Probabilistic Gompertz model of irreversible growth

Characterizing organism growth within populations requires the application of well-studied individual size-at-age models, such as the deterministic Gompertz model, to populations of individuals whose characteristics, corresponding to model parameters, may be highly variable. A natural approach is to assign probability distributions to one or more model parameters. In some contexts, size-at-age data may be absent due to difficulties in ageing individuals, but size-increment data may instead be available (e.g., from tag-recapture experiments). A preliminary transformation to a size-increment model is then required. Gompertz models developed along the above lines have recently been applied to strongly heterogeneous abalone tag-recapture data. Although useful in modelling the early growth stages, these models yield size-increment distributions that allow negative growth, which is inappropriate in the case of mollusc shells and other accumulated biological structures (e.g., vertebrae) where growth is irreversible. Here we develop probabilistic Gompertz models where this difficulty is resolved by conditioning parameter distributions on size, allowing application to irreversible growth data. In the case of abalone growth, introduction of a growth-limiting biological length scale is then shown to yield realistic length-increment distributions.     

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.     

Dynamical facilitation of the ideal free distribution in nonideal populations

The ideal free distribution (IFD) requires that individuals can accurately perceive density‐dependent habitat quality, while failure to discern quality differences below a given perception threshold results in distributions approaching spatial uniformity. Here, we investigate the role of population growth in restoring a nonideal population to the IFD. We place a simple model of discrete patch choice under limits to the resolution by which patch quality is perceived and include population growth driven by that underlying quality. Our model follows the population's distribution through both breeding and dispersal seasons when perception limits differ in their likely influence. We demonstrate that populations of perception limited movers can approximate an IFD provided sufficient population growth; however, the emergent IFD would be temporally inconstant and correspond to reproductive events. The time to emergence of the IFD during breeding is shorter under exponential growth than under logistic growth. The IFD during early colonization of a community persists longer when more patches are available to individuals. As the population matures and dispersal becomes increasingly random, there is an oscillation in the observance of IFD, with peaks most closely approximating the IFD occurring immediately after reproductive events, and higher reproductive rates producing distributions closer to the IFD.     

AGE and SEX COMPOSITION OF THE STRIPED DOLPHIN DIE-OFF IN THE WESTERN MEDITERRANEAN

During the morbillivirus epizootic that affected the Mediterranean striped dolphins ( Stenella coeruleoalba )in 1990–1992, several thous and individuals are believed to have died. In order to determine the segments of the population that were affected by the event, the sex- and age-frequency distributions of the animals that were washed ashore on the Spanish coasts were studied. The age of the animals was determined by counting dentine growth layer groups in the teeth. The results obtained indicate that both sexes were affected similarly by the disease and that the population component that suffered the largest mortality was that of sexually mature individuals, although substantial mortality of calves, probably still dependent on their mothers, was also observed. Juveniles, in contrast, appeared to be only slightly affected by the epizootic. This pattern of mortality is not consistent with the epidemiology of morbillivirus infections previously observed in other mammals. Possible explanations of this particular age distribution include behavioral factors, increased susceptibility to the disease in adults due to the effects of pollution, high temperatures and decreased food availability, or allopatric geographical distribution of population components and, therefore, of their associated mortality.     

The diet and dentition of Smooth newt larvae (Triturus vulgaris)

This paper describes the dentition and diet of a population of Smooth newt larvae. The development of the teeth and their increase in number with age are discussed. The number of teeth on all five tooth-bearing bones appear to be controlled by a single developmental system. Young larvae eat chydorids, daphniids and cyclopoid copepods; after they reach a total length of about 15 mm, chironomid larvae comprise the greater part of the diet. In the study population, ostracods were not eaten, and cannibalism was not observed. There was no tendency for larger larvae to select larger individuals of a given species of prey.
It is suggested that the exponential rate of growth in weight forces larvae of more than about 15 mm total length to switch from passive to active hunting. This enables them to catch larger prey, at the expense of incurring a higher rate of mortality. This increase in mortality is associated with a reduction in the variation of morphological characters, including dentition, which is thought to be caused by natural selection. The function of different components of the dentition are discussed. It was found that larvae of a given age which have more teeth than average have in their guts fewer prey than average, and an explanation is suggested.     

Y-chromosome mismatch distributions in Europe.

Ancient demographic events can be inferred from the distribution of pairwise sequence differences (or mismatches) among individuals. We analyzed a database of 3,677 Y chromosomes typed for 11 biallelic markers in 48 human populations from Europe and the Mediterranean area. Contrary to what is observed in the analysis of mitochondrial polymorphisms, Tajima's test was insignificant for most Y-chromosome samples, and in 47 populations the mismatch distributions had multiple peaks. Taken at face value, these results would suggest either (1) that the size of the male population stayed essentially constant over time, while the female population size increased, or (2) that different selective regimes have shaped mitochondrial and Y-chromosome diversity, leading to an excess of rare alleles only in the mitochondrial genome. An alternative explanation would be that the 11 variable sites of the Y chromosome do not provide sufficient statistical power, so a comparison with mitochondrial data (where more than 200 variable sites are studied in Europe) is impossible at present. To discriminate between these possibilities, we repeatedly analyzed a European mitochondrial database, each time considering only 11 variable sites, and we estimated mismatch distributions in stable and growing populations, generated by simulating coalescent processes. Along with theoretical considerations, these tests suggest that the difference between the mismatch distributions inferred from mitochondrial and Y-chromosome data are not a statistical artifact. Therefore, the observed mismatch distributions appear to reflect different underlying demographic histories and/or selective pressures for maternally and paternally transmitted loci.     

Survival analysis of three clones of Brachionus plicatilis (Rotifera)

Age-specific survival schedules of females from three genetically different clones of Brachionus plicatilis were analyzed at several environmental conditions in the laboratory.Lifespan showed the expected decrease with increasing temperature, but a general trend with salinity or genotype was not observed. Probability of death increased with age, as tested by polynomial regression analysis of the survival curve and using theoretical mortality distributions. Three two-parameter models (linear-exponential model, Weibull model, and Gompertz model) were fitted to the survival data. Fitting of these models to data was rather poor, but the Gompertz model and, to a lesser extent, the Weibull model fitted the data better than the linear-exponential model. Parameters obtained from the survival curve analyses were related to other demographic parameters. A significant relationship between the shape parameter of the Gompertz model and the cohort generation time was detected, suggesting, but not proving, an effect of reproductive effort on aging.     

Natural expansion versus translocation in a previously human‐persecuted bird of prey

Many threatened species in Europe have been expanding their distributions during recent decades owing to protection measures that overcome historical human activity that has limited their distributions. Range expansion has come about via two processes, natural expansion from existing range and reintroductions to new ranges. Reintroductions may prove to be a better way to establish populations because individuals are less subject to competitive relationships lowering breeding success than individuals expanding from existing populations. Whether this is true, however, remains uncertain. We compared success of breeding pairs of an expanding and a reintroduced population of spanish imperial eagles monitored for over 15 years in the south of Spain. We found significant differences in productivity between breeding pairs of each population. Newly established territories in reintroduction areas were almost three times more productive than new territories established as individuals expanded out from an existing population. We conclude that among these eagle populations reintroduced to new areas may fare as well or better than individuals expanding out form existing populations.     

Post-reproductive life span and demographic stability

Recent field studies suggest that it is common in nature for animals to outlive their reproductive viability. Post-reproductive life span has been observed in a broad range of vertebrate and invertebrate species. But post-reproductive life span poses a paradox for traditional theories of life history evolution. The commonly cited explanation is the “grandmother hypothesis”, which applies only to higher, social mammals. We propose that post-reproductive life span evolves to stabilize predator-prey population dynamics, avoiding local extinctions. In the absence of senescence, juveniles would be the most susceptible age class. If juveniles are the first to disappear when predation pressure is high, this amplifies the population’s risk of extinction. A class of older, senescent individuals can help shield the juveniles from predation, stabilizing demographics and avoiding extinction. If, in addition, the life history is arranged so that the older individuals are no longer fertile, the stabilizing effect is further enhanced.     

Growth modelling of different ram breeds using computer tomography

In this study the growth of rams of 3 different sheep breeds with extremely different growth patterns (Hungarian Merino, HM; American Suffolk, AS; and Dutch Texel, DT) were modelled. Two models (modified Gompertz and logistic) were fitted to experimental data generated from successive computer tomography (CT) measurements. In each breed the data fitted the Gompertz model with better precision (lower RSS values). However, the symmetric logistic function fitted the late maturing fat and long loin of the AS lambs more accurately. These models have consequently been validated to give in vivo predictions of market specific products and the optimal slaughter weight of each breed. Based on the results of the Gompertz model, medium sized sheep breeds with low growth capacity (e.g. HM) should be slaughtered when their live weight is between 21 and 33 kg at an age of 3–5 months. The large-sized, slow maturing breeds (AS) should be slaughtered between 27 and 45 kg, at a similar age to the HM lambs. The early maturing breed (DT) should not be reared older than 2–3.5 months of age, with a live weight varying between 24 and 36 kg.     

Short alleles revealed by PCR demonstrate no heterozygote deficiency at minisatellite loci D1S7, D7S21, and D12S11.

Short VNTR alleles that go undetected after conventional Southern blot hybridization may constitute an alternative explanation for the heterozygosity deficiency observed at some minisatellite loci. To examine this hypothesis, we have employed a screening procedure based on PCR amplification of those individuals classified as homozygotes in our databases for the loci D1S7, D7S21, and D12S11. The results obtained indicate that the frequency of these short alleles is related to the heterozygosity deficiency observed. For the most polymorphic locus, D1S7, approximately 60% of those individuals previously classified as homozygotes were in fact heterozygotes for a short allele. After the inclusion of these new alleles, the agreement between observed and expected heterozygosity, along with other statistical tests employed, provide additional evidence for lack of population substructuring. Comparisons of allele frequency distributions reveal greater differences between racial groups than between closely related populations.     

The adequacy of aging techniques in vertebrates for rapid estimation of population mortality rates from age distributions

As a key parameter in population dynamics, mortality rates are frequently estimated using mark–recapture data, which requires extensive, long‐term data sets. As a potential rapid alternative, we can measure variables correlated to age, allowing the compilation of population age distributions, from which mortality rates can be derived. However, most studies employing such techniques have ignored their inherent inaccuracy and have thereby failed to provide reliable mortality estimates. In this study, we present a general statistical model linking birth rate, mortality rate, and population age distributions. We next assessed the reliability and data needs (i.e., sample size) for estimating mortality rate of eight different aging techniques. The results revealed that for half of the aging techniques, correlations with age varied considerably, translating into highly variable accuracies when used to estimate mortality rate from age distributions. Telomere length is generally not sufficiently correlated to age to provide reliable mortality rate estimates. DNA methylation, signal‐joint T‐cell recombination excision circle (sjTREC), and racemization are generally more promising techniques to ultimately estimate mortality rate, if a sufficiently high sample size is available. Otolith ring counts, otolithometry, and age‐length keys in fish, and skeletochronology in reptiles, mammals, and amphibians, outperformed all other aging techniques and generated relatively accurate mortality rate estimation with a sample size that can be feasibly obtained. Provided the method chosen is minimizing and estimating the error in age estimation, it is possible to accurately estimate mortality rates from age distributions. The method therewith has the potential to estimate a critical, population dynamic parameter to inform conservation efforts within a limited time frame as opposed to mark–recapture analyses.     

Differentiation and frequency distributions of body weights in plants and animals

The basic and simplest system that one can consider in ecology is a group of individuals of equal age and representing one species, that is, a cohort. This paper is an attempt to show that analysis of such a system may be of great importance to understanding basic ecological problems, such as, intraspecific competition and the dynamics of a single population. It is easy to observe that in even-aged populations individuals differ in weights. A close look can show that weight distributions in even-aged populations may have different skewness. Most common are distributions with coefficients of skewness greater than zero. Sometimes weight distributions are symmetrical or with skewness coefficients less than zero. In a cohort of growing individuals the coefficient of skewness changes with time: most often starting from zero (symmetrical distribution), it increases in time; sometimes after an initial increase it can decrease in the final stage of growth, which is related to an increased mortality of individuals. The rate of change in skewness, and the skewness itself depend on the density of individuals in a cohort and on food conditions. They are greater at higher densities and increase with deteriorating food conditions. Weight distributions are symmetrical at low densities and optimal food conditions. The differences in individual weights measured by variance of weight distributions or coefficient of variation follow the same pattern, but observed changes with time, density and food conditions are not so clear. These conclusions rest upon the review of numerous papers concerning both plants and animals, which is presented in this paper. In the past, the properties of weight distributions in even-aged populations were explained not by interactions between individuals, but rather as a natural outcome of the growth process of non-interacting individuals. The exponential equation of growth, with relative growth rate having a normal distribution in populations, was used to support this hypothesis. Obtained weight distributions were of positive skewness; however, this model, which in fact is able to describe the growth process only in its initial stage, cannot explain the changes of skewness of weight distributions with density and food conditions. A model has been developed which includes competitive interactions among members of even-aged populations to explain observed properties of weight distributions in them. The basic assumption is that intraspecific competition leads to uneven partitioning of resources, which are the object of competition. Functions describing resource partitioning among individuals are included into the model.(ABSTRACT TRUNCATED AT 400 WORDS)     

Inbreeding effects on bilateral asymmetry of dermatoglyphic patterns

Bilateral correlations are higher and bilateral variances within individuals smaller in the samples of inbred individuals than in matched control groups of the same sex for pattern intensities on fingers in four series of data and also for pattern intensities on palms, toes, and soles and the palmer main line indices in the data collected from a Muslin population of West Bengal. This trend is not apparent in two series of data from the Yanadi tribe, in which the inbred and noninbred samples are not controlled for random variation of genes and environment. Increased variances between individuals and changes in means and distributions of the traits in the inbred samples of the matched data indicate some influence of homozygosity of genes for the traits on their asymmetry. The reduced variability of asymmetry of the traits in the inbred cannot be explained by homozygosity of genes for either directional or absolute asymmetry. One possible explanation is that heterozygotes for these dermatoglyphic triats are more responsive to environmental stress than homozygotes and/or increased selection in the homozygotes against genetic disorders associated with dermatoglyphic asymmetry may reduce the variability of such asymmetry.     

Age and growth of an Iberian cyprinodont, Aphanius iberus (Cuv. & Val.), in its most northerly population

Age and growth of an Iberian cyprinodont, Aphanius iberus (Cuv. & Val.), in its most northerly population, La Rubina lagoon (Alt Empordà wetlands, NE Spain), was studied. The age groups for this Mediterranean population (O +, 1 + and 2 +) agree with those reported for the Atlantic population (R. Guadalquivir marshes), in the southern limit of the species distribution in the Iberian peninsula. Differences in age structure between these populations and the one previously studied in La Tancada lagoon (R. Ebro delta marshes) can be attributed to age estimation bias. Male A. iberus data appear to fit similarly to a Gompertz growth function and to a von Bertalanffy growth function, but L _x, was clearly underestimated. A Gompertz growth function was not a good fit for females, perhaps because female growth is clearly faster and less attenuated than male growth. The life history and growth pattern ofthis species is similar to that in other cyprinodontiform fishes, typified by a short longevity. The growth model of this species does not seem to fit types I and II of Sebens's classification, which are characteristic of fish.     

On fitness and partial migration in a large herbivore – migratory moose have higher reproductive performance than residents

Partially migratory populations comprise both resident and migratory individuals. These tactics may coexist if their demographic contribution to future generations (i.e. fitness) are equal or vary temporally with environmental conditions, or if individuals switch between being migrant and resident. Alternatively, the choice of movement tactic can be based on individual attributes such as age, competitive ability or personality. In the latter cases, the two tactics are not expected to have similar average fitness. In this study, we examined the effect of movement tactic on reproductive performance and survival of 82 GPS‐marked female moose and their offspring in a partial migratory population in central Norway. The results indicated higher growth in the migrating part of the population because migrating females produced more twins than resident females. We found no differences in pregnancy rates or survival of adults or their offspring, indicating a net fitness benefit of being migrant. We found the average shoulder height of residents to be slightly lower than of migrants, but doubt that this affected their migration ability. A more likely explanation is that migratory females are both more fecund and grow bigger because of better conditions in their summer ranges. This may be a temporal phenomenon if the fitness differences between migratory and resident moose vary according to environmental fluctuations.     

Times from Infection to Disease-Induced Death and their Influence on Final Population Sizes After Epidemic Outbreaks

For epidemic models, it is shown that fatal infectious diseases cannot drive the host population into extinction if the incidence function is upper density-dependent. This finding holds even if a latency period is included and the time from infection to disease-induced death has an arbitrary length distribution. However, if the incidence function is also lower density-dependent, very infectious diseases can lead to a drastic decline of the host population. Further, the final population size after an epidemic outbreak can possibly be substantially affected by the infection-age distribution of the initial infectives if the life expectations of infected individuals are an unbounded function of infection age (time since infection). This is the case for lognormal distributions, which fit data from infection experiments involving tiger salamander larvae and ranavirus better than gamma distributions and Weibull distributions.     

An Old Mom Keeps You Young: Mother’s Age at Last Birth and Offspring Longevity in Nineteenth-Century Utah

This study analyzes the intergenerational effects of late childbearing on offspring’s adult longevity in a population in Utah (United States) that does not display evidence of parity-specific birth control—a so-called natural fertility population. Studies have found that for women who experience late menopause and prolonged reproduction, aging is postponed and longevity is increased. This is believed to indicate female “robustness” and the impact of biological or genetic factors. If indeed there is a genetic component involved, one would expect to also find evidence for the intergenerational transmission of longevity benefits. Our study investigates the relationship between prolonged natural fertility of mothers and their offspring’s survival rates in adulthood. Gompertz regression models (N = 7,716) revealed that the offspring of mothers who were naturally fertile until a relatively advanced age lived significantly longer. This observed positive effect of late reproduction was not independent of but conditional upon survival of the mother to the end of her fecundity (defined as age 50). Offspring’s relative risks at death beyond age 50 were 6–12 percent lower than those of their counterparts born to mothers who had an average age at last birth. Our results, which account for various early, adult, and later-life conditions, as well as shared frailty, suggest that there is a positive relationship between mother’s age at last birth and offspring longevity, and strengthen the notion that age at menopause is a good predictor of this relationship.     

On the 'rate of aging' in heterogeneous populations

It is well known that the rate of aging is constant for populations described by the Gompertz law of mortality. However, this is true only when a population is homogeneous. In this note, we consider the multiplicative frailty model with the baseline distribution that follows the Gompertz law and study the impact of heterogeneity on the rate of aging in this population. We show that the rate of aging in this case is a function of age and that it increases in (calendar) time when the baseline mortality rate decreases.