Estimation and inference of R0 of an infectious pathogen by a removal method

The basic reproductive ratio, R0, is a central quantity in the investigation and management of infectious pathogens. The standard model for describing stochastic epidemics is the continuous time epidemic birth-and-death process. The incidence data used to fit this model tend to be collected in discrete units (days, weeks, etc.), which makes model fitting, and estimation of R0 difficult. Discrete time epidemic models better match the time scale of data collection but make simplistic assumptions about the stochastic epidemic process. By investigating the nature of the assumptions of a discrete time epidemic model, we derive a bias corrected maximum likelihood estimate of R0 based on the chain binomial model. The resulting 'removal' estimators provide estimates of R0 and the initial susceptible population size from time series of infectious case counts. We illustrate the performance of the estimators on both simulated data and real epidemics. Lastly, we discuss methods to address data collected with observation error.     

Divergence in male mating tactics between two populations of the soapberry bug: I. Guarding versus nonguarding

I compared male allocation to prolonged mate guarding versusnot guarding between two populations of the soapberry bug (Jaderahaematoloma) that differ in adult sex ratio: Oklahoma, USA (mean± SD adult sex ratio, 2.70 ± 0.95 males per female),and Florida, USA (1.09 ± 0.26 males per female). To predictthe reproductive performance of each mating tactic in each population,I collected data on search time per mating, time required forguarding to be effective, sperm competition, female rematingpropensity, and female resistance to guarding. Search time alonediffered significantly between the populations, being much greaterin Oklahoma (estimated as 26.2 h per mate) than in Florida (estimatedas 9.6 h per mate). For males in each region, these data wereused to model the costs and benefits of guarding for differentnumbers of oviposition bouts versus not guarding. The reproductiverate of nonguarders in Oklahoma is exceeded by that of guarderswho remain with a female for more than one oviposition bout,but in Florida, the reproductive rate of nonguarders is onlyexceeded by that of guarders who remain with a female for atleast three ovipositions. Consistent with the model, Oklahomamales in field arenas guarded more frequently than did Floridamales. However, nonguarding was common in both populations,and guarding durations were highly variable.     

Parental investment, sexual selection and sex ratios

Conventional sex roles imply caring females and competitive males. The evolution of sex role divergence is widely attributed to anisogamy initiating a self‐reinforcing process. The initial asymmetry in pre‐mating parental investment (eggs vs. sperm) is assumed to promote even greater divergence in post‐mating parental investment (parental care). But do we really understand the process? Trivers [Sexual Selection and the Descent of Man 1871–1971 (1972), Aldine Press, Chicago] introduced two arguments with a female and male perspective on whether to care for offspring that try to link pre‐mating and post‐mating investment. Here we review their merits and subsequent theoretical developments. The first argument is that females are more committed than males to providing care because they stand to lose a greater initial investment. This, however, commits the ‘Concorde Fallacy’ as optimal decisions should depend on future pay‐offs not past costs. Although the argument can be rephrased in terms of residual reproductive value when past investment affects future pay‐offs, it remains weak. The factors likely to change future pay‐offs seem to work against females providing more care than males. The second argument takes the reasonable premise that anisogamy produces a male‐biased operational sex ratio (OSR) leading to males competing for mates. Male care is then predicted to be less likely to evolve as it consumes resources that could otherwise be used to increase competitiveness. However, given each offspring has precisely two genetic parents (the Fisher condition), a biased OSR generates frequency‐dependent selection, analogous to Fisherian sex ratio selection, that favours increased parental investment by whichever sex faces more intense competition. Sex role divergence is therefore still an evolutionary conundrum. Here we review some possible solutions. Factors that promote conventional sex roles are sexual selection on males (but non‐random variance in male mating success must be high to override the Fisher condition), loss of paternity because of female multiple mating or group spawning and patterns of mortality that generate female‐biased adult sex ratios (ASR). We present an integrative model that shows how these factors interact to generate sex roles. We emphasize the need to distinguish between the ASR and the operational sex ratio (OSR). If mortality is higher when caring than competing this diminishes the likelihood of sex role divergence because this strongly limits the mating success of the earlier deserting sex. We illustrate this in a model where a change in relative mortality rates while caring and competing generates a shift from a mammalian type breeding system (female‐only care, male‐biased OSR and female‐biased ASR) to an avian type system (biparental care and a male‐biased OSR and ASR).     

Queen-worker conflict over sex ratio: A comparison of primary and secondary sex ratios in the Argentine ant,Iridomyrmex humilis

We compare the primary sex ratio (proportion of haploid eggs laid by queens) and the secondary sex ratio (proportion of male pupae produced) in the Argentine ant Iridomyrmex humilis with the aim of investigating whether workers control the secondary sex ratio by selectively eliminating male brood. The proportion of haploid eggs produced by queens was close to 0.5 in late winter, decreased to less than 0.3 in spring and summer, and increased again to a value close to 0.5 in fall. Laboratory experiments indicate that temperture is a proximate factor influencing the primary sex ratio with a higher proportion of haploid eggs being laid at colder temperatures. Production of queen pupae ceased in mid-June, about three weeks before that of male pupae. After this time only worker pupae were produced. During the period of production of sexuals, the proportion of male pupae ranged from 0.30 to 0.38. Outside this period no males were reared although haploid eggs were produced all the year round by queens. Workers thus exert a control on the secondary sex ratio by eliminating a proportion of the male brood during the period of sexual production and eliminating all the males during the remainder of the cycle. These data are consistent with workers preferring a more female-biased sex ratio than queens. The evolutionary significance of the production of male eggs by queens all the year round is as yet unclear. It may be a mechanism allowing queen replacement in the case of the death of the queens in the colony.     

Influence of genotype-temperature interaction on pollen performance

Pollen competition and selection have significant evolutionary consequences, but very little is known about how they can be modulated. We have examined in cherry (Prunus avium L.) how pollen performance is affected by the genotype of the pollen and by the environmental conditions under which it grows, namely the pistilar tissue and temperature. The different pollen donor genotypes tested in this work differed in their behaviour both in vitro and in vivo and this behaviour was modulated depending on the female recipient they grew on. Furthermore, there was a significant temperature-genotype interaction that affected the pollen tube population census that succeeded in reaching the base of the style. The combination of these three factors, while enabling a capacity of response to variations in environmental pressures, could maintain variability in pollen performance avoiding the fixation of the genes that control pollen tube growth rate.     

Equal sex ratios of a marine green alga, Bryopsis plumosa

By finding some important culture conditions as below, we succeeded in experimentally controlling the whole life history of a dioecious marine green alga, Bryopsis plumosa (Hudson) C. Agardh. In this study, we focused on the primary and secondary sex ratios (i.e. at inception and maturity) using these culture techniques. Gametogenesis was induced by culturing haploid gametophytes with Provasoli's enriched seawater (PES) medium under a 1410 h light dark cycle at 14 ℃. Formed zygotes grew into diploid sporophytes, which were cultured for 3 months with PES medium under a 1410 h light nbsp;dark cycle at 18℃. Then they were transferred into Schreiber medium and cultured under a 1014 h light dark cycle at 22℃. Within 1 week, zoosporogenesis was observed. Zoospores were released within a couple of days. Each zoospore soon germinated and grew into a unisexual gametophyte. The primary sex ratio was examined in gametophytes that originated from a single sporophyte. The secondary sex ratio was studied in the field. Both were estimated as 11.Synchronized meiotic cell divisions might occur during zoosporogenesis dividing each sex-determining factor evenly among zoospores. Given the equal sex ratio at maturity, there seems to be no environmental factor that differentially affects the survival of male or female gametophytes in nature.     

The presence–absence matrix reloaded: the use and interpretation of range–diversity plots

Aim A great deal of information on distribution and diversity can be extracted from presence–absence matrices (PAMs), the basic analytical tool of many biogeographic studies. This paper presents numerical procedures that allow the analysis of such information by taking advantage of mathematical relationships within PAMs. In particular, we show how range–diversity (RD) plots summarize much of the information contained in the matrices by the simultaneous depiction of data on distribution and diversity. Innovation We use matrix algebra to extract and process data from PAMs. Information on the distribution of species and on species richness of sites is computed using the traditional R (by rows) and Q (by columns) procedures, as well as the new Rq (by rows, considering the structure of columns) and Qr (by columns, considering the structure by rows) methods. Matrix notation is particularly suitable for summarizing complex calculations using PAMs, and the associated algebra allows the implementation of efficient computational programs. We show how information on distribution and species richness can be depicted simultaneously in RD plots, allowing a direct examination of the relationship between those two aspects of diversity. We explore the properties of RD plots with a simple example, and use null models to show that while parameters of central tendency are not affected by randomization, the dispersion of points in RD plots does change, showing the significance of patterns of co‐occurrence of species and of similarity among sites. Main conclusion Species richness and range size are both valid measures of diversity that can be analysed simultaneously with RD plots. A full analysis of a system requires measures of central tendency and dispersion for both distribution and species richness.     

Rainfall, phycocyanin, and N:P ratios related to cyanobacterial blooms in a Korean large reservoir

Nutrient concentrations and other environmental factors were measured in the Daechung Reservoir for 25 weeks from spring until autumn in 1999. The high irradiance after heavy rainfall provided optimal meteorological conditions for bloom formation during summer, therefore, rain would also appear to forecast imminent bloom. The bloom formation was largely governed by cyanobacteria, in particular, Microcystis spp. and Anabaenaspp. Phycocyanin showed higher correlation with cyanobacteria (r = 0.744, P < 0.001) compared to chlorophyll-a(r = 0.599, P < 0.01). Therefore, phycocyanin was more accurate and useful than chlorophyll-a in quantitatively measuring cyanobacterial blooms. The atomic N:P ratio of the particulate form also showed a high correlation with cyanobacteria (r = 0.541, P < 0.01), increasing from 4.3 to 14.6 during bloom formation, while that of the dissolved form decreased from 25.5 to 8.7. These results indicated that the algae assimilated N significantly without comparable P uptake during the blooming season, which was in sharp contrast to the excessive storage of P during the spring.