Estimation of completeness and adjustment of age-specific and age-standardized incidence rates.

This note discusses the use of capture-mark-recapture methods and log-linear, linear, product models for incomplete tables (Espeland, 1986, Communications in Statistics--Simulation and Computing 15, 405-424) to estimate completeness of reporting in a disease registry and to estimate incompleteness-adjusted incidence rates. The method had several desirable features, including the ability to handle complex experimental designs, to incorporate auxiliary data (that may be related to the likelihood of reporting), to test the contribution of model terms, and to generate point estimates and associated standard errors.     

On a stochastic version of a modified Nicholson-Baily model

‘Deterministic’ models in population dynamics often are really approximations to stochastic models, justified by an appeal to ‘the law of large numbers’. It is proposed to call such models ‘pseudodeterministic’. Four questions are discussed in this article: (1) What errors may be made by equating deterministically predicted values to expectations? (2) When, and in what sense, may numbers be assumed to be large? (3) How large are the variances, coefficients of variations, etc., as assigned to the variables in the stochastic versions of the models? (4) What role may pseudodeterministic models play in empirical research, where problems of statistical reliability arise? As an example, a modified Nicholson-Bailey model of the interaction between insect parasitoids and their hosts is discussed; the modification consists of assigning a random (density-independent) mortality to the parasitoid population. A stochastic version of this model is discussed. The expectation of the final host density is compared with the value computed from the deterministic model. The latter value is systematically lower than the former. The magnitude of the difference depends on parameter values. The variability to be expected with the stochastic model is characterized by the coefficient of variation of the final host density; its dependence on parameter values and initial conditions is discussed. It is concluded that it is worthwhile in practical applications to estimate parasitoid mortality, and that the coefficient of variation in real situations may be far from negligible.     

Local adjustment of sex ratio in the spider Pityohyphantes phrygianus

The sex ratio in five populations of the sheetweb spider Pityohyphantes phrygianus in southwest Sweden was investigated in July and September, the spiders being juveniles and subadults, respectively. In July, no heterogeneity between the five populations was found and the pooled samples revealed a sex ratio of 36% males and 64% females. A significant heterogeneity in sex ratio was observed in the September samples; the proportion of males varied between 23% and 40%. In several cases, male mean weight differed significantly between the five populations, comparing the July and September samples separately. This suggests that the prey availability varied considerably between the sites. In September, dead spiders were collected in two sites. This mortality was probably caused by starvation and the mortality rates differed significantly between the two sites. Indirect evidence suggested that the local sex ratio was affected by the prey availability, males being at a relative disadvantage in poor sites. Local environmental conditions may govern the adult sex ratio in this spider by causing differential mortality and/or migration.     

Properties of behavior under different random ratio and random interval schedules: A parametric study

Four pigeons were trained to peck a key under different values of a temporally defined independent variable (T) and different probabilities of reinforcement (p). Parameter T is a fixed repeating time cycle and p the probability of reinforcement for the first response of each cycle T. Two dependent variables were used: mean response rate and mean postreinforcement pause. For all values of p a critical value for the independent variable T was found (T=1 sec) in which marked changes took place in response rate and postreinforcement pauses. Behavior typical of random ratio schedules was obtained at T

1 sec and behavior typical of random interval schedules at T

1 sec.     

An alternative stochastic framework for estimating pure measures of fertility

A stochastic fertility model is developed that incorporates a state of "viable pregnancy" within parity i. This model is used as a framework to derive formulas expressing relationships between various central rates and probabilities within parity i. Specifically, formulas are derived to relate the total fertility rate with the parity progression probability, a pregnancy rate with a pregnancy progression probability, and a direct fertility rate with a direct parity progression probability.     

Quantitative genetic tests of recent senescence theory: age-specific mortality and male fertility in Drosophila melanogaster

Quantitative genetic models of aging predict that additive genetic variance for fitness components should increase with age. However, recent studies have found that at very late ages, the genetic variance components decline. This decline may be due to an age-related drop in reproductive effort. If genetic variance in reproductive effort affects the genetic variance in mortality, the decline in reproductive effort at late ages should lead to a decrease in the genetic variance in mortality. To test this, we carried out a large-scale quantitative genetic analysis of age-specific mortality and fertility in virgin male Drosophila melanogaster. As in earlier studies, we found that the additive variance for age-specific mortality and fertility declined at late ages. Also, recent theoretical developments provide new predictions to distinguish between the mutation accumulation (MA) and antagonistic pleiotropy (AP) models of senescence. The deleterious effects of inbreeding are expected to increase with age under MA, but not under AP. This prediction was supported for both age-specific mortality and male fertility. Under AP, the ratio of dominance to additive variance is expected to decline with age. This predicition, too, was supported by the data analyzed here. Taken together, these analyses provide support for both the models playing a role in the aging process. We argue that the time has come to move beyond a simple comparison of these genetic models, and to think more deeply about the evolutionary causes and consequences of senescence.     

The dissimilar costs of love and war: age-specific mortality as a function of the operational sex ratio

Lifespan and ageing are strongly affected by many environmental factors, but the effects of social environment on these life-history traits are not well understood. We examined effects of social interaction on age-specific mortality rate in the sexually dimorphic neriid fly Telostylinus angusticollis. We found that although interaction with other individuals reduced longevity of both sexes, the costs associated with variation in operational sex ratio were sex specific: males' early-life mortality rate increased, and lifespan decreased, with increasing male bias in the sex ratio, whereas surprisingly, the presence of males had no effect on early-life mortality or lifespan of females. Intriguingly, early-life (immediate) mortality costs did not covary with late-life (latent) costs. Rather, both sexes aged most rapidly in a social environment dominated by the opposite sex. Our findings suggest that distinct reproductive activities, such as mating and fighting, impose different age-specific patterns of mortality, and that such costs are strongly sex specific.     

Minimizing the dependency ratio in a population with below-replacement fertility through immigration

Many industrialized countries face fertility rates below replacement level, combined with declining mortality especially in older ages. Consequently, the populations of these countries have started to age. One important indicator of age structures is the dependency ratio which is the ratio of the nonworking age population to the working age population. In this work we find the age-specific immigration profile that minimizes the dependency ratio in a stationary population with below-replacement fertility. It is assumed that the number of immigrants per age is limited. We consider two alternative policies. In the first one, we fix the total number of people who annually immigrate to a country. In the second one, we prescribe the size of the receiving country’s population. For both cases we provide numerical results for the optimal immigration profile, for the resulting age structure of the population, as well as for the dependency ratio.     

Nutritional factors affecting the egg sex ratio adjustment by a honeybee queen

Summary. To determine whether and how honeybee (Apis mellifera L.) queens control the proportion of male reproductives, experiments were done with colonies under two nutritional conditions at two seasons. During the reproductive season the proportion of male eggs laid by queens under insufficiently-food-supplied conditions was lower than that under sufficiently-food-supplied conditions. The smaller proportion of male egg production could not be accounted for by cannibalization of male eggs by workers. The workers' allocation to male cell construction did not differ between sufficiently- and insufficiently-food-supplied conditions. During the non-reproductive season, however, queens showed much reduced or nearly no production of male eggs, even if the colonies were sufficiently supplied with food. These results suggest that the honeybee queen adjusts the egg sex ratio by referring to both the nutritional resources and their own intrinsic seasonal factors.     

On the adjustment of the sex ratio and the gregarious behavior of animal populations.

Ribosome synthesis in bacteria is linked to RNA polymerase synthesis; both synthesis rates depend upon the values of six parameters: (1) fraction of total ribosomes that is functioning, (2) fraction of total RNA polymerase that is functioning, (3) fraction of functioning RNA polymerase engaged in rRNA synthesis, (4) fraction of total protein that is RNA polymerase protein, (5) peptide chain elongation rate, (6) rRNA chain elongation rate. If these parameters are constant in time, then the numbers of both ribosomes and RNA polymerase molecules increase exponentially. It is shown how the rate constant (fractional increase per unit of time) relates to these parameters and how the kinetics of ribosome and RNA polymerase synthesis respond to a change in any of these parameters.     

Overshadowing of responding on ratio and interval schedules by an independent predictor of reinforcement

This experiment replicated previous demonstrations that interposing a brief stimulus between reinforced responses and the presentation of the reinforcer reduces responding maintained by intermittent reinforcement schedules. Furthermore, we could find no significant difference between the relative size of the reduction during training on ratio and interval schedules when the predictive significance of the response and stimulus was controlled by a yoking procedure.     

Contingency discriminability and the generalized matching law describe choice on concurrent ratio schedules of wheel-running reinforcement

Belke (2010) showed that on concurrent ratio schedules, the difference in ratio requirements required to produce near exclusive preference for the lower ratio alternative was substantively greater when the reinforcer was wheel running than when it was sucrose. The current study replicated this finding and showed that this choice behavior can be described by the matching law and the contingency discriminability model. Eight female Long Evans rats were exposed to concurrent VR schedules of wheel-running reinforcement (30s) and the schedule value of the initially preferred alternative was systematically increased. Two rats rapidly developed exclusive preference for the lower ratio alternative, but the majority did not - even when ratios differed by 20:1. Analysis showed that estimates of slopes from the matching law and the proportion of reinforcers misattributed from the contingency discriminability model were related to the ratios at which near exclusive preference developed. The fit of these models would be consistent with misattribution of reinforcers or poor discrimination between alternatives due to the long duration of wheel running.