On a Problem of Allocation of Sample Size in Stratified Random Sampling

In this paper we shall consider the problem of judging how good an actual compromise allocation is compared to Neyman's optimum allocation for the case of stratified random sampling by obtaining a bound to the ratio of the corresponding variances. A solution to a more general version of the problem considered by COCHRAN (1977) and RAO (1983) has been obtained and the results have been empirically demonstrated.     

Identifying fitness and optimal life-history strategies for an asexual filamentous fungus

Filamentous fungi are ubiquitous and ecologically important organisms with rich and varied life histories, however, there is no consensus on how to identify or measure their fitness. In the first part of this study we adapt a general epidemiological model to identify the appropriate fitness metric for a saprophytic filamentous fungus. We find that fungal fitness is inversely proportional to the equilibrium density of uncolonized fungal resource patches which, in turn, is a function of the expected spore production of a fungus. In the second part of this study we use a simple life history model of the same fungus within a resource patch to show that a bang-bang resource allocation strategy maximizes the expected spore production, a critical fitness component. Unlike bang-bang strategies identified in other life-history studies, we find that the optimal allocation strategy for saprophytes does not entail the use of all of the resources within a patch.     

Effect of stochasticity in the availability of pollinators on the resource allocation within a flower

In this article, we develop a simple model to study the effect of stochasticity in pollination on evolutionarily stable (ES) resource allocation within a hermaphrodite flower of animal-pollinating plants. For simplicity, we consider trade-off in resource allocation between attractive structure (petals etc.) and female function (seeds and fruits) with neglecting the amount of resource allocated to male function (pollens and stamens). We show that ES resource allocation does not much depend on the detail of the probability distribution of the number of pollinator visit on a flower, but on the probability that a flower fails to be visited. We also find that: (1) When the flowers are self-incompatible, the ES allocation to the attractive structure monotonically increases as the availability of pollinators in the environment decreases. (2) When there is strong positive correlation among flowers in the number of pollinator visit, the ES allocation is larger than the case without the correlation. (3) When the flowers are self-compatible and engage prior selfing, the ES allocation monotonically increases as the availability of pollinators in the environment decreases to a threshold, under which it suddenly decreases to zero.     

Sperm competition and sex allocation in simultaneous hermaphrodites

Summary Sex allocation theory is developed for hermaphrodites having frequent copulations and long-term sperm storage. Provided the sperm displacement mechanisms are similar to those known in insects, the ESS allocation to sperm versus eggs satisfies a rather simple rule. There are no data to test this rule, as yet.     

A model of the long-term response of carbon allocation and productivity of forests to increased CO2concentration and nitrogen deposition

We present a simple theoretical analysis of the long term response of forest growth and carbon allocation to increased atmospheric [CO₂] and N deposition. Our analysis is based on a recent model which predicts that plant light-use efficiency increases with [CO₂] but is independent of plant N supply. We combine that model with simple assumptions for nitrogen fluxes in the soil. A quasi-equilibrium analysis of the short term tree and soil pools is then used to develop a simple graphical depiction of the long term carbon and nitrogen supply constraints on total growth, stem growth and foliar allocation. Our results suggest that long-term growth responses to [CO₂] and N deposition depend strongly on the extent to which stem allocation and foliage allocation are coupled. At one extreme (‘no coupling’), when stem allocation is fixed and independent of foliage allocation, there is no response of total growth or stem growth to increased [CO₂] unless N deposition increases. At the other extreme (‘linear coupling’), when stem allocation is proportional to foliage allocation, there is a significant long-term increase in total growth following a doubling of [CO₂], even when N deposition is unchanged, but stem growth decreases because of a long-term decrease in foliage allocation. For both types of coupling, total growth and stem growth increase with increasing N deposition. In the case of linear coupling, however, the N deposition response of stem growth is significantly larger than that of total growth, because of a long-term increase in foliage allocation. We compare our results with those obtained previously from an alternative model of canopy light-use efficiency involving a dependence on the foliar N:C ratio in addition to [CO₂]. Our results highlight the need for more experimental information on (i) the extent to which canopy light-use efficiency is independent of N supply, and (ii) the relationship between foliage allocation and stem allocation.     

Generation of an Industry-specific Physico-chemical Allocation Matrix. Application in the Dairy Industry and Implications for Systems Analysis (9 pp)

Background, Aims and Scope Allocation is required when quantifying environmental impacts of individual products from multi-product manufacturing plants. The International Organization for Standardization (ISO) recommends in ISO 14041 that allocation should reflect underlying physical relationships between inputs and outputs, or in the absence of such knowledge, allocation should reflect other relationships (e.g. economic value). Economic allocation is generally recommended if process specific information on the manufacturing process is lacking. In this paper, a physico-chemical allocation matrix, based on industry-specific data from the dairy industry, is developed and discussed as an alternative allocation method. Methods Operational data from 17 dairy manufacturing plants was used to develop an industry specific physico-chemical allocation matrix. Through an extensive process of substraction/substitution, it is possible to determine average resource use (e.g. electricity, thermal energy, water, etc) and wastewater emissions for individual dairy products within multi-product manufacturing plants. The average operational data for individual products were normalised to maintain industry confidentiality and then used as an industry specific allocation matrix. The quantity of raw milk required per product is based on the milk solids basis to account for dairy by-products that would otherwise be neglected. Results and Discussion Applying fixed type allocation methods (e.g. economic) for all input and outputs based on the quantity of product introduces order of magnitude sized deviations from physico-chemical allocation in some cases. The error associated with the quality of the whole of factory plant data or truncation error associated with setting system boundaries is insignificant in comparison. The profound effects of the results on systems analysis are discussed. The results raise concerns about using economic allocation as a default when allocating intra-industry sectoral flows (i.e. mass and process energy) in the absence of detailed technical information. It is recommended that economic allocation is better suited as a default for reflecting inter-industry sectoral flows. Conclusion The study highlights the importance of accurate causal allocation procedures that reflect industry-specific production methods. Generation of industry-specific allocation matrices is possible through a process of substitution/subtraction and optimisation. Allocation using such matrices overcomes the inherit bias of mass, process energy or price allocations for a multi-product manufacturing plant and gives a more realistic indication of resource use or emissions per product. The approach appears to be advantageous for resource use or emissions allocation if data is only available on a whole of factory basis for several plants with a similar level of technology. Recommendation and Perspective The industry specific allocation matrix approach will assist with allocation in multi-product LCAs where the level of technology in an industry is similar. The matrix will also benefit dairy manufacturing companies and help them more accurately allocate resources and impacts (i.e. costs) to different products within the one plant. It is recommended that similar physico-chemical allocation matrices be developed for other industry sectors with a view of ultimately coupling them with input-output analysis.     

Unbalanced ranked set sampling for estimating a population proportion

The application of ranked set sampling (RSS) techniques to data from a dichotomous population is currently an active research topic, and it has been shown that balanced RSS leads to improvement in precision over simple random sampling (SRS) for estimation of a population proportion. Balanced RSS, however, is not in general optimal in terms of variance reduction for this setting. The objective of this article is to investigate the application of unbalanced RSS in estimation of a population proportion under perfect ranking, where the probabilities of success for the order statistics are functions of the underlying population proportion. In particular, the Neyman allocation, which assigns sample units for each order statistic proportionally to its standard deviation, is shown to be optimal in the sense that it leads to minimum variance within the class of RSS estimators that are simple averages of the means of the order statistics. We also use a substantial data set, the National Health and Nutrition Examination Survey III (NHANES III) data, to demonstrate the feasibility and benefits of Neyman allocation in RSS for binary variables.     

Incorporating Prior Beliefs in Treatment Allocation for Clinical Trials

Recently Faraggi and Reiser (1991) introduced a general dynamic treatment allocation scheme which incorporates the permuted block allocation procedure and the Begg Iglewicz procedure as special cases. A drawback of previous allocation methods is that they did not allow incorporation of prior knowledge of the relative importance of the prognostic factors. In this paper we extend our allocation model to incorporate the weighting of prognostic factors. A simulation study examines the effects of this procedure and an example of its implementation is given.     

Size‐dependent resource allocation and sex allocation in herbaceous perennial plants

Individuals within a population often differ considerably in size or resource status as a result of environmental variation. In these circumstances natural selection would favour organisms not with a single, genetically determined allocation, but with a genetically determined allocation rule specifying allocation in relation to size or environment. Based on a graphical analysis of a simple evolutionarily stable strategy (ESS) model for herbaceous perennial plants, we aim to determine how cosexual plants within a population should simultaneously adjust their reproductive allocation and sex allocation to their size. We find that if female fitness gain is a linear function of resource investment, then a fixed amount of resources should be allocated to male function, and to post‐breeding survival as well, for individuals above a certain size threshold. The ESS resource allocation to male function, female function, and post‐breeding survival positively correlate if both male and female fitness gains are a saturating function of resource investment. Plants smaller than the size threshold are expected to be either nonreproductive or functionally male only.     

Complex Genetic Effects on Early Vegetative Development Shape Resource Allocation Differences Between Arabidopsis lyrata Populations

Costs of reproduction due to resource allocation trade-offs have long been recognized as key forces in life history evolution, but little is known about their functional or genetic basis. Arabidopsis lyrata, a perennial relative of the annual model plant A. thaliana with a wide climatic distribution, has populations that are strongly diverged in resource allocation. In this study, we evaluated the genetic and functional basis for variation in resource allocation in a reciprocal transplant experiment, using four A. lyrata populations and F₂ progeny from a cross between North Carolina (NC) and Norway parents, which had the most divergent resource allocation patterns. Local alleles at quantitative trait loci (QTL) at a North Carolina field site increased reproductive output while reducing vegetative growth. These QTL had little overlap with flowering date QTL. Structural equation models incorporating QTL genotypes and traits indicated that resource allocation differences result primarily from QTL effects on early vegetative growth patterns, with cascading effects on later vegetative and reproductive development. At a Norway field site, North Carolina alleles at some of the same QTL regions reduced survival and reproductive output components, but these effects were not associated with resource allocation trade-offs in the Norway environment. Our results indicate that resource allocation in perennial plants may involve important adaptive mechanisms largely independent of flowering time. Moreover, the contributions of resource allocation QTL to local adaptation appear to result from their effects on developmental timing and its interaction with environmental constraints, and not from simple models of reproductive costs.     

Spatial dynamics of adaptive sex ratios

According to Fisherian sex allocation theory, parents that can adjust their offspring sex ratio in response to skews in population sex ratio will maximize their fitness over parents lacking this ability. There is good evidence that adaptive sex ratio adjustment occurs in many natural populations, but deviations from theoretical predictions have also been observed. These anomalies may be more apparent than real. When the spatial dimension of sex ratio variation is ignored, then a mismatch between empirical data and theoretical predictions based on panmictic mating is to be expected. We illustrate this with data on human sex ratio variation in 21 preindustrial populations, and with a cellular automaton model built to obey Fisherian sex allocation rules. The results from the model generally match with the data. When information about the ambient sex ratio is limited, then the sex allocation decisions may appear locally maladaptive. In general, the results indicate that Fisher's sex-ratio theory may have greater explanatory power than previously thought.     

Sex‐allocation conflict and sexual selection throughout the lifespan of eusocial colonies

Models of sex‐allocation conflict are central to evolutionary biology but have mostly assumed static decisions, where resource allocation strategies are constant over colony lifespan. Here, we develop a model to study how the evolution of dynamic resource allocation strategies is affected by the queen‐worker conflict in annual eusocial insects. We demonstrate that the time of dispersal of sexuals affects the sex‐allocation ratio through sexual selection on males. Furthermore, our model provides three predictions that depart from established results of classic static allocation models. First, we find that the queen wins the sex‐allocation conflict, while the workers determine the maximum colony size and colony productivity. Second, male‐biased sex allocation and protandry evolve if sexuals disperse directly after eclosion. Third, when workers are more related to new queens, then the proportional investment into queens is expected to be lower, which results from the interacting effect of sexual selection (selecting for protandry) and sex‐allocation conflict (selecting for earlier switch to producing sexuals). Overall, we find that colony ontogeny crucially affects the outcome of sex‐allocation conflict because of the evolution of distinct colony growth phases, which decouples how queens and workers affect allocation decisions and can result in asymmetric control.     

Allocation of carbon and nitrogen as a function of the internal nitrogen status of a plant: Modelling allocation under non-steady-state situations

In this paper we model allocation of carbon and nitrogen to roots and leaves as a function of the nitrogen status of a plant. Under steady-state conditions, allocation of carbon and nitrogen to leaves is exponentially (positively) correlated with plant nitrogen concentration, whereas allocation to roots is correlated negatively, also in an exponential manner.Allocation functions derived under steady-state conditions are used to simulate biomass partitioning under non-steady-state nutrient conditions. Upon nitrogen deprivation, measured and simulated values are rather similar with time, suggesting that allocation functions derived under steady-state conditions also hold under non-steady-state conditions.     

青藏高原特有植物露蕊乌头（毛茛科）从冰期避难所扩张后繁殖资源分配的变化

物种分布范围的形成是进化生态学研究的基本问题之一。但植物的资源分配策略是否与物种边界形成有关一直没有相关研究。青藏高原特有植物露蕊乌头在末次最大冰期时有4个避难所,但冰期后只有一个避难所的种群发生了扩张并最终形成了现代分布格局。以露蕊乌头的避难所种群（同仁种群）和扩张后邻近分布区边缘的两个种群（兴海种群和海北种群）为研究对象,通过比较避难所种群和边缘种群的资源分配方式,探讨露蕊乌头的资源分配与该植物分布区及边界形成的关系。结果发现：1）兴海和海北种群的营养结构（包括根、植株高度和茎叶生物量）均显著低于同仁种群．海北种群的繁殖结构（花数量和花生物量）显著低于同仁和兴海种群,但海北和兴海的繁殖分配均显著高于同仁种群;2）3个种群的繁殖资源与个体大小呈现显著的正相关关系,投入到繁殖资源的比例（繁殖分配）与个体大小呈显著的负相关关系。对露蕊乌头的研究结果一方面进一步证明了个体大小依赖的繁殖分配,但不符合“植物开始繁殖必须达到一定的大小（阈值）”这一结论,这可能与露蕊乌头的生活史特征有关：而另一方面,露蕊乌头在扩张过程中逐渐增加了对繁殖资源投资的比例,说明胁迫生境中有性繁殖对该植物具有更为重要的意义,且露蕊乌头在扩张过程中可能逐渐实现繁殖产出最大化,并可能在边缘种群实现最优繁殖分配进而最终形成该物种分布区的边界,但这一结论仍需在更多的植物类群中验证。     

青藏高原特有植物露蕊乌头 (毛茛科) 从冰期避难所扩张后繁殖资源分配的变化

物种分布范围的形成是进化生态学研究的基本问题之一,但植物的资源分配策略是否与物种边界形成有关一直没有相关研究。青藏高原特有植物露蕊乌头在末次最大冰期时有4个避难所,但冰期后只有一个避难所的种群发生了扩张并最终形成了现代分布格局。以露蕊乌头的避难所种群（同仁种群）和扩张后邻近分布区边缘的两个种群（兴海种群和海北种群）为研究对象,通过比较避难所种群和边缘种群的资源分配方式,探讨露蕊乌头的资源分配与该植物分布区及边界形成的关系。结果发现：1）兴海和海北种群的营养结构（包括根、植株高度和茎叶生物量）均显著低于同仁种群,海北种群的繁殖结构（花数量和花生物量）显著低于同仁和兴海种群,但海北和兴海的繁殖分配均显著高于同仁种群;2）3个种群的繁殖资源与个体大小呈现显著的正相关关系,投入到繁殖资源的比例（繁殖分配）与个体大小呈显著的负相关关系。对露蕊乌头的研究结果一方面进一步证明了个体大小依赖的繁殖分配,但不符合“植物开始繁殖必须达到一定的大小（阈值）”这一结论,这可能与露蕊乌头的生活史特征有关;而另一方面,露蕊乌头在扩张过程中逐渐增加了对繁殖资源投资的比例,说明胁迫生境中有性繁殖对该植物具有更为重要的意义,且露蕊乌头在扩张过程中可能逐渐实现繁殖产出最大化,并可能在边缘种群实现最优繁殖分配进而最终形成该物种分布区的边界,但这一结论仍需在更多的植物类群中验证。     

The effect of allometric partitioning on herbivory tolerance in four species in South China

Herbivory tolerance can offset the negative effects of herbivory on plants and plays an important role in both immigration and population establishment. Biomass reallocation is an important potential mechanism of herbivory tolerance. To understand how biomass allocation affects plant herbivory tolerance, it is necessary to distinguish the biomass allocations resulting from environmental gradients or plant growth. There is generally a tight balance between the amounts of biomass invested in different organs, which must be analyzed by means of an allometric model. The allometric exponent is not affected by individual growth and can reflect the changes in biomass allocation patterns of different parts. Therefore, the allometric exponent was chosen to study the relationship between biomass allocation pattern and herbivory tolerance. We selected four species (Wedelia chinensis, Wedelia trilobata, Merremia hederacea, and Mikania micrantha), two of which are invasive species and two of which are accompanying native species, and established three herbivory levels (0%, 25% and 50%) to compare differences in allometry. The biomass allocation in stems was negatively correlated with herbivory tolerance, while that in leaves was positively correlated with herbivory tolerance. Furthermore, the stability of the allometric exponent was related to tolerance, indicating that plants with the ability to maintain their biomass allocation patterns are more tolerant than those without this ability, and the tendency to allocate biomass to leaves rather than to stems or roots helps increase this tolerance. The allometric exponent was used to remove the effects of individual development on allocation pattern, allowing the relationship between biomass allocation and herbivory tolerance to be more accurately explored. This research used an allometric model to fit the nonlinear process of biomass partitioning during the growth and development of plants and provides a new understanding of the relationship between biomass allocation and herbivory tolerance.     

Nutritional requirements for web synthesis in the tetragnathid spider Nephila clavipes

Trap-constructing organisms provide a unique opportunity for the study of resource allocation, because an observer can unambiguously determine the allocation to foraging. In species that synthesize a trap from physiologically important compounds, there is the further advantage that there may be direct trade-offs between allocation of resources to foraging and physiological functions. We examined the ability of the spider Nephila clavipes (L.; Araneae: Tetragnathidae) to synthesize resources that are known to be used for both web synthesis and non-foraging physiological functions. We found that choline, required for both web function and physiological function, is an essential nutrient: it is not synthesized by this spider. Under laboratory conditions with a diet of fruit flies, choline is limiting, and the spiders make allocation trade-offs between investing choline in foraging (the web) or in their body.     

Changes in Reproductive Allocation after Expansion from the Glacial Refugium and Implications for the Distribution Range in the Qinghai Tibet Plateau Native Herb,Gymnaconitum gymnandrum (Ranunculaceae)

A fundamental goal of ecology and evolution is to explain patterns of species distribution and abundance. However, the way in which stable distribution ranges are shaped by natural selection is still poorly understood, especially whether patterns of resource allocation have contributed to the range size and the formation of range boundary received little attention. For annual herb, the maximum reproductive allocation is predicted to be 50%, and thus we predicted that reproductive allocation might contribute to the formation of range boundary since plant will enhance allocations to reproduction in stressful environments. In this study, we presented our data on resource allocation between population from the glacial refegium and those from the marginal populations in Gymnaconitum gymnandrum, an alpine biennial native to the Qinghai Tibet Plateau, aiming to find the contribution of resource allocation to the formation of range boundary. Our results showed that resource allocations to vegetative organs, including roots, plant height and stem leaf biomass, were significantly higher in the refugium population that in the two marginal populations, and allocations to reproductive organs, including flower number and flower biomass, were significantly lower in one marginal population (Haibei population) than in the other marginal population (Xinghai population) and the refugium population (Tongren population). However, reproductive allocation was significantly higher in the marginal populations than in the refugium population. In addition, in each of the three populations, we found a positive relationship between the plant size and flower biomass but a negative relationship between the plant size and reproductive allocation. Our results indicated a size dependent reproductive allocation in Ggymnandrum, but we did not find a size threshold for reproduction in each of the three populations of this plant, which might be attributed to the life history of this biennial herb. We also suggested that reproductive allocation was increased during the process of range expansion and may rise to the optimal reproductive allocation in the marginal populations, which suggested the important role of sexual reproduction for plants in more stressful environments and the formation of range boundary. However, these conclusions need to be further proved in other plant species.     

How geitonogamous selfing affects sex allocation in hermaphrodite plants

Does the mode of self-pollination affect the evolutionarily stable allocation to male vs. female function? We distinguish the following scenarios. (1) An ‘autogamous’ species, in which selfing occurs within the flower prior to opening. The pollen used in selfing is a constant fraction of all pollen grains produced. (2) A species with ‘abiotic pollination’, in which selfing occurs when pollen dispersed in one flower lands on the stigma of a nearby flower on the same plant (geitonogamy). The selfing rate increases with male allocation but a higher selfing rate does not mean a reduced export of pollen. (3) An ‘animal-pollinated’ species with geitonogamous selfing. Here the selfing rate also increases with male allocation, but pollen export to other plants in the population is a decelerating function of the number of simultaneously open flowers. In all three models selfing selects for increased female allocation. For model 3 this contradicts the general opinion that geitonogamous selfing does not affect evolutionarily stable allocations. In all models, the parent benefits more from a female-biased allocation than any other individual in the population. In addition, in models 2 and 3, greater male allocation results in more local mate competition. In model 3 and in model 2 with low levels of inbreeding depression, hermaphroditism is evolutionarily stable. In model 2 with high inbreeding depression, the population converges to a fitness minimum for the relative allocation to male function. In this case the fitness set is bowed inwards, corresponding with accelerating fitness gain curves. If the selfing rate increases with plant size, this is a sufficient condition for size-dependent sex allocation (more allocation towards seeds in large plants) to evolve. We discuss our results in relation to size-dependent sex allocation in plants and in relation to the evolution of dioecy.     

Linking flowering and reproductive allocation in response to nitrogen addition in an alpine meadow

Aims Plants can change in phenology and biomass allocation in response to environmental change. It has been demonstrated that nitrogen is the most limiting resource for plants in many terrestrial ecosystems. Previous studies have usually focused on either flowering phenology or biomass allocation of plants in response to nitrogen addition; however, attempts to link flowering phenology and biomass allocation are still rare. In this study, we tested the effects of nitrogen addition on both flowering phenology and reproductive allocation in 34 common species. We also examined the potential linkage between flowering time and reproductive allocation in response to nitrogen addition.Methods We conducted a 3-year nitrogen addition experiment in Tibetan alpine meadow. We measured first flowering date and the reproductive allocation for 34 common plant species in control, low and high nitrogen added plots, respectively. One-way analysis of variance was used to examine differences of first flowering date and reproductive allocation among treatments. The relationships between the change in species first flowering date and change in reproductive allocation in response to nitrogen addition were examined by calculating Pearson correlation coefficients.Important findings For most species, both first flowering date and reproductive allocation significantly responded to nitrogen addition. Nitrogen addition significantly delayed the first flowering date and reduced the reproductive allocation for all graminoid species, but accelerated flowering and increased reproductive allocation for most forb species. We found that changes in first flowering date significantly negatively correlated with the changes in reproductive allocation over species in response to nitrogen, which indicated a positive relationship between flowering response and plant performance in reproductive allocation. Species that advanced their flowering time with nitrogen addition increased their reproductive allocation, whereas those that delayed flowering time tended to decline in reproductive allocation with nitrogen addition. Our results suggest that species-specific switch from vegetative growth to reproductive growth could influence species performance.