Lifetime growth in wild meerkats: incorporating life history and environmental factors into a standard growth model

Lifetime records of changes in individual size or mass in wild animals are scarce and, as such, few studies have attempted to model variation in these traits across the lifespan or to assess the factors that affect them. However, quantifying lifetime growth is essential for understanding trade-offs between growth and other life history parameters, such as reproductive performance or survival. Here, we used model selection based on information theory to measure changes in body mass over the lifespan of wild meerkats, and compared the relative fits of several standard growth models (monomolecular, von Bertalanffy, Gompertz, logistic and Richards). We found that meerkats exhibit monomolecular growth, with the best model incorporating separate growth rates before and after nutritional independence, as well as effects of season and total rainfall in the previous nine months. Our study demonstrates how simple growth curves may be improved by considering life history and environmental factors, which may be particularly relevant when quantifying growth patterns in wild populations.     

Climate and mammalian life histories

Mammals display considerable geographical variation in life history traits. To understand how climatic factors might influence this variation, we analysed the relationship between life history traits – adult body size, litter size, number of litters per year, gestation length, neonate body mass, weaning age and age at sexual maturity – and several environmental variables quantifying the seasonality and predictability of temperature and precipitation across the distribution range of five terrestrial mammal groups. Environmental factors correlated strongly with each other; therefore, we used principal components analysis to obtain orthogonal climatic predictors that could be used in multivariate models. We found that in bats, primates and even‐toed ungulates adult body size tends to be larger in species inhabiting cold, dry, seasonal environments, whereas in carnivores and rodents a smaller body size is characteristic of warm, dry environments, suggesting that low food availability might limit adult size. Species inhabiting cold, dry, seasonal habitats have fewer, larger litters and shorter gestation periods; however, annual fecundity in these species is not higher, implying that the large litter size of mammals living at high latitudes is probably a consequence of time constraints imposed by strong seasonality. On the other hand, the number of litters per year and annual fecundity were greater in species inhabiting environments with higher seasonality in precipitation. Lastly, we found little evidence for specific effects of environmental variability. Our results highlight the complex effects of environmental factors in the evolution of life history traits in mammals. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 111 , 719–736.     

Many lifetime growth trajectories for a single mammal

Despite their importance in shaping life history tactics and population dynamics, individual growth trajectories have only been rarely explored in the wild because their analysis requires multiple measurements of individuals throughout their lifetime and some knowledge of age, a key timer of body growth. The availability of long‐term longitudinal studies of two wild boar populations subjected to contrasting environments (rich vs. poor) provided an opportunity to analyze individual growth trajectories. We quantified wild boar growth trajectories at both the population and the individual levels using standard growth models (i.e., Gompertz, logistic, and monomolecular models) that encompass the expected range of growth shapes in determinate growers. Wild boar is a rather altricial species, with a polygynous mating system and is strongly sexually dimorphic in size. According to current theories of life history evolution, we thus expect wild boar to display a sex‐specific Gompertz type growth trajectory and lower sexual size dimorphism in the poorer environment. While wild boar displayed the expected Gompertz type trajectory in the rich site at the population level, we found some evidence for potential differences in growth shapes between populations and individuals. Asymptotic body mass, growth rate and timing of maximum growth rate differed as well, which indicates a high flexibility of growth in wild boar. We also found a cohort effect on asymptotic body mass, which suggests that environmental conditions early in life shape body mass at adulthood in this species. Our findings demonstrate that body growth trajectories in wild boar are highly diverse in relation to differences of environmental context, sex and year of birth. Whether the intermediate ranking of wild boar along the precocial–altricial continuum of development at birth may explain the ability of this species to exhibit this high diversity of growth patterns remains to be investigated.     

Shapes and functions of bird-growth models: how to characterise chick postnatal growth

We compare four candidate models (logistic, Gompertz, von Bertalanffy, and extreme value function) for modelling the growth of birds. We fitted the models to two empirical data sets of chick growth (six biometric measurements) of African black oystercatchers Haematopus moquini from South Africa and little stints Calidris minuta from Russia, and identified the best-fitting growth curves by Akaike's information criterion. We also determine fitted and derived parameters, including the relative value (size) at hatching, the placement of inflection, the (normalised) growth rate constant, and the adult value (upper asymptote). The preferred model together with these factors describes how fast (or abruptly) the curves asymptote, and illustrates why growth is poorly characterised by the growth rate constant alone. Though the extreme value function model has not (as far as we know) been applied to chick growth data before, it appears to return the best fit for some parameters in our data sets. For example, we found that in African black oystercatchers two very different models best characterise two of the measurements: the extreme value function model and the Bertalanffy model for tarsus growth and body mass growth, respectively. In addition, we discuss the usefulness of fixing the upper asymptote to the adult value (e.g., adult body mass) and recommend a fixed upper asymptote in most cases.     

The maximum attainable body size of herbivorous mammals: morphophysiological constraints on foregut,and adaptations of hindgut fermenters

An oft-cited nutritional advantage of large body size is that larger animals have lower relative energy requirements and that, due to their increased gastrointestinal tract (GIT) capacity, they achieve longer ingesta passage rates, which allows them to use forage of lower quality. However, the fermentation of plant material cannot be optimized endlessly; there is a time when plant fibre is totally fermented, and another when energy losses due to methanogenic bacteria become punitive. Therefore, very large herbivores would need to evolve adaptations for a comparative acceleration of ingesta passage. To our knowledge, this phenomenon has not been emphasized in the literature to date. We propose that, among the extant herbivores, elephants, with their comparatively fast passage rate and low digestibility coefficients, are indicators of a trend that allowed even larger hindgut fermenting mammals to exist. The limited existing anatomical data on large hindgut fermenters suggests that both a relative shortening of the GIT, an increase in GIT diameter, and a reduced caecum might contribute to relatively faster ingesta passage; however, more anatomical data is needed to verify these hypotheses. The digestive physiology of large foregut fermenters presents a unique problem: ruminant-and nonruminant-forestomachs were designed to delay ingesta passage, and they limit food intake as a side effect. Therefore, with increasing body size and increasing absolute energy requirements, their relative capacity has to increase in order to compensate for this intake limitation. It seems that the foregut fermenting ungulates did not evolve species in which the intake-limiting effect of the foregut could be reduced, e.g. by special bypass structures, and hence this digestive model imposed an intrinsic body size limit. This limit will be lower the more the natural diet enhances the ingesta retention and hence the intake-limiting effect. Therefore, due to the mechanical characteristics of grass, grazing ruminants cannot become as big as the largest browsing ruminant. Ruminants are not absent from the very large body size classes because their digestive physiology offers no particular advantage, but because their digestive physiology itself intrinsically imposes a body size limit. We suggest that the decreasing ability for colonic water absorption in large grazing ruminants and the largest extant foregut fermenter, the hippopotamus, are an indication of this limit, and are the outcome of the competition of organs for the available space within the abdominal cavity. Our hypotheses are supported by the fossil record on extinct ruminant/tylopod species which did not, with the possible exception of the Sivatheriinae, surpass extant species in maximum body size. In contrast to foregut fermentation, the GIT design of hindgut fermenters allows adaptations for relative passage acceleration, which explains why very large extinct mammalian herbivores are thought to have been hindgut fermenters.     

The influence of local environment on the aging and mortality ofAedes aegypti (L.): Case study in Fortaleza‐CE,Brazil

It is generally assumed that the daily probability of survival of mosquitoes is independent of age. To test this assumption we have conducted a three‐year experimental fieldwork study (2005–2007) at Fortaleza‐CE in Brazil, determining daily survival rates of the dengue vector Aedes aegypti (L.). Survival rates of adult Ae. aegypti may be age‐dependent and the statistical analysis is a sensitive approach for comparing patterns of mosquito survival. The mosquito survival data were better fit by a Weibull survival function than by the more traditionally used Gompertz or logistic survival functions. Gompertz, Weibull, or logistic survival functions often fit the survival, and the tails of the survival curves usually appear to fall between the values predicted by the three functions. We corroborate that the mortality of Ae. aegypti in semi‐natural conditions may no more be considered as a constant phenomenon during the life of adult mosquitoes but varies according to the age and environmental conditions under a tropical climate. This study estimates the variability in the survival rate of Ae. aegypti and environmental factors that are related to such variability. The statistical analysis shows that the fitting ability, concerning the hazard function, was in decreasing order: Seasonal Cox, the three‐parameter Gompertz, and the three‐parameter Weibull, that was similar to the three‐parameter logistic. The advantage of using the Cox model is that it is convenient for exploring the relationship between survival and several explanatory variables. The Cox model has the advantage of preserving the variable in its original quantitative form and of using a maximum of information. The survival analyses indicate that mosquito mortality is both age‐ and environment‐dependent.     

Evaluation of the growth rate of MCF-7 breast cancer multicellular spheroids using three mathematical models

Abstract. Growth data on 60 multicellular spheroids of MCF-7 human breast cancer cells were fitted, on an individual basis, by the Gompertz, Bertalanffy and logistic equations. MCF-7 spheroids, initiated and grown in medium containing oestrogens, exhibited a growth rate that decreased continuously as spheroid size increased. Plots of spheroid volume v. time generated sigmoid curves that showed an early portion with an approximately exponential volume increase; a middle region or retardation phase characterized by a continuously decreasing growth rate; and, finally, a late segment or plateau phase approaching zero growth rate, that permitted an estimate of the maximum spheroid size (V_max). Growth curves generated by MCF-7 spheroids under different experimental conditions (hormones, drugs and radiation exposures) can be compared after normalization. Linearized forms of the fitted Gompertz curves provided a convenient way to express differences in growth rate.     

Characterization of commercial and biological growth curves in the Segureña sheep breed

Non-linear models were analysed to describe both the biological and commercial growth curves of the Segureña sheep, one of the most important Spanish breeds. We evaluated Brody, von Bertalanffy, Verhulst, logistic and Gompertz models, using historical data from the National Association of Segureña Sheep Breeders (ANCOS). These records were collected between 2000 and 2013, from a total of 129 610 weight observations ranging from birth to adulthood. The aim of this research was to establish the mathematical behaviour of body development throughout this breed’s commercial life (birth to slaughter) and biological life (birth to adulthood); comparison between both slopes gives important information regarding the best time for slaughter, informs dietary advice according to animals’ needs, permits economical predictions of productions and, by using the curve parameters as selection criteria, enables improvements in growth characteristics of the breed. Models were fitted according to the non-linear regression procedure of statistical package SPSS version19. Model parameters were estimated using the Levenberg–Marquardt algorithm. Candidate models were compared using the determinative coefficient, mean square error, number of iterations, Akaike information coefficient and biological coherence of the estimated parameters. The von Bertalanffy and logistic models were found to be best suited to the biological and commercial growth curves, respectively, for both sexes. The Brody equation was found to be unsuitable for studying the commercial growth curve. Differences between the parameters in both sexes indicate a strong impact of sexual dimorphism on growth. This can emphasize the value of the highest growth rate for females, indicating that they reach maturity earlier.     

Growth rates and body condition factors of Alligator mississippiensis in coastal Louisiana wetlands: A comparison of wild and farm-released juveniles

• 1.1. Growth rates and body condition factors for native wild and captive-raised juvenile alligators (Alligator mississippiensis) that had been released to the wild were studied using tag-recapture methods for 274 alligators over a 4-year period. Alligators were grouped by sex, size class, source (farm-released vs native wild) and as to whether they had overwintered or not.
• 2.2. In most groups, the farm-released alligators grew significantly better than wild alligators matched for sex and size; in the remaining groups the post-release alligators grew as well as their counterparts, though not better.
• 3.3. Overwintering tended to slow growth rates in both groups, but farm-released alligators still demonstrated superior growth over native wild alligators even after overwintering.
• 4.4. Males tended to grow faster than females, though this trend was not always significantly greater. In no matched group did females grow faster than males.
• 5.5. Growth rates diminished with increasing size in native wild alligators (smaller alligators grew faster), but growth rates of farm-released alligators remained accelerated even at the larger size classes.
• 6.6. Growth curves were constructed using known recapture data with three growth models (von Bertlanffy, Gompertz and logistic); the calculated maximum attainable length and growth parameters were significantly larger (P < 0.01) for farm-released alligators than wild using all three models.
• 7.7. Body condition factors were not different in captive-raised post-released alligators than native wild alligators.

     

Structured latent growth curves for twin data.

We describe methods to fit structured latent growth curves to data from MZ and DZ twins. The well-known Gompertz, logistic and exponential curves may be written as a function of three components - asymptote, initial value, and rate of change. These components are allowed to vary and covary within individuals in a structured latent growth model. Such models are highly economical, requiring a small number of parameters to describe covariation across many occasions of measurement. We extend these methods to analyse longitudinal data from MZ and DZ twins and focus on the estimation of genetic and environmental variation and covariation in each of the asymptote, initial and rate of growth factors. For illustration, the models are fitted to longitudinal Bayley Infant Mental Development Scale data published by McArdle (1986). In these data, all three components of growth appear strongly familial with the majority of variance associated with the shared environment; differences between the models were not great. Occasion-specific residual factors not associated with the curve components account for approximately 40% of variance of which a significant proportion is additive genetic. Though the growth curve model fit less well than some others, they make restrictive, falsifiable predictions about the mean, variance and twin covariance of other (not yet measured) occasions of measurement.     

Female fecundity and early offspring growth in the guppy, <Emphasis Type="Italic">Poecilia reticulata</Emphasis>

We examined the relationships between family (female parentage), body size of females, brood retention time between mating and parturition, female fecundity, and early growth of offspring in the guppy Poecilia reticulata. Mature, virgin females from a single brood were mated with a single male. Results of generalized linear models indicate that the effect of the family on female fecundity and offspring growth was significant, which suggested that these traits are genetically determined to a certain extent. Larger females at the time of mating produced larger broods, although female body size at the time of parturition did not affect brood size, in contrast to the results of some previous studies in guppies. Brood size was negatively associated with the body size of neonates. Results highlighted significant associations between brood retention time and female fecundity as well as offspring growth. In addition, the interaction between the family and brood retention time was significantly associated with female fecundity and offspring growth. Females of some families had longer retention times of larger broods, whereas those of other families had shorter retention times of smaller broods. On the other hand, females with longer brood retention times produced smaller neonates with slower growth. Since the family also affected the brood retention time, selection may work against the duration of brood retention of females via the size, growth and number of offspring, depending on environmental factors such as the intensity of predation or competition in neonates.     

Geographical range expansion of alien birds and environmental matching

The international wildlife trade is a significant source of introduced alien species, some of which proceed to become invasive and cause negative environmental and economic effects. However, not all introduced aliens establish viable populations, and it is important to identify the factors that determine establishment success. We explore the role of environmental suitability (including anthropogenic influences, climate and habitat types) in the establishment success of alien bird species introduced to Taiwan. Using maximum entropy modelling, we employed a recursive feature elimination and Akaike information criterion (AIC)‐based stepwise model selection approach to assess whether the environmental suitability, native range size, body size, residence time and the numbers of birds for sale in the shops affect variation in the extent of alien bird range size in Taiwan. We show that species with larger native range sizes and larger body sizes tend to have larger alien range sizes in Taiwan. There was no effect of environmental suitability on alien range size in Taiwan, but environmental suitability influenced the establishment success of bird species there.     

Length of activity season drives geographic variation in body size of a widely distributed lizard

Understanding the factors that drive geographic variation in life history is an important challenge in evolutionary ecology. Here, we analyze what predicts geographic variation in life‐history traits of the common lizard, Zootoca vivipara, which has the globally largest distribution range of all terrestrial reptile species. Variation in body size was predicted by differences in the length of activity season, while we found no effects of environmental temperature per se. Females experiencing relatively short activity season mature at a larger size and remain larger on average than females in populations with relatively long activity seasons. Interpopulation variation in fecundity was largely explained by mean body size of females and reproductive mode, with viviparous populations having larger clutch size than oviparous populations. Finally, body size‐fecundity relationship differs between viviparous and oviparous populations, with relatively lower reproductive investment for a given body size in oviparous populations. While the phylogenetic signal was weak overall, the patterns of variation showed spatial effects, perhaps reflecting genetic divergence or geographic variation in additional biotic and abiotic factors. Our findings emphasize that time constraints imposed by the environment rather than ambient temperature play a major role in shaping life histories in the common lizard. This might be attributed to the fact that lizards can attain their preferred body temperature via behavioral thermoregulation across different thermal environments. Length of activity season, defining the maximum time available for lizards to maintain optimal performance, is thus the main environmental factor constraining growth rate and annual rates of mortality. Our results suggest that this factor may partly explain variation in the extent to which different taxa follow ecogeographic rules.     

A stochastic discrete generation birth,continuous death population growth model and its approximate solution

This paper describes a single species growth model with a stochastic population size dependent number of births occurring at discrete generation times and a continuous population size dependent death rate. An integral equation for a suitable transformation of the limiting population size density function is not in general soluble, but a Gram-Charlier representation procedure, previously used in storage theory, is successfully extended to cover this problem. Examples of logistic and Gompertz type growth are used to illustrate the procedure, and to compare with growth models in random environments. Comments on the biological consequences of these models are also given.Currently at Department of Mathematics, University of MarylandWork partially supported by the Danish Natural Science Research Council and Monash University     

Scaling of Soaring Seabirds and Implications for Flight Abilities of Giant Pterosaurs

The flight ability of animals is restricted by the scaling effects imposed by physical and physiological factors. In comparisons of the power available from muscle and the mechanical power required to fly, it is predicted that the margin between the powers should decrease with body size and that flying animals have a maximum body size. However, predicting the absolute value of this upper limit has proven difficult because wing morphology and flight styles varies among species. Albatrosses and petrels have long, narrow, aerodynamically efficient wings and are considered soaring birds. Here, using animal-borne accelerometers, we show that soaring seabirds have two modes of flapping frequencies under natural conditions: vigorous flapping during takeoff and sporadic flapping during cruising flight. In these species, high and low flapping frequencies were found to scale with body mass (mass ^−0.30 and mass ^−0.18) in a manner similar to the predictions from biomechanical flight models (mass ^−1/3 and mass ^−1/6). These scaling relationships predicted that the maximum limits on the body size of soaring animals are a body mass of 41 kg and a wingspan of 5.1 m. Albatross-like animals larger than the limit will not be able to flap fast enough to stay aloft under unfavourable wind conditions. Our result therefore casts doubt on the flying ability of large, extinct pterosaurs. The largest extant soarer, the wandering albatross, weighs about 12 kg, which might be a pragmatic limit to maintain a safety margin for sustainable flight and to survive in a variable environment.     

Hyperbolastic growth models: theory and application

Background  

Mathematical models describing growth kinetics are very important for predicting many biological phenomena such as tumor volume, speed of disease progression, and determination of an optimal radiation and/or chemotherapy schedule. Growth models such as logistic, Gompertz, Richards, and Weibull have been extensively studied and applied to a wide range of medical and biological studies. We introduce a class of three and four parameter models called "hyperbolastic models" for accurately predicting and analyzing self-limited growth behavior that occurs e.g. in tumors. To illustrate the application and utility of these models and to gain a more complete understanding of them, we apply them to two sets of data considered in previously published literature.     

Predictive modeling of β-carotene accumulation by Dunaliella salina as a function of pH,NaCI, and irradiance

Predictive modeling of β-carotene accumulation by Dunaliella salina as a function of NaCI, pH, and irradiance was studied. Modified Logistic, Gompertz, Schnute, Richards, and Stannard models were fitted to describe β-carotene accumulation by the alga under various environmental conditions. Lag time (λ, days), maximum accumulation (A, pg/cell), and the maximum production rate (μ, 1/day) for β-carotene accumulation were calculated by modified Logistic and Gompertz models. Values of λ, A, and μ for β-carotene accumulation varied between 0.26 and 20.14 days, 57.48 to 198.76 pg β-carotene/cell, and 1.80 to 3.68 1/day, respectively. Results revealed that Logistic and Gompertz models could be used to describe the accumulation of β-carotene by D. salina as a function of salt concentrations, pH, and irradiance. The highest asymptotic value was predicted from Logistic and Gompertz models at pH 9.0, 48 kerg/(cm² s) light intensity, and 20% NaCl concentration.     

Sensitivity of intraspecific latitudinal clines of body size for tetrapods to sampling, latitude and body size

Recent studies have shown that most tetrapod groups (mammals,birds, chelonians, amphibians) show general intraspecific tendenciesfor increasing body size with latitude, whereas squamates (lizardsand snakes) show an intraspecific tendency towards decreasingbody size with latitude. Here I evaluate whether these sizetrends are general by using independent contrasts analysis toinvestigate the dependence of intraspecific size-latitude relationships(r), and the magnitude alone of size-latitude relationships([r]), for tetrapod vertebrates, on sample size, range of latitudessampled, average latitude sampled, and body size. Range of latitudessampled, average latitude sampled, and body size did not influencebody size-latitude relationships (r) or the magnitude aloneof body size-latitude relationship ([r]). Sample size did notinfluence size-latitude relationships (r), but did influencethe magnitude alone of size-latitude relationships ([r]), possiblyindicating increased precision of estimating size-latitude relationshipswith increased sampling. In short, intraspecific size-latituderelationships are similar for species of different sizes, occurringat different latitudes, sampled over different latitudinal ranges,and differing in number of populations sampled (though magnitudealone is influenced by sample size). These results suggest thatintraspecific size-latitude trends are general, and biologicallysignificant (i.e., are not artifacts of sampling), thus deservingexplanation.