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1 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. * 2 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 3 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 4 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 5 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: 6 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 n1 g1 s2 0 0 g2 0 s n1 0 0 g n1 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 , 7 (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 8 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 9 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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Nat. 113: 511-530. 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 x1 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 ' ii 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