Low levels of genetic structuring in King George whiting Sillaginodes punctatus across two geographic regions.

Postlarvae of King George whiting Sillaginodes punctatus, a commercially important fish species in southern Australia, were collected from multiple locations across south and south-eastern Australia. Genetic analyses using seven microsatellite markers found little evidence of genetic structure suggesting high levels of connectivity between the regions. The results found no evidence of a distinct source spawning population within the south-eastern range sampled in this study.

Sperm competition and offspring viability at hybridization in Australian tree frogs, Litoria peronii and L. tyleri.

Hybridization between closely related species often leads to reduced viability or fertility of offspring. Complete failure of hybrid offspring (post-zygotic hybrid incompatibilities) may have an important role in maintaining the integrity of reproductive barriers between closely related species. We show elsewhere that in Peron's tree frog, Litoria peronii, males more closely related to a female sire more offspring in sperm competition with a less related rival male. Observations of rare 'phenotypic intermediate' males between L. peronii and the closely related L. tyleri made us suggest that these relatedness effects on siring success may be because of selection arising from risks of costly hybridization between the two species. Here, we test this hypothesis in an extensive sperm competition experiment, which shows that there is no effect of species identity on probability of fertilization in sperm competition trials controlling for sperm concentration and sperm viability. Instead, there was a close agreement between a male's siring success in isolation with a female and his siring success with the same female in competition with a rival male regardless of species identity. Offspring viability and survival, however, were strongly influenced by species identity. Over a 14-day period, hybrid offspring suffered increasing mortality and developed more malformations and an obvious inability to swim and right themselves, leading to compromised probability of survival. Thus, hybridization in these sympatric tree frogs does not compromise fertilization but has a strong impact on offspring viability and opportunity for reinforcement selection on mate choice for conspecific partners.

Males with high genetic similarity to females sire more offspring in sperm competition in Peron's tree frog Litoria peronii.

Recent work has confirmed that genetic compatibility among mates can be an important determinant of siring success in sperm competition experiments and in free-ranging populations. Most of this work points towards mate choice of less related mates. However, there may also be the potential for mate choice for intermediate or even genetically similar mates to prevent outbreeding depression or hybridization with closely related taxa. We studied relatedness effects on post-copulatory gametic choice and/or sperm competition in an external fertilizer, Peron's tree frog (Litoria peronii), since external fertilizers offer exceptional control in order to test gametic interaction effects on probability of paternity and zygote viability. Sperm competition experiments were done blindly with respect to genetic relatedness among males and females. Thereafter, paternity of offspring was assigned using eight microsatellite loci. Three hybridization trials between L. peronii and a closely related sympatric species Litoria tyleri were also carried out. In the sperm competition trials, males that are more genetically similar to the female achieved higher siring success compared with less genetically similar males. The hybridization trials confirmed that the two species can interbreed and we suggest that the risk of hybridization may contribute to selection benefits for genetically more similar males at fertilization. To our knowledge, this study is the first to show evidence for post-copulatory selection of sperm from genetically more similar individuals within a natural population.

Mating system variation in the hermaphroditic brooding coral, Seriatopora hystrix.

Self-compatible, hermaphroditic marine invertebrates have the potential to self-fertilize in the absence of mates or under sperm-limited conditions, and outcross when sperm is available from a variety of males. Hence, many hermaphroditic marine invertebrates may have evolved mixed-mating systems that involve facultative self-fertilization. Such mixed-mating strategies are well documented for plants but have rarely been investigated in animals. Here, I use allozyme markers to make estimates of selfing from population surveys of reef slope and reef flat sites, and contrast this with direct estimates of selfing from progeny-array analysis, for the brooding coral Seriatopora hystrix. Consistent heterozygote deficits previously reported for S. hystrix suggests that inbreeding (including the extreme of selfing) may be common in this species. I detected significant levels of inbreeding within populations (F(IS)=0.48) and small but significant differentiation among all sites (F(ST)=0.04). I detected no significant differentiation among habitats (F(HT)=0.009) though among site differentiation did occur within the reef slope habitat (F(SH)=0.06), but not within the reef flat habitat (F(SH)=0.015). My direct estimates of outcrossing for six colonies and their progeny from a single reef flat site revealed an intermediate value (t(m) (+/-s.d.)=0.53+/-0.20). Inbreeding coefficients calculated from progeny arrays (F(e)=0.31) were similar to indirect estimates based on adult genotype frequencies for that site (F(IS)=0.38). This study confirms that the mating system of this brooding coral is potentially variable, with both outcrossing and selfing.

Calculation of the cumulative distribution function of the time to a small observable tumor.

Multistage mathematical models of carcinogenesis (when applied to tumor incidence data) have historically assumed that the growth kinetics of cells in the malignant state are disregarded and the formation of a single malignant cell is equated with the emergence of a detectable tumor. The justification of this simplification is, from a mathematical point of view, to make the estimation of tumor incidence rates tractable. However, analytical forms are not mandatory in the estimation of tumor incidence rates. Portier et al.(1996b, Math. Biosci. 135, 129-146) have demonstrated the utility of the Kolmogorov backward equations in numerically calculating tumor incidence. By extending their results, the cumulative distribution function of the time to a small observable tumor may be numerically obtained.

The two-stage model of carcinogenesis: overcoming the nonidentifiability dilemma.

The two-stage mathematical model of carcinogenesis has been shown to be nonidentifiable whenever tumor incidence data alone is used to fit the model (Hanin and Yakovlev, 1996). This lack of identifiability implies that more than one parameter vector satisfies the optimization criteria for parameter estimation, e.g., maximum likelihood estimation. A question of greater concern to persons using the two-stage model of carcinogenesis is under what conditions can identifiable parameters be obtained from the observed experimental data. We outline how to obtain identifiable parameters for the two-stage model.

Calculating tumor incidence rates in stochastic models of carcinogenesis.

Multistage models of carcinogenesis are increasingly used in the estimation of risks from exposure to environmental agents. The two-stage model of carcinogenesis is routinely used because it agrees with much of the existing tumor incidence data, parallels the biological two-stage model, and has much of its mathematical details derived. However, recent findings on the mechanisms of carcinogenesis has led researchers to believe that there are a greater number of stages and a more complex structure to these models than a single pathway. In this paper, a method for readily computing tumor incidence rates for arbitrarily complex multistage models is derived. The formulas for the two-stage model with time-varying rates are given explicitly. Simple rules for more complicated models are given, and computer code able to implement these formulas are provided.

Stochastic simulation of a multistage model of carcinogenesis.

Stochastic mathematical models of carcinogenesis have been used to quantify cancer risks for about 40 years. As more detailed data of the cancer process are obtained, mathematical models try to incorporate this information and as a result become more complex and sometimes analytically and numerically intractable. Simulation studies have become an important tool for examining the operating characteristics of the models of interest. The many quantities one can examine using this tool include bias in parameter estimates, adequacy of approximation methods, and the appropriateness of large sample generalizations to small studies. This manuscript describes a general method of stochastic simulation that may be carried out for arbitrarily complicated stochastic models of carcinogenesis.

Modeling the number and size of hepatic focal lesions following exposure to 2,3,7,8-TCDD.

Data on the size and number of placental glutathione S-transferase-positive (PGST+) foci were collected from a two-stage hepatocarcinogenesis model in female Sprague-Dawley rats. the study consisted of multiple 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD)-exposed dose groups including both diethylnitrosomine (DEN)-initiated and uninitiated animals. Groups were observed after 15 or 31 weeks of TCDD exposure. The parameters in the first half of a two-stage mathematical model of carcinogenesis were estimated from these data. If the model is valid, the results suggest that TCDD stimulates the production of PGST+ foci and promotes the growth of PGST+ foci. This finding suggests a complicated mechanism for TCDD-induced production of Hepatic foci that we refer to as activation, labeling TCDD as an activator. The analysis also indicates that there is an interaction between DEN and TCDD which results in dose-related formation of initiated cells throughout the study period. Best-fitting curves (using maximum likelihood methods) for TCDD-induced activation and promotion reached saturation levels at low doses of TCDD. In summary, the model fit the data well, but leads to an interpretation of the data which either questions the validity of the model or implies that our understanding of the effects of TCDD and DEN is incomplete.

Quantitative analysis of multiple phenotype enzyme-altered foci in rat hepatocarcinogenesis experiments: the multipath/multistage model.

The promotional effect of phenobarbital and 1-hydroxymethyl-pyren on enzyme altered lesions in the rat liver were quantified within the framework of two separate multipath/multistage models. The experiment analyzed followed an initiation-promotion protocol in which female Wistar rats were initiated with a single dose of diethylnitrosamine at 0.15 mumol/g body wt followed by a 3 week treatment-free period. A promotor, 1-hydroxymethyl-pyren or phenobarbital was then administered continuously in the diet for 120 days. All animals were sacrificed 3 weeks after treatment and their livers were examined for enzyme histological changes. Focal lesions were classified into three phenotype categories: adenosine triphosphatase altered (ATPase), sulfotransferase altered (ST) and jointly altered lesions (ATPase and ST). Quantitative methods were used to analyze the data, which consisted of the number and sizes of these enzyme-altered lesions. Both multipath/multistage models fitted to the data clearly demonstrate that phenobarbital promotion produced more observable and larger foci than promotion via 1-hydroxymethyl-pyren and that the growth kinetics of the jointly altered lesions were elevated relative to the lesions expressing a single marker. It was not possible with these data to determine if there was a predominant sequence in the formation of jointly altered lesions.

Multistage models of carcinogenesis: an approximation for the size and number distribution of late-stage clones.

Multistage models have become the basic paradigm for modeling carcinogenesis. One model, the two-stage model of carcinogenesis, is now routinely used in the analysis of cancer risks from exposure to environmental chemicals. In its most general form, this model has two states, an initiated state and a neoplastic state, which allow for growth of cells via a simple linear birth-death process. In all analyses done with this model, researchers have assumed that tumor incidence is equivalent to the formation of a single neoplastic cell and the growth kinetics in the neoplastic state have been ignored. Some researchers have discussed the impact of this assumption on their analyses, but no formal methods were available for a more rigorous application of the birth-death process. In this paper, an approximation is introduced which allows for the application of growth kinetics in the neoplastic state. The adequacy of the approximation against simulated data is evaluated and methods are developed for implementing the approximation using data on the number and size of neoplastic clones.

The exact formula for tumor incidence in the two-stage model.

An exact formula for the tumor incidence rate in the usual two-stage model of carcinogenesis is presented. This formula is simple and easily implemented on calculators and computers.

Using cell replication data in mathematical modeling in carcinogenesis.

Risk estimation involves the application of quantitative models of dose versus response to carcinogenicity data. Recent advances in biology, computing, and mathematics have led to the application of mathematically complicated, mechanistically based models of carcinogenesis to the estimation of risks. This paper focuses on two aspects of this application, distinguishing between models using available data and the development of new models to keep pace with research developments.