On Haldane's formulation of Luria and Delbrück's mutation model

Two formulations of Luria and Delbrück's mutation model have been in common use since the 1940s. While mathematicians focused their attention on the formulation of Lea and Coulson that assumes asynchronous cell growth, biologists found more appealing the formulation of Haldane that assumes synchronous cell growth. This article attempts to solve several outstanding issues for the latter formulation. First, it provides an exact, closed-form expression for the mutant distribution by correcting a minor error in the literature. Second, it presents a novel algorithm for computing the mutant distribution, which leads to novel methods for computing point and interval estimates of mutation rates based on the maximum likelihood principle. Third, it critically examines existing methods based on the mean number of mutants. Finally, it compares the two formulations to underline their strengths and shortcomings.     

The influence of cyclic heating and cooling on <Emphasis Type="Italic">Escherichia coli</Emphasis> survival

Repeated heating and cooling in lethal (2–52°C) and nonlethal (2–37°C) temperature ranges resulted in cell death of Escherichia coli B/r and E. coli B_S?1 suspended in 0.01 M phosphate buffer, pH 7.0 at varying osmotic pressure, but not in cow’s milk. The lethal effect increased with the rate of heating and cooling and with increasing suspension media tonicity; it may be caused by the temperature destabilization of cellular osmotic homeostasis.     

Are correlations among foliar traits in ferns consistent with those in the seed plants?

Broad-based studies of gymnosperms and angiosperms reveal consistent and functionally significant correlations among foliar traits such as leaf mass per area (LMA), maximum photosynthetic rate (A(area)), foliar nitrogen (N(area)), foliar chlorophyll (Chl) and leaf longevity. To assess the generality of these relationships, we studied 20 fern species growing in the understorey of a temperate deciduous forest. We found that foliar N(area) increases with LMA, and that foliar N(area) and A(area) are positively correlated with one another, as are foliar N(area) and Chl. The ferns in general have very low LMA compared with most seed plants; A(area), N(area) and Chl are below median values for seed plants but are not extreme. Species with overwintering fronds have significantly higher LMA than species with fronds that senesce at the end of the growing season, as well as a significantly higher C : N ratio in frond tissue and relatively high foliar N on an areal basis. Correlations among foliar traits associated with gas exchange in these forest understorey ferns are in accordance with patterns reported for seed plants, suggesting a high degree of functional constraint on the interrelationships among key elements in foliar design.     

Novel mannose-sequestration technique reveals variation in subcellular orthophosphate pools do not explain the effects of phosphorus nutrition on photosynthesis in Eucalyptus globulus seedlings

Although only a small proportion of plant phosphorus (P) is used for photosynthesis, the relationships between P and photosynthesis can be strong. It was hypothesized, in this study, that variation in the allocation of orthophosphate (Pi) between active (cytoplasmic) and nonactive (vacuolar) pools would underpin differences in rates of photosynthesis in 4-month-old Eucalyptus globulus seedlings grown with a varying P supply. Photosynthetic biochemistry was assessed by the response of net photosynthesis to increasing intercellular [CO2]. Cytoplasmic Pi was sequestered as mannose 6-phosphate. Total P and the proportion of P as Pi were positively related to P supply. The ratios of active : stored Pi (10-24%) varied little over the range of treatments. Active Pi was positively related to P supply, as was photosynthesis (7 micromol CO2 m(-2) s(-1) with 0 mM P vs. 16 micromol CO2 m(-2) s(-1) with 0.32 mM P). Positive relationships between P supply and photosynthesis were explained best by leaf P content, not by active pools of Pi. The distribution of Pi between the vacuole and the cytoplasm had little impact on the photosynthetic phosphorus-use efficiency (PPUE), and reductions in cytoplasmic Pi had little effect on photosynthesis. Hence, PPUE is an unsuitable guide for assessing plant responses to increasingly unavailable P in the environment.     

Predator–prey encounter rates in freshwater piscivores: effects of prey density and water transparency

One of the most fundamental components of predator–prey models is encounter rate, modelled as the product of prey density and search efficiency. Encounter rates have, however, rarely been measured in empirical studies. In this study, we used a video system approach to estimate how encounter rates between piscivorous fish that use a sit-and-wait foraging strategy and their prey depend on prey density and environmental factors such as turbidity. We first manipulated prey density in a controlled pool and field enclosure experiments where environmental factors were held constant. In a correlative study of 15 freshwater lakes we then estimated encounter rates in natural habitats and related the results to both prey fish density and environmental factors. We found the expected positive dependence of individual encounter rates on prey density in our pool and enclosure experiments, whereas the relation between school encounter rate and prey density was less clear. In the field survey, encounter rates did not correlate with prey density but instead correlated positively with water transparency. Water transparency decreases with increasing prey density along the productivity gradient and will reduce prey detection distance and thus predator search efficiency. Therefore, visual predator–prey encounter rates do not increase, and may even decrease, with increasing productivity despite increasing prey densities.     

Effects of resource level and habitat type on behavioral and morphological plasticity in Eurasian perch

Spatial and temporal heterogeneity in the environment is a common feature affecting many natural populations. For example, both the resource levels and optimal habitat choices of individuals likely change over time. One way for organisms to cope with environmental variation is to display adaptive plasticity in traits such as behavior and morphology. Since trait plasticity is hypothesized to be a prerequisite for character divergence, studies of mechanisms behind such plasticity are warranted. In this study, we looked at the interaction of two potentially important environmental variables on behavioral and morphological plasticity in Eurasian perch (Perca fluviatilis L.). More specifically, the plastic responses in activity and morphology of perch exposed to different resource levels and simulated habitat types were studied in an aquarium experiment. The resource level experienced had a large influence on plasticity in both activity and morphology. Behavioral adaptations have been thought to mediate morphological transitions, and we suggest that the morphological response to the resource level was mediated by differences in activity and growth rates. The habitat type also affected morphological plasticity but to a lesser extent, and there was no effect on activity from habitat type. Based on these results, we suggest that it is essential to include several environmental factors acting in concert when studying mechanisms behind trait plasticity. We also propose that variation in resource levels might play a key role in fostering trait plasticity in at least fish populations, while other environmental variables such as divergent habitat complexities and prey types might be less influential. Dynamics in resource levels and optimal habitat choices might thus be important factors influencing character divergence in natural populations.     

Root foraging traits and competitive ability in heterogeneous soils

The responses of plant roots to nutrient patches in soil may be an important component of competitive ability. In particular, the scale, precision, and rate of foraging for patchy soil resources may influence competitive ability in heterogeneous soils. In a target–neighbor experiment in the field, per-individual and per-gram competitive effects were measured for six old-field species with known root foraging scale, precision, and rate. The presence and number of nutrient patches were also manipulated in a full factorial design. Number and presence of patches did not influence the outcome of competition. Competitive ability was not related to total plant size, growth rate, or root:shoot allocation, or to root foraging precision. Per-individual competitive effects were marginally correlated with root foraging scale (biomass of roots) and root foraging rate (time required to reach a patch). Therefore, competitive ability was more closely related to ability to quickly fill a soil volume with roots than to ability to preempt resource-rich patches.     

When is breeding for drought tolerance optimal if drought is random?

* Increasing climatic unpredictability associated with characteristics of some species makes plant drought-tolerance an important drought-adaptation strategy. Using norm-of-reaction functions, or empirically determined functions that enable us to predict the state of a trait given the state of an environmental variable, allows modelling of plant performance when water availability varies randomly. * A mathematical model is proposed to evaluate drought-tolerance and growth strategies given a set of environmental parameters: the frequency of rainy days, the soil water-storage capacity, plant water use and plant growth rates. This model compares the performance of genotypes that differ in drought tolerance expressed as the ability to grow in drier soils, and assumes a general trade-off function between drought tolerance and maximum plant growth rate. * It is worth selecting plants with a greater degree of drought tolerance, expressed by the ability to grow in drier soils whenever the frequency of rains is smaller than the rate of soil water depletion. Otherwise, maximizing growth rate at the expense of drought tolerance is the best strategy. The nature of the trade-off between drought tolerance and plant growth rate also constrains the selection for optimal drought-adapted genotypes. * Breeders will have to consider these aspects of plant-environment interactions before establishing selection programs for drought adaptation.     

How to compute the effective size of spatiotemporally structured populations using separation of time scales

Calculations to derive effective population size become highly complicated when complex population structure is considered. We provide an easy method of computing the effective size of a subdivided population with overlapping generations (a spatiotemporally structured population) using an approximation based on separation of time scales. We also numerically compute the effective size to verify the accuracy of the derived formula. Various interesting quantities, including moments of coalescent time, are readily derived using this approach.     

A Markov chain Monte Carlo strategy for sampling from the joint posterior distribution of pedigrees and population parameters under a Fisher-Wright model with partial selfing

A simple population genetic model is presented for a hermaphrodite annual species, allowing both selfing and outcrossing. Those male gametes (pollen) responsible for outcrossing are assumed to disperse much further than seeds. Under this model, the pedigree of a sample from a single locality is loop-free. A novel Markov chain Monte Carlo strategy is presented for sampling from the joint posterior distribution of the pedigree of such a sample and the parameters of the population genetic model (including the selfing rate) given the genotypes of the sampled individuals at unlinked marker loci. The computational costs of this Markov chain Monte Carlo strategy scale well with the number of individuals in the sample, and the number of marker loci, but increase exponentially with the age (time since colonisation from the source population) of the local population. Consequently, this strategy is particularly suited to situations where the sample has been collected from a population which is the result of a recent colonisation process.