no other stage is a reproductive stage.
The conversion of the age-specific survival (lx) and maternity (mx) curves to the stage-specific
functions (si, gi and fi) can be carried out by a process of eight steps (Ebert 1999) by calculating:
(1) the average time duration of each stage (),
(2) the stage-specific survival (l’i), by dividing lx+x by lx (where x is the duration of each
stage in terms of age-specific classes x),
(3) the survival rate (p) per unit time, as p=  l' x ,
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(4) the fraction of members of a stage class leaving that stage (FLi), as the reciprocal of the
average time spent in the stage (also known as residence time) (i.e., FLi= 1/ ; note that this
means we assume that all individuals in the stage behave identically and move from stage
to stage synchronically),
(5) the fraction members of a stage class remaining in that stage (FSi), as the complement of
FLi (i.e., FSi = 1- FLi),
(6) the probability (gi) of transferring (alive) from stage i to the next stage i+1, as gi = pFLi ,
(7) the probability (si) of staying (alive) in the same stage i), as si = pFSi , and
(8) the stage specific fecundity value (fi) as the sum of all eggs laid divided by the number of
time units of reproduction.
The procedure for these calculations can be visualized in Fig. 1b (called a stage-structured lifecycle graph), and were carried out in a spreadsheet.
More precision and realism can be added to this procedure by relaxing the condition that all
individuals in a given stage move to the next stage synchronically (as required by step (4) above).
That is, we can now introduce an age associated condition by which some members of a particular
stage have live longer than others and thus are readier to move to the next stage. Ebert (1999)
provides the following formula to compute the fraction ready to leave a stage:
(1  p) p i 1
FLi 
1  p i
where p is the survival rate per unit time as defined in step (c) above, and represents the average
duration (in number of time units) of stage i. Note that if p= 1, then FLi= 1/i as in step (4) above.
A final improvement in the estimation of the elements of the transition matrix A’ is obtained by
correcting for the fact that the fraction of the members of a given stage that are ready to move to
the next stage is sensitive to the population growth rate. This occurs because, for any given stage
class, the higher the population growth rate at each time unit there will be a larger number of
individuals added than in the previous time unit, and so the proportion of the terminal age group,
just before they pass to the next stage, becomes smaller. A correction for this effect is taken into
account by dividing all the elements of the transition matrix A’ (i.e., si, gi and fi) by the finite
population growth rate () (Ebert 1999). This is shown in the life-cycle graph of Fig. 1c, and the
procedure is equivalent to what is called the Z-transform of a Lefkovitch matrix (Caswell 1989).
However, as the value of  is still not known, a first approximation based on matrix A’ can be
obtained and used in an iterative way, until new estimates change less than an acceptable
proportion (0.001, say). These calculations were also carried out with the special program
developed by the authors in Delphi 2007 language as a PC computer application.
Once the Z-transform of a Lefkovitch matrix had been created, we estimated various population
parameters and statistics in a desktop PC using the package “popbio” (Stubben and Milligan 2007)
under the R programming language (version 2.6.2), a free software program that is primarily used
for statistical computing and graphics (R Development Core Team 2007). The following “popbio”
routines were used: (i) “eigen” to calculate the transition matrix eigenvalues, being the maximum
positive eigenvalue the finite rate of population growth (), where r0= ln() is the intrinsic rate of
natural increase; (ii) “generation.time” and (iii) “net.reproductive.rate” to calculate the generation
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time (T’) and the net reproductive rate (R’0), respectively; (iv) “eigen.analysis” that provides the
stable age distribution, sensitivities, elasticities, reproductive values and damping ratio (time to
reach the stable age distribution); and (v) “fundamental.matrix”, that provides the mean and the
variance of the time spent in each stage (and the corresponding coefficient of variation), and the
mean of time to death and its variance. Definitions and details of some of these parameters and
statistics are given in part II of the Appendix.
Results
Vital statistics. The survival and maternity curves of R. neglectus for the average of the five
cohorts, in terms of female individuals, is given in Fig. 2. Application of the procedures to convert
the weekly age structured population into a stage structured population resulted in the following
transition matrix, also for the average of the five cohorts:
0
0
0
0
0
7.224
 0.551
0.449 0.502
0
0
0
0
0 

 0
0.347 0.547
0
0
0
0 


A'   0
0
0.439 0.551
0
0
0 
 0
0
0
0.449 0.551
0
0 


0
0
0
0.449 0.818
0 
 0
 0
0
0
0
0
0.175 0.955

Table 1 provides a statistical summary of life-cycle statistics. Average time from oviposition to
hatching was slightly over 2 weeks. Development times of all instars were very similar, except for
instar V, which took almost as twice as the rest to complete development. However, instars I and
IV show the most variable development times. The average development time from egg to adult
was 15 weeks (std. dev. 1.4 weeks); the average minimum and maximum development times from
instar I to the adult stage were 8.4 weeks (std. dev. 0.55 weeks) and 23.8 weeks (std. dev. 8.5
weeks), respectively. The sex ratio (♀/(♂+♀)) when entering the adult stage favored males: the
average among cohorts was 0.411 (std. dev. 0.029) not statistically different from 0.5 (p= 0.0167).
After entering the adult stage, average (45.16 weeks) and maximum (65.8 weeks) female longevity
was about 20% longer than for males (35.7 and 52.8 weeks, respectively); differences in the
average and the maximum longevity between males and males were statistically significant (p=
0.000). The most extreme longevity cases were observed in cohort 5 with a male that lived for 60
weeks and a female that lived for 71 weeks as imagoes.
Mortality per instar follows the usual pattern in triatomines of a high mortality in the younger
stages; particularly in R. neglectus stages I and II account for approximately 50% of the total
mortality from egg to adult. However, instar V shows an increase in mortality. Instars III and IV
have a lower mortality rate but that rate is extremely variable among cohorts. On average, about
70% of all initial eggs of the cohorts arrive to the adult stage. In general the lx curve shows a
relatively steep slope up to the instar I, a quite gentle decrease during the instars II, III and IV, and
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another abrupt drop during instar V (Fig. 2); survival remained stable for a few weeks after
becoming imagoes, as if with the last molt a severe mortality risk had been overcome; after those
few weeks adult females showed a fairly linear age-specific schedule of survival.
Fig. 2 also shows the age-specific schedule of oviposition expressed as number of
eggs/female/week for the average among cohorts. The general pattern can be considered as
unimodal, even if very irregular; and the bell-shape is relatively similar among cohorts (not
shown), peaking when aged about 40 weeks from the egg stage.
Table 1 also provides a statistical summary of the reproductive characteristics of female R.
neglectus. The age of first reproduction (of the cohort, for there was not an individual follow-up) is
a very important parameter in population dynamics, and resulted in 15.4 weeks from the egg stage
(std. dev. 0.55 weeks; coefficient of variation = 3.56%). On average a female laid eggs at a rate of
7.58 eggs/week/♀ during an average period of 45.37 weeks after the start of reproduction.
It was of interest to determine if nymphal mortality was related to developmental time. A
regression analysis (not shown) proved no statistically significant relationship between absolute
nymphal mortality and developmental time (R2 = 0.074).
Population growth parameters. The main population growth parameters and stage-specific
demographic features of R. neglectus are given in Table 2. Population growth rates show very little
difference between cohorts (coefficient of variation is between 1 and 15%, depending on the
parameter). The difference between the various parameters calculated as age-specific and as stagespecific populations is extremely small. The main apparent differences are in generation time (T)
and net reproductive rate (R0) because of the way these parameters are calculated in age-specific
and in stage-specific populations (see Appendix, part II). On average 317 females will replace
each female in the population in the course of one generation (R0).
Figs. 3 and 4 show the stage-specific reproductive values and stable stage distribution (SSD) of R.
neglectus, calculated from the stage-structured matrix created from lx and m’x curves as averages
of the five cohorts (thus, not necessarily identical, though quite similar, to the values presented in
Table 2). The female adults are the ones with the highest reproductive value, followed by instar V;
the SSD is dominated by eggs, followed by the other stages in the form of a classical age pyramid.
The average damping ratio () was 1.13, indicating that, if perturbed from the SSD, it would return
to it rather rapidly.
Sensitivity analysis. The results of the sensitivity analysis on the instantaneous rate of natural
increase (r0) are presented here as elasticities (Table 3), and show that the highest elasticity is the
adult female survival (0.22) transition matrix element, followed by the proportion of instar V
nymphs that remain in that stage (0.12). The fertility of the transition matrix (♀ eggs/♀/week) as
well as the other life-history traits of this matrix showed fairly low elasticity values (between 0.05
and 0.06).
Discussion
Vital statistics. Few of our results can be compared with previously published information,
because most of the work with R. neglectus was limited to development times or mortality
10
estimates, and no estimation of lifetime reproduction or population parameters exists. Furthermore,
previous work with R. neglectus was carried out under a variety of laboratory conditions:
temperature and humidity (usually uncontrolled), size of jars, feeding frequency and duration,
density of insects per jar, species of host offered for feeding, and other factors that rarely coincided
with our experimental conditions, and all of them have important consequences on the population
parameters being estimated. Additionally, in evaluating our results, it is important that the
following aspects of this cohort study be taken into account:
(1) In most cohort studies the individual history of the insects are not known. In particular in
triatomines, because of the intensive labor that individual rearing and feeding demands, each
cohort is usually followed as a group; thus possible interactions between individuals of a given
cohort are not known. Ryckman (1951) notes that in Triatoma phyllosoma pallidipennis, older
nymphs crowd up to the host to the exclusion of younger members of the colony; and that the
considerable amount of warm blood ingested by older nymphs stimulates a thermotrophic response
in unengorged younger nymphs, elicits a probing reaction that leads to a type of cannibalism he
called "kleptohemodeipnonism". We do not know to what degree, if at all, these two phenomena
might have affected our experiments with R. neglectus; however, we think that in our study it can
be considered negligible because due to the progression of the development from egg to adults,
older nymphs do not co-exist with the very younger ones. Perlowagora-Szumlewicz (1953) shows
the importance of the time of the 1st meal, and in general it is known that the volume of the blood
meal in one or successive feedings in different instars drastically affects the process of molting and
of production and viability of eggs (Goodchild 1955, Danilov 1968, Perlowagora-Szumlewicz
1969); in our experimental set-up feeding of each individual insect was not recorded, so if this
factor also occurred with R. neglectus it may have influenced the results of our cohort study.
Another disadvantage of treating the cohort as a group is that the reproductive performance cannot
be evaluated individually; some information is lost, such as individual periodicity in oviposition.
(2) As individuals die the density (number of individuals per jar) decreases during the
development of a cohort study. Perlowagora-Szumlewicz (1969) demonstrates an apparent density
effect upon longevity and fecundity in T. infestans. In particular it was shown that R. neglectus
females which mated only once and were regularly fed had a fertility rate lower than the females
which mated several times (Costa et a1. 1967); as copulation (by direct observation or by the
presence of spermatophores) was not recorded in our study, the consequences of this effect is
unknown, although at the initiation of the adult life males were abundantly available to females in
the cohort jars, particularly in the fist half of their adult life, when this effect is most important.
(3) Calendar age is not the same as physiological age. As a result of interactions referred to above,
as well as a result of the usual biological variability, individual triatomines do not molt
synchronously even if they developed from eggs laid simultaneously. Consequently as the insects
develop into more advanced stages there is a larger amount of overlap between stages, and
individuals with the same calendar age may belong to, say, 3rd, 4th, or 5th nymphal instars. It is
not known if these differences affected the results of this study. For example, the probability of
dying may differ between a 5th instar nymph 25 days old and a 5th instar nymph 40 days old.
With these 3 reservations in mind, however, our results can be compared to results found in the
literature and analyzed demographically. A discussion of some particular aspects of the results of
this cohort study follows.
11
Mello (1977), Diotaiuti and Pinto Dias (1987), and Silva Rocha et al. (2001) studied the
development time of R. neglectus and mortality by stages. Garcia da Silva and Silva (1988) also
studied the development time but not mortality. Fig. 5 showed their results with our own. There
were no statistically significant differences with Mello (1977) (with a t test p= 0.01 for eggs, and
p= 0 for all instars); the differences with Garcia da Silva and Silva (1988), although small, were
statistically significant. However, they proved to be consistent as a function of the feeding
conditions: although Garcia da Silva and Silva (1988) used environmental conditions similar to
ours (25 ± 0.5 C and 70 ± 5 % RH), and were also fed with hens, the feeding was less frequent:
every 12, 15, 20 and 25 days for nymphs of instars 2, 3, 4, and 5, respectively. So it is not
surprising to find longer development times in their results. The mean development times of
different stages of R. neglectus obtained by Diotiauti and Pinto Días (1987) are longer than this
study, although we would have expected a shorter development time because the feeding
conditions were the same, but rearing temperature was higher (28 ± 1 C); however, due to the
high variance of their results the differences are not statistically significant. The same happened
when comparing the development times obtained by Silva Rocha et al. (2001) (with the exception
of instar I (p= 0.089) the other stages were not statistically different from our study). When
comparing the total development times from egg to adults our results (15 weeks) are only larger
than the 12.3 weeks obtained by Freitas et. al (1967), but shorter than the development time values
of 17.1 weeks of Mello (1977), 21.3 weeks of Silva and Silva (1988), 22 weeks of Silva et al.
(2001) and 19.5 weeks of Diotaiuti and Pinto Días (1987). Those references did not provide
variance estimates, so no statistical comparison was possible.
Mortality by stages was compared in Fig. 6, and the differences among studies are notorious. For
most developmental stages few of the other studies compared well with our results (most of the
stage mortality values of previous studies fall outside the one standard deviation bars of our
results). This is also evident from the large differences in the total (accumulated) mortality from
egg to instar V: 10.6% (Mello 1977), 68.2% (Silva et. al 2001), 40.2% (Diotaiuti and Pinto Días
1987), at least 46.2% (Freitas et al. 1967; egg mortality was not estimated by the authors), and
31.6% in this study. Either stage mortality is more sensitive than development time to small
differences in environmental and feeding experimental conditions, or differences in manipulation
of the bugs during the cohort experiments greatly affect the chances of survival.
Of the five studies amenable to comparison with our results, only Mello (1977) provided an
estimate of the sex-ratio (expressed here as ♀/♀+♂): 0.53, which is slightly larger than the sexratio of our study (0.41), a difference not statistically significant (p= 0.047). As the sex-ratio in R.
neglectus does not differ statistically from 0.5, and as in triatomines sex ratio is assumed to be 0.5
at the egg stage, R. neglectus females seem to have the same intrinsic mortality risks than males
during development. In terms of fecundity and fertility our result of 18.05 eggs/♀/week and 92.2%
hatching rate conforms well with the 17.1 eggs/♀/week and 95.1% hatching rate values obtained
by Costa et al. (1967).
Population parameters. The five previous studies on R. neglectus do not provide estimates on
adult longevity and/or on fecundity during the females’ lifetime, nor on the population growth
parameters. Thus it was of interest to see how R. neglectus ranked within the genus Rhodnius in
terms of its population parameters. We compiled over 60 sources of data on development time
12
and/or mortality from this genus, but many of them had no population parameter estimates (or the
data was not amenable to calculation with the raw data provided), and in many cases, when they
were available, the experimental conditions were too different from the ones of this study. After a
selection of those cases with conditions as similar as possible to our experimental setting we were
left with 10 cases representing five Rhodnius species (in addition to R. neglectus). The comparison
of the population parameter values indicates that R. neglectus has an intermediate population
growth rate within those six species of Rhodnius (Table 4). After the intrinsic rate of natural
increase (r0) was averaged for the three values available for R. neivai and R. prolixus, Fig. 7 was
constructed, showing that R. neglectus has an intermediate value, smaller than the r0 for R. prolixus
and R. domesticus, but larger than the r0 for R. neivai, R. robustus and R. nasutus. In terms of the
finite rate of population growth (= exp(r0)) the differences are relatively important, ranging from
a weekly 27% of population increase in the case of R. prolixus, to a weekly 13% of population
increase in the case of R. nasutus., with R. neglectus having an intermediate  value of 21%
increase. Congruent with these results R. prolixus has the shortest generation time (22.4 weeks), R.
nasutus the longest generation time (43.4 weeks), with R. neglectus with an intermediate
generation time (39.8 weeks).
Despite having an intermediate value of population growth rate, R. neglectus ranks as the
Rhodnius species with the highest fecundity potential (in terms of average total eggs per female
per life) (Fig. 8). When fecundity is expressed as the average number of female eggs per female
per day, there is little difference between the Rhodnius species, mainly because the total eggs per
female per life is compensated by difference if female longevity (also shown in Fig. 8).
Sensitivity analysis. The sensitivity analysis gives information about how sensitive the population
growth rate () is to changes in terms of the transition matrix A elements or in terms in the lifecycle graph (Fig. 1). It is particularly useful in providing insight into hat parts of the life cycle
should be under the most intense selective pressure or, from the vector management point of view,
which components of the life-history traits of triatomines should be the main target for population
control (Ebert 1999). The population growth rate () is an accepted measurement of fitness, and
how  changes with the changes in a trait ai, that is, ai, has been called the “selective
pressure” on that trait and, being a partial derivative, it is also called the sensitivity of  to changes
in ai (Emlen 1970). However, as the elements ai usually have different units, the different
contributions of the traits ai to are better measured by their elasticity, which is a sort of
proportional sensitivity, and after Caswell (1989) defined as ei= (ai/)(ai). The elasticities of
the life-history traits of R. neglectus, as given in Table 3, proved to be quite surprising and even
counter-intuitive, with a clear dominant contribution to  by the survival of the adult females, and
followed exclusively by the proportion of instar V nymphs remaining in that stage (i.e., not
molting into adult females). These two life-history traits are 3.5 and 2 times larger, respectively,
than any other life-history trait, even the fecundity term. In other words, at least from the
demographic point of view, any control measure targeting adult survival and/or arresting the
development of instar V nymphs (i.e., delaying their molt into adults) would be 2-3 times more
effective than any other control measure.
Damping ratio. The damping ratio () is related to the period of recovery to a stable stage
distribution (SSD) if the SSD has been disturbed. To convert that ratio into a calendar value we
have to specify the time required (tx) for the contribution of the second root (2) to a reduction of a
13
certain multiple (x) of the dominant root (1). A decline of 5%, say, of that of the dominant root
implies calculating t20 (x=1/0.05= 20). Caswell (1989) shows that tx can be estimated by tx=
ln(x)/ln(). As the value of the damping ratio for R. neglectus was  (from the stagestructured matrix for the average of the five cohorts), t20 becomes 24.5 weeks. As the cohorts were
maintained at 26 C, the t20 value represents 1715 degree-days (assuming a developmental
threshold of 16 C) which falls within the range of 1000-3000 degree-days, a normal a growing
season for insects in temperate regions. This is a relatively fast recovery period of a SSD, although
it depends on the doubtful assumption that the vital rates remain constant during that recovery
period. Taylor (1979) calculated the t20 value of 36 populations of 30 species of insects and mites,
and the values ranged from 280 degree-days (in a species of mite) to 115,120 degree-days (in a
species of moth). Taylor (1979) concluded that most part of insect species existing in seasonal
environments never experience, or spend a small proportion of their time in a SSD. But most
interesting is Taylor’s (1979) conclusion that the time of convergence to SSD was nearly
independent of survivorship and the reproductive capacity, but that the higher the age of first
reproduction () and the larger the variance in mx the faster the convergence to the SSD.
Different degree-days values will permit different proportion of the population that attains a SSD;
thus conclusions about the recovery period of a SSD are relative to the value of the multiple (x) of
the contribution of the second root (2) in relation to the dominant root (1); in an environment
with a given degree-days value, the higher the percent decline, the higher the percent of the bug
population that will have time to converge to a SSD. E.g., for the typical range of 1000-3000
degree-days, a 10% threshold (t10), 55-75% of the population will have time to converge to a SSD;
with a 20% threshold (t5), 65-80% of the population will have time to do so (Caswell 1989).
An extradomiciliary population of R. neglectus in San Pablo State, Brazil, showed that in a
population of 23 individuals 8 were nymphs (35%) and 15 were adults (65%) (Forattini et al.
1977). This is almost the reverse of what was expected from a stable stage distribution (about 56%
nymphs), indicating that this sylvatic population of R. neglectus was either a recent colony or a
population that was recently altered and had no time to recover a SSD. However, in a field
experiment where artificial chicken coops were established near peridomiciles in Sacramento, in
the State of Minas Gerais, Brazil, Forattini et al. (1983a) found that in almost two years (from
January 1977 to October 1978) a population of 17 R. neglectus individuals that spontaneously
colonized a chicken coop had only one female adult (5.9%) and 16 nymphs (nymphs I and II)
(94.1%), again quite different from a SSD. Nevertheless, in cactus habitats in the State of Bahia
(Brazil) Días-Lima et al. (2003) found 66.2% of nymphs (N= 65) which conforms better with the
prediction of SSD from our demographic study. The value of the damping ratio for R. neglectus
was and the calendar time to recover a SSD was estimated around 25 weeks, much
shorter than the chicken coop colonization experiment. These results suggest a very high or
permanent perturbation condition in the sylvatic environment that impedes R. neglectus
populations to achieve a SSD. However, this interpretation has to be taken with caution, for there
are several factors, not related to perturbations, that may be resulting in a non stage age
distribution. One is a sampling artifact, for it has been shown that in R. prolixus (a very similar
species) small nymphs have a much lower catchability than larger nymphs and adults (Rabinovich
et al 1995). Another factor may be related to the natural dispersal behavior of individuals in a
sylvatic population, with adults usually flying away from their natural habitat. Forattini et al.
(1983a) after following spontaneous colonization of artificial biotopes for 30 consecutive months
14
in Brazil, found that the proportion of adults of the newly established colony oscillated between a
minimum of 8.9% and a maximum of 44.8%. But Forattini et al. (1983a) also show that the
proportion of adults falls periodically after the months of May and June. These authors compared
the dispersal of individuals of R. neglectus to those of T. infestans and T. sordida, and concluded
that the former tend to leave their colonized habitats earlier and that their dispersal activity was
more intense.
Forattini et al. (1983a) estimated the average stage duration of R. neglectus nymphs under field
conditions in experimental chicken coops, and obtained development times much longer (between
8 and 11 weeks) than our experimental cohorts (between 2 and 4 weeks) under constant
conditions. It is an important difference of a factor between three and five times longer. However,
this should not be surprising for under the field conditions of Forattini et al. (1983a) the hosts were
occasional visitors and the temperature fluctuated along the year.
Population growth. The population growth of R. neglectus after the spontaneous colonization of
artificial chicken coops near peridomicialiary habitats for seven consecutive trimesters obtained by
Forattini et al. (1983a) in Sacramento, Brazil, was used to fit the classical logistic model of
population growth in order to estimate the intrinsic rate of natural increase (r0) and the carrying
capacity of the chicken coops (K). Fig. 9 shows the observed and predicted values for two chicken
coops; in chicken coop a2 R. neglectus colonized by itself, while in chicken coop f1 it developed a
population co-existing with T. sordida. In chicken coop a2 R. neglectus arrived in the sixth
trimester and the population was growing a at a rate given by r0 = 0.163 per week and a carrying
capacity (K) value of 226 individuals (r = 0.945, 2= 1049.7, df = 6, p = 0.000000). The r0 value
of 0.163 is lower than the average laboratory value indicating that R. neglectus populations under
natural conditions possibly grow at a rate smaller than under optimal laboratory conditions. In
chicken coop f1 R. neglectus arrived in much earlier (in the third trimester) and the population was
growing a at a rate given by r0 = 0.081 per week and a carrying capacity (K) value of 368
individuals (r = 0.947, 2= 71.73, df = 8, p = 0.000000). The difference between the population
growth rates of chicken coops a2 and f1 probably can be explained by two compounded factors:
(a) chicken coop a2 received a smaller founder population, and (b) there was a competition with T.
sordida that pressed for a higher population growth rate; on the contrary, in chicken coop f1 an
earlier arrival and larger initial colonizing population lead to an earlier action of the densitydependent population regulation, resulting in a lower growth rate. It is interesting to note that the
estimated carrying capacity for R. neglectus in chicken coop f1 was much bigger (368 individuals)
than the one in the chicken coop a2 (226 individuals) where it had to compete with T. sordida. In
both cases R. neglectus populations under natural conditions seem to grow at a rate much smaller
than the one estimated under optimal laboratory conditions.
Conclusions. We conclude that the population parameters here estimated for R. neglectus will be
useful for laboratory and field applications. For example, R. neglectus seems to be an excellent
vector of T. cruzi; and when tested for its use in xenodiagnostics it was found that it was more
efficient than T. infestans (Forattini et al. 1976). Thus in the need of massive laboratory rearing the
population parameters can be used to optimize bug production of this species. Additionally
(Forattini et al. 1977) found that 47% of 23 insects collected in extra-domiciliary habitats were
positive for T. cruzi, and as R. neglectus is in the process of becoming a truly domestic species
(Lent and Wygodzinsky 1979, Forattini et al. 1984) the application of the population parameters
15
here estimated is decisive in anticipating control measures. For example, as stated by Chaves et al.
(2004) in relation to R. prolixus, the mortality rate of this triatomine vector has epidemiological
importance through the demography of their populations.
As a stable stage distribution (SSD) implies a well established colony (sylvatic or domiciliary), it
will be extremely useful to evaluate the damping ratio () of other triatomine species, in order to
compare their relative times of convergence to SSD as an indicator of the effectiveness of vector
control measures. In view of the global climatic change taking place, and its consequences in
terms of new geographic ranges of triatomine species, this kind of studies gain more and more
importance for the epidemiology of Chagas disease, so we encourage new studies to calculate
these parameters in other triatomine species.
Acknowledgements
Rodolfo Carcavallo (deceased) kindly provided the original specimens for starting the colony of R.
neglectus. C. Stubben kindly advised on the usage of package “popbio” in R language.
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Guarneri, A. A., C. J. Carvalho Pinto, C. J. Schofield, and M. Steindel. 1998. Population Biology
of Rhodnius domesticus Neiva & Pinto 1923 (Hemiptera: Reduviidae) under Laboratory
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Lefkovitch, L. P. 1965. The Study of Population Growth in Organisms Grouped by Stages.
Biometrics 21: 1-18.
Lent, H., and P. Wygodzinsky. 1979. Revision of the Triatominae (Hemiptera, Reduviidae), and
their significance as vectors of chagas' disease. Bull. Am. Mus. Nat. Hist. 163: 123-520.
Lent, H., R. U. Carcavallo, A. Martínez, I. Galíndez Girón, J. Jurberg, C. Galvao, and D. M.
Canale. 1998. Anatomic relationships and characterization of the species. pp. 245-264. Volume I.
Chapter 5. In: R. U. Carcavallo, I. Galíndez Girón, J. Jurberg and H. Lent (eds.). Atlas of Chagas'
Disease Vectors in the Americas. Editorial Fiocruz, Rio de Janeiro, Brasil.
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and Fertility of Panstrongylus megistus (Burm. , 1835) in the Laboratory. Mem. Inst. Oswaldo
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Med. Trop. 11: 63-66.
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Scientific Publications No. 318.
19
Monteiro, F. A., D. M. Wesson, E. M. Dotson, C. J. Schofield, and C. B. Beard. 2000. Phylogeny
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20
Appendix
Definition of terms and formulae used in the calculation of vital statistics and
population parameters of Rhodnius neglectus.
I. Terms and formulae used in the Life Table calculations
Symbol
B
Name and/or Definition
Instantaneous birth-rate
d
Tx
Instantaneous death-rate
Number of days yet to live to females aged
x
Expectation of life or average future
lifetime
Number of weeks lived by the cohort
between ages x and x+l
Probability of an individual
being alive at the end of age x
Age-specific fecundity (eggs/♀/week)
♀age-specific fecundity (♀eggs/♀/week)
Individuals alive at the end of age x
Sex ratio
Intrinsic rate of natural increase
e
Lx
lx
mx
m’x
Nx
p
r0
R0
Net reproduction rate
Calculation
(r0  ) /( e r0  1)
b-r0
 Lx
x
Tx / lx
(lx + lx+1) / 2
Nx / N0
Observed value
mx p
Observed value
♀/(♀+♂)
Solving  lx m' x e  r0 x  1
 lx m' x
x
x
T
vx
Generation time
Age-specific reproductive value
x
Age in weeks
Female’s first age of egg laying
Finite birth rate


loge(R0)/r0
e r0 x  r0 x
 e l x mx
l x x
Observed value
Observed value
1 /  l x e r0 x1
x


Finite rate of increase or reproduction rate
Female’s last age of egg laying
r0
e
Observed value
II. Terms and formulae used in the Leslie and Lefkovitch matrices calculations
In the Leslie matrix analyses of age-structured populations, the net reproductive rate R0 follows the
classical definition of a measure of the replacement rate of a population, i.e., the average number
of individuals replaced by one individual after one generation time (T); it can also be thought of as
the mean number of offspring produced by a single newborn individual during its lifetime
(Stubben and Milligan 2007).
21
The generation time (T) for a population has been defined in different ways; the classical
definition based upon the age-specific life table analysis considers T to be the average time
between two successive generations. This is simple in populations with strictly discrete
generations, but is more complicated when generations overlap. For the latter case the equivalent
to the discrete generation time was defined algebraically by demographers (Dublin and Lotka
1925) as (see section I of this Appendix):

T
 x lx mx
x 

 lx mx
x 
where x represents age, lx and mx are the age-specific survival and maternity functions, and  and
 are the first and last age of reproduction.
Laughlin (1965) proposes still another interpretation of generation time as the average age of the
individuals of a population such that if all the reproductive effort would be concentrated at that age
the net reproductive rate R0 would be same (assuming a stable age distribution). Laughlin (1965)
calls this the “mean age-of-mother-at-birth-of-offspring”, and relates to R0 and the population
growth parameter rc by:
rc 
log R0
Tc
Where antilog(rc) gives the number of times a population multiplies itself per unit time; Laughlin
(1965) calls rc the “capacity for increase” and recommends this parameter instead of r0 for studies
such as comparative demography.
However, in terms of a stage-structured population (one egg stage, five developmental instars and
the adult, for the case of triatomines), the generation time is defined as the time required for a
population to increase by a factor of R0 (Stubben and Milligan 2007, Caswell 1989); to
differentiate it from the classical T definition the values obtained from this definition as used in the
“popbio” package, we have identified it with the notation of T’. The generation time based upon
the stage-structured transition matrix is calculated using the finite rate of population growth as:
T '   ii i
i
where i= P1 P2 … Pi-1 Fi, i represents the age and  is the finite rate of population growth, which
results in a generation time lower than the one calculated from the life table.
The damping ratio () is proportional to the convergence to the SSD (Ebert 1999); it is a ratio
between the dominant real eigenvalue and the modulus of the largest subdominant eigenvalue (=
1/|2|)) of the characteristic equation of a stage-structured matrix. It is an indicator of how rapidly
a population would return to the SSD if perturbed.
22
Table 1. Development time, mortality, reproductive features, and sex ratio of R. neglectus. Development time is in
weeks, with standard deviation and N given in parenthesis. Sex ratio (♀/(♂+♀)) was determined at time of adult
emergence; in parenthesis the number of females and males are given separated by a colon. Average and standard
deviation (in parenthesis) of reproductive features were based on a number of observations given by the number of
reproductive weeks. The average adult longevity includes in parenthesis the standard deviation, with the minimum and
maximum values after the semicolon and separated by a dash.
Cohort
Cohort statistics
Std.
Coeff
1
2
3
4
5
Mean
Dev. Var (%)
Development time
Egg
2.4
1.9
2.3
2.3
2.3
2.22
0.20
9.13
2.1
1.4
1.9
2.7
1.5
Instar I
1.91
0.49 25.84
(0.377;86) (0.723;95) (0.764;92) (0.752;96) (0.687;92)
2.3
2.5
2.3
2.4
2.5
Instar II
2.40
0.12
5.08
(0.493;72) (0.735;91) (0.562;84) (0.617;88) (0.611;84)
2
2.1
2.2
2.5
2.1
Instar III
2.18
0.19
8.71
(0.12;70) (0.317;85) (0.544;74) (0.595;80) (0.309;76)
2
2.2
3.2
2.8
2.2
Instar IV
2.49
0.49 19.72
(0.204;70) (0.472;85) (1.241;72) (1.328;77) (0.481;73)
3.6
3.4
4.1
4.6
3.5
Instar V
3.83
0.49 12.72
(0.753;70) (0.585;83) (0.79;72) (1.386;74) (0.805;72)
Egg to adult
14.4
13.5
15.9
17.2
14.1
15.03 1.41 10.99
Mortality (%)*
Egg
14
5
8
4
8
7.80
3.90 49.98
Instar I
16.28
4.21
8.7
8.33
8.7
9.24
4.37
47.24
Instar II
2.78
6.59
11.9
9.09
9.52
7.98
3.46
43.42
Instar III
0
0
2.7
3.75
3.95
2.08
1.96
94.08
Instar IV
0
2.35
0
3.9
1.37
1.52
1.66
108.74
Instar V
2.86
2.41
9.72
21.62
2.78
7.88
8.27
104.95
Instar I to adult
20.93
14.74
29.35
39.58
23.91
25.70
9.38
36.51
42
30
31.60
8.38
26.53
15
15
15.4
0.55
3.56
63
67
64.40
3.21
4.98
Egg to adult
32
Age of first reproduction by cohort
16
19
35
Reproduction
15
16
Reproductive weeks by cohort
60
64
Total eggs laid by cohort
68
25,428
30,121
24,005
26,885
26,976 26,683 2,274.49
38.57
46.36
44.72
50.47
46.71
45.37 4.34
Reproductive weeks /♀
(17.37)
(15.99)
(15.29)
(13.64)
(16.91) (15.84) 1.47
20.80
18.26
16.99
19.19
15.01
Eggs/♀/week
18.05 2.20
(7.94)
(9.90)
(9.83)
(11.55)
(8.58)
9.18
7.22
7.58
7.28
6.65
♀ eggs/♀/week
7.58
0.95
(3.50)
(3.91)
(4.39)
(4.38)
(3.80)
0.441
0.395
0.446
0.379
0.443
Sex ratio
0.42
0.03
(30,38)
(32,49)
(29,36)
(22,36)
(31,39)
♀ adult mean longevity
39.53
42.78
46.21
47.09
50.19
45.16 4.11
(15.2;8-58) (14.9;3-60) (17.4;1-70) (15.2;5-70) (15.5;10-71)
♂ adult mean longevity
31.63
34.94
37.94
32.75
41.26
35.70 3.93
(9.1;10-45) (11.6;7-56) (13.3;2-53) (11.8;5-50) (11.4;16-60)
* Relative mortality within each stage i (Ni / Ni-1), where N is the number of individuals entering each stage.
8.52
9.57
9.28
12.17
12.59
7.45
9.09
11.01
23
Table 2. Demographic and population growth parameters of R. neglectus. Parameters were
calculated based upon a 1-week time unit. SSD represents “stable stage distribution”. The values
of , r0, R0 and of T were calculated from the age-structured life table; the values of ', r’0, R0 and
of T’ were calculated from the stage-structured matrix A’. See Appendix for differences in their
calculations. Reproductive values of eggs are always one, and have not been included. See
Appendix for definitions and interpretation.
Cohort
1
2
3
4
5
Finite rate of population increase ()
1.21
1.23
1.19
1.20
1.23
Cohort statistics
Std.
Coeff
Mean
Dev.
Var (%)
1.21
0.02
1.24
Finite rate of population increase (')
1.25
1.23
1.24
1.24
1.23
1.24
0.01
0.45
Intrinsic rate of natural increase (r0)
0.19
0.20
0.18
0.18
0.20
0.19
0.01
6.50
Intrinsic rate of natural increase (r’0)
0.22
0.21
0.21
0.22
0.21
0.21
0.004
2.11
Replacement rate (R0)
248.66
294.08
236.02
266.85
266.52
262.43
21.94
8.36
Replacement rate (R’0)
133.07
108.73
119.31
122.03
109.91
118.61
9.93
8.37
Generation time (T)
40.30
38.50
39.18
41.23
39.71
39.78
1.04
2.62
Generation time (T')
22.28
22.50
22.40
22.35
22.44
22.39
0.09
0.38
Instantaneous birth rate (b)
0.27
0.27
0.25
0.24
0.28
0.26
0.02
6.25
Instantaneous mortality rate (d)
0.08
0.07
0.07
0.06
0.07
0.07
0.01
10.90
Reproductive value
Instar I
1.55
1.52
1.53
1.54
1.52
1.53
0.01
0.91
Instar II
3.35
3.20
3.27
3.28
3.21
3.26
0.06
1.84
Instar II
5.34
4.99
5.15
5.19
5.01
5.14
0.14
2.76
Instar IV
8.29
7.58
7.89
7.97
7.61
7.87
0.29
3.68
Instar V
12.86
11.50
12.10
12.25
11.57
12.06
0.56
4.61
Female adult
31.90
27.28
29.32
29.78
27.44
29.15
1.90
6.51
Damping ratio ()
1.13
1.13
1.13
1.13
1.13
1.13
0.0005
0.04
Stable stage distribution (SSD)
Egg
0.42
0.40
0.41
0.41
0.40
0.41
0.01
1.39
Instar I
0.25
0.25
0.25
0.25
0.25
0.25
0.001
0.49
Instar II
0.12
0.12
0.12
0.12
0.12
0.12
0.001
0.44
Instar II
0.08
0.08
0.08
0.08
0.08
0.08
0.001
1.36
Instar IV
0.05
0.05
0.05
0.05
0.05
0.05
0.001
2.26
Instar V
0.05
0.06
0.06
0.05
0.06
0.06
0.002
3.49
Female adult
0.03
0.04
0.03
0.03
0.04
0.03
0.002
6.34
24
Table 3. Elasticities of matrix elements aij for R. neglectus. The matrix element names and
descriptions correspond to the ones given for matrix A’ in the Materials and Methods section, and
the matrix element values correspond to the stage structured population transition matrix presented
in the Results section. The table was sorted from largest to smallest by the matrix elements
elasticities.
Matrix
element
identification
a77
a66
a21
a32
a43
a54
a65
a76
a17
a11
a44
a55
a33
a22
Matrix
element
name
s7
s6
g1
g2
g3
g4
g5
g6
f7
s1
s4
s5
s3
s2
Matrix element description
Adult female survival
Proportion remaining as instar V
Proportion of eggs hatched
Proportion molting from instar I to II
Proportion molting from instar II to III
Proportion molting from instar III to IV
Proportion molting from instar IV to V
Proportion molting from instar V to ♀
Average ♀ eggs/♀/week
Proportion remaining as egg
Proportion remaining as instar III
Proportion remaining as instar IV
Proportion remaining as instar II
Proportion remaining as instar I
Matrix
element
value
0.955
0.818
0.449
0.347
0.439
0.449
0.449
0.175
7.224
0.551
0.502
0.547
0.551
0.818
Matrix
element
elasticity
0.2153
0.1214
0.0606
0.0606
0.0606
0.0606
0.0606
0.0606
0.0606
0.0495
0.0495
0.0495
0.0488
0.0420
25
Table 4. Population parameters of five species of the genus Rhodnius selected for comparison with
this study (highlighted in bold) because they had been estimated under similar experimental
conditions. The species are presented sorted from bigger to smaller intrinsic rate of natural
increase (r0) values (on a per/week basis).
Environmental condition
Species
Mean
temperature
(C)
Relative
humidity (%)
Food
source
Population parameter
Intrinsic
rate of
Population Generation
natural
replacement
time
increase
rate (R0)
(wk)
(r0)
Data source
Rodríguez and
R. prolixus*
27
80
Hen
0.298
42.0
22.2
Rabinovich 1980
R. prolixus
27
65
Rat
0.244
Pippin 1970
R. neivai
27
60
Hen
0.235
30.5
20.9
Cabello et al. (1988)
R. neivai
27
60
Rabbit
0.202
41.6
26.3
Cabello et al. (1988)
R. domesticus
28
75
Rat
0.195
10.1
34.9
Guarneri et al. (1998)
R. neglectus**
27
80
Hen
0.188
45.3
39.8
This study
R. robustus**
27
80
Hen
0.1690
18.8
34.0
Rabinovich (unpubl.)
R. prolixus***
27
80
Hen
0.1688
6.6
22.5
Rabinovich (unpubl.)
R. nasutus**
27
80
Hen
0.121
12.8
43.4
Rabinovich (unpubl.)
R. neivai**
27
80
Hen
0.098
4.8
38.5
Rabinovich (unpubl.)
* Seven experimental densities were used in this study, but the value here presented corresponds to the smallest
density used (2 individuals/jar).
** Average of five cohorts.
*** Average of five cohorts of first generation of field-captured individuals.
26
Figure Legends
Fig. 1. Age- and stage-structured life-history graphs for a general triatomine. (a) Age-structured
graph, where Pi is the probability of transferring to the next age in one time unit, and FA is the
fertility of all adult individuals of any age as imagoes, (b) stage-structured graph; as the main
difference with the age-structured graph, all individuals have a given probability of transferring
(alive) from stage i to the next stage i+1 (gi) and also a probability of staying (alive) in the same
stage i (si). fA represents the adult stage specific fecundity value; (c) same as (b), but as in any
stage the probability of moving to the next stage is sensitive to the population growth rate, a
correction is applied (called the Z-transform of a Lefkovitch matrix) by dividing all the elements
of the transition matrix A’ (i.e., si, gi and fi) by the finite population growth rate ().
Fig. 2. Weekly age-specific survival (proportion surviving from the egg stage to age x) and agespecific maternity curve (average ♀ eggs/♀/week) of R. neglectus from the average among five
cohorts.
Fig. 3. Stable stage distribution of a R. neglectus population calculated from the stage-structured
matrix A’, with A’ elements based on the average of five cohorts.
Fig. 4. Stage-specific reproductive value of R. neglectus, calculated from the stage-structured
matrix A’, with A’ elements based on the average of five cohorts.
Fig. 5. Mean development time (weeks) of the eggs and the nymphal instars of R. neglectus from
Mello (1977), Silva and Silva (1988), Silva et al. (2001), Diotaiuti and Pinto Días (1987), Freitas
et al. (1967), and this study. Vertical bars are one standard deviation; in the Silva and Silva (1988)
data they are extremely small (0.000, 0.036, 0.000, 0.055, 0.071, and 0.103) and vertical bars do
not show clearly. Data values are shown slightly shifted to avoid symbol overlapping.
Fig. 6. Stage mortality (%) of the eggs and the various nymphal instars of R. neglectus from Mello
(1977), Silva et al. (2001), Diotaiuti and Pinto Días (1987), Freitas et al. (1967), and this study.
Standard deviations were not provided by previous publications. Vertical bars on data of this study
are one standard deviation. Data values are shown slightly shifted to avoid symbol overlapping.
Fig. 7. Intrinsic rate of natural increase (r0) of R. neglectus and five other species of the genus
Rhodnius estimated under very similar experimental conditions, ranked from largest to smallest r0.
The images are shown proportional to the total average length of each species, and indicated by its
value (in mm), as given by Lent at al. (1998).
Fig. 8. Female longevity (weeks) and female reproductive potential (average total number of eggs
per female per life and average number of female eggs per day) of R. neglectus and five other
species of the genus Rhodnius reared under very similar experimental conditions. The species were
ranked from largest to smallest according to the average number of total eggs per female per life.
Fig. 9. Fit of the logistic population growth model to natural populations of R. neglectus that
colonized spontaneously artificial chicken coops placed near peridomiciles in Brazil (field data
from Forattini et al. 1983a). In chicken coop a2 R. neglectus developed in co-existence with T.
sordida; in chicken coop f1 R. neglectus developed without competition with other triatomine
species.
27
Fig. 1.
a
FA
P1
Age 1
(♀ Egg)
Age 2
Age n-1
b
gE
♀ Egg
sE
Age n
fA
1st
instar
g1
s1
2nd
instar
g2
s2
3rd
instar
g3
s3
4th
instar
g4
s4
5th
instar
g5
s5
♀
adult
sA
fAλ-1
c
gE λ-1
Pn-1
P2
♀ Egg
1st
instar
sEλ-1
s1λ-1
g1 λ-1
2nd
instar
s2λ-1
g2 λ-1
3rd
instar
s3λ-1
g3 λ-1
4th
instar
s4λ-1
g4 λ-1
5th
instar
s5λ-1
g5 λ-1
♀
adult
sAλ-1
lx (proportion surviving from the egg stage)
0.8
0.6
0.4
0.2
mx (female eggs/female/week)
28
Fig. 2.
1.0
lx
mx
0.0
0
10
20
30
40
50
60
x (age in weeks)
70
80
90
100
29
Fig. 3.
0.5
Stable age distribution (SAD)
0.4
0.3
0.2
0.1
0.0
Egg
Instar 1
Instar 2
Instar 3
Instar 4
Instar 5
Female adult
30
Fig. 4.
30
Stage-specific reproductive value
25
20
15
10
5
0
Instar 1
Instar 2
Instar 3
Instar 4
Instar 5
Female adult
31
Fig. 5.
Development time (weeks)
8
7
6
5
4
3
2
1
0
-1
0
1
2
3
4
5
Developmental stage (0= Eggs; 1- 5= instars)
Mello (1977)
Silva & Silva (1988)
Silva et. al (2001)
This study
Diotaiuti & Pinto Días (1987)
Freitas et al. (1967)
6
32
Fig. 6
35
Stage mortality (%)
30
25
20
15
10
5
0
-1
0
1
2
3
4
5
Developmental stage (0= Eggs; 1- 5= instars)
Mello (1977)
Silva et. al (2001)
This study
Diotaiuti & Pinto Días (1987)
Freitas et al. (1967)
6
33
0.25
(r0 ) (on a weekly basis)
Intrisic rate of natural increase
Fig. 7.
0.20
19.5
16.5
0.15
19
19
23
15
0.10
prolixus
domesticus
neglectus
neivai
Rhodnius species
rob ustus
nasutus
34
50
45
1000
900
40
35
30
800
700
600
25
20
15
10
500
400
300
200
5
0
100
0
neglectus
neivai
prolixus
robustus domesticus
nasutus
Rhodnius species
Female longevity (weeks)
Female eggs/female/day
Total eggs/female/life
Total eggs/female/life
Longevity and Female
eggs/female/day
Fig. 8.
35
Fig. 9
300
Chicken coop a2
Totral population
250
200
150
100
Observed
Logistic model
50
0
0
1
450
2
3
4
5
Trimester
6
7
8
9
10
Chicken coop f1
Total population
400
350
300
250
200
150
100
Observed
Logistic model
50
0
0
1
2
3
4
5
Trimester
6
7
8
9
10
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