Concentration Evolution of Gas Species within a Collapsing Bubble in a Liquid Medium

In this study numerical methods are used to investigate the relationship between chemical concentration of gas species within a cavitating bubble, equilibrium radius of the gas bubble and pressure variations in the ambient liquid. For this purpose, governing equations are developed to describe the dynamic equilibrium of a bubble in a flowing fluid and mass transfer between gas and liquid phases, where it was assumed that gases undergo isothermal compression, obey the ideal gas law, Henry law. It is further assumed that the concentration of each phase within the bubble is uniform. The resulting nonlinear equations are solved using implicit Trapezoidal method with Newton iteration. Four gas species are modeled under various initial and ambient pressure variation conditions. These conditions maybe considered to represent typical cavitation events. The numerical results obtained are presented in terms of dimensionless numbers. These results indicate that chemical damage maybe an important component of cavitation surface damage, since high concentration profiles may develop within a collapsing bubble. Proposed formulation and numerical solutions are simple and cost effective to implement. The results presented in this study maybe used to benchmark experimental investigations or other more complex solutions, which are outside the scope of this study.     

Adaptive significance of phytoplankton stickiness with emphasis on the diatom Skeletonema costatum

Diatom aggregate formation was analyzed using coagulation theory. Population dynamics models show that coagulation has an important impact on species succession during diatom blooms. When different species collide and form mixed aggregates this process causes interspecific interference competition within the diatom community. The outcome can be predicted by a set of simple differential equations. For a twospecies system the equations reduce to the Lotka-Volterra two-species competition model. The outcome of this interference competition depends on species-specific growth rates, cell sizes, stickiness and on the species composition of the seeding populations of a bloom. Due to mutual flocculation some species may disappear from the environment. Small and fast growing diatoms are favoured by high stickiness coefficients. The impact of stickiness on species succession was found to be most pronounced in eutrophic and hydrographically isolated environments. The sticking properties of the diatom Skeletonema costatum are discussed in an evolutionary context; we suggest that mutual coagulation increases the abundance of S. costatum relative to other diatom species in coastal areas. The model was tested on field data, and the predicted dynamics of a spring bloom was very similar to that observed.     

Extinction Rate Estimates for Plant Populations in Revisitation Studies: Importance of Detectability

Abstract:  Many researchers have obtained extinction-rate estimates for plant populations by comparing historical and current records of occurrence. A population that is no longer found is assumed to have gone extinct. Extinction can then be related to characteristics of these populations, such as habitat type, size, or species, to test ideas about what factors may affect extinction. Such studies neglect the fact that a population may be overlooked, however, which may bias estimates of extinction rates upward. In addition, if populations are unequally detectable across groups to be compared, such as habitat type or population size, comparisons become distorted to an unknown degree. To illustrate the problem, I simulated two data sets, assuming a constant extinction rate, in which populations occurred in different habitats or habitats of different size and these factors affected their detectability. The conventional analysis implicitly assumed that detectability equalled 1 and used logistic regression to estimate extinction rates. It wrongly identified habitat and population size as factors affecting extinction risk. In contrast, with capture-recapture methods, unbiased estimates of extinction rates were recovered. I argue that capture-recapture methods should be considered more often in estimations of demographic parameters in plant populations and communities.     

On stochastic differential equations and equilibrium distribution: a conditional moment approach

In the recent past there have been several attempts to obtain the equilibrium distribution of multiple populations and their moments in the context of some biological or ecological processes (e.g., Matis and Kiffe in Biometrics 52:155, 1996; Matis and Kiffe in Environ Ecol Stat 9:237, 2002; Renshaw in J Math Appl Med Biol, 15:1, 1998). In particular, the method of cumulant truncation (Matis and Kiffe in Biometrics 52:155, 1996) is a pioneering work in this field. However it requires solving a large number of cumulant functions even in the case of two simultaneous differential equations. Besides the solutions are approximate and depend on the precision of the software. Renshaw (Math Biosci 168:57, 2000) provided a nice extension of the univariate truncated saddle point procedure to multivariate scenarios. But this approach involves a multivariate Newton-Raphson type iterative algorithm whose performance and convergence are critically dependent on the choice of the initial values. In the present paper we propose a new and simple approach to obtain the equilibrium distribution of populations and their conditional moments in a system of differential equations of any dimension. Our proposed method, which is a natural extension of the classical variational matrix approach, has several advantages which are discussed in detail in the paper; among other things it includes the derivation of additional conditions which can be interpreted as environmental surrogates.     

Multiseasonal management of an agricultural pest. I: Development of the theory

A framework for analyzing the trade-off between economic yield from a crop and buildup of resistance to pesticide caused by repeated applications of pesticide is developed. The analysis begins with the case of age-independent pest dynamics, in which pests infest a field by arriving from an external pool. Initially, it is assumed that the pest genetics of interest are single locus, two allele, with resistance to pesticide dominant and susceptible pests more fit in the absence of spraying. The pesticide is applied only once during the season, with timing and intensity of the application as control variables. Interseasonal pest and crop dynamics are studied by solving appropriate ordinary differential equations. Intraseasonal pest dynamics are assumed to follow the Hardy-Weinberg formula. It is shown that the three class diploid model can be replaced by a two class haploid model with essentially no change in the results. A model based on partial differential equations is developed, for the case in which pest dynamics depend upon age, and it is shown that the partial differential equation model can be replaced by a pair of coupled ordinary differential equations. The main operational conclusion in this paper is that the timing of the application of pesticide can be used to control buildup of resistance and that the intensity of the application can be used to control the crop yield.     

Control targets for the management of biological systems

Attention is focused on biological systems which are describable in terms of ordinary differential equations subject to human control inputs. The concept of an isochronal system is introduced in order to include systems for which the differential equations are valid only over regularly reoccurring time intervals.It is assumed that the control inputs are to be chosen so that an integral cost function of the state of the system, the control used, current time, and the time interval of the control program is minimized. Problems associated with minimizing this cost function over an infinitely long time interval is then considered. Difficulties inherent with minimizing a cost integral on an infinite time interval are shown to be avoided by minimizing an average of the cost function over an unknown but periodic time interval. Under proper circumstance, the optimal control program for the average cost function is either identical to or a good approximation to the optimal control program for the original cost function over an infinitely long time interval.Necessary conditions are obtained for minimizing an average cost function over an unspecified time interval subject to the system equations. For a given problem the necessary conditions will yield but a single system trajectory in the state space. For management purposes this trajectory may be thought of as a target to which the system should be driven and maintained.A number of examples illustrate the use of the necessary conditions to obtain control targets. Certain problems associated with the stability of the target solutions are illustrated with the examples.     

A resource-based approach to modelling the dynamics of interacting populations

The procedure for modelling the growth of single-species populations [Sakanoue, S., 2007. Extended logistic model for growth of single-species populations. Ecol. Model. 205, 159–168] is improved to be applicable to the study of the dynamics of interacting populations. The improved procedure is based on three assumptions: resource availability changes with population size as a variable, resource supply to populations and population demand for resources are defined as functions of resource availability and population size, and the variables of resource availability and population size shift in the supply function attracted to the demand function. These assumptions are organized into three equations. The equations can generate the dynamics models of plant, herbivore, and detritivore populations, and their own resources. The models can be used to describe prey–predator dynamics. They naturally contain nonlinear terms for the predator’s numerical and functional responses. Depending on the terms, the fluctuations in resource availability and population size stabilize. The three equations can also generate the dynamics models of different populations consuming the same resources. The analysis of zero isoclines of the models shows that a superior population can be simply defined as one with a higher intrinsic rate of natural increase, that a stable coexistence may be realized with the intraspecific interference or the interspecific facilitation of superiors, and that the interspecific interference or the intraspecific facilitation of inferiors may make the coexistence unstable and the inferiors winners depending on their initial population size.     

Among- and within-population variation in sperm quality in the simultaneously hermaphroditic land snail Arianta arbustorum

Sperm competition models on the evolution of sperm size assume associations with another sperm quality trait, sperm longevity. Sperm length can also provide an indication of possible mechanisms affecting motility and thus fertilization success. Despite their importance, however, detailed mechanisms of sperm competition at the gamete level are poorly understood. In simultaneously hermaphroditic land snails, sperm traits and cryptic female choice are assumed to be crucial in determining fertilization success. We examined the variation in sperm length and number among individuals from four natural populations of the land snail Arianta arbustorum, a species with multiple mating and long-term sperm storage. We also assessed variation in velocity, motility and longevity of sperm in snails from two of the four populations. Independent of shell size, sperm length differed among populations and, to a minor extent, even among individuals within populations. Mean sperm length of a snail was not correlated with the number of sperm delivered in a spermatophore. The mean sperm velocity (=VCL) did not differ between snails from two populations. However, VCL varied among snails. Percentage motility and longevity of sperm differed between snails from the two populations. No correlations were found between length, velocity, percentage motility and longevity of sperm. To conclude, individual snails differed in sperm quality, and this variation may partly explain the differential fertilization success between A. arbustorum snails. Moreover, our findings did not support the positive association between sperm length and longevity assumed by sperm competition models for internally fertilizing species.     

Minimise long-term loss or maximise short-term gain?: Optimal translocation strategies for threatened species

Translocation is a useful management option for conservation of threatened animal species. It can be used to increase the range of a species, augment the numbers in a critical population, or establish new populations and hence spread the risk of extinction through local catastrophes. As it is an important and expensive conservation tool, translocation management decisions must be carefully considered, with the objective of the translocation project in mind. By analysing the translocation problem within a decision-theory framework, we find optimal management decisions that are rational and transparent. We illustrate our approach using a case study of the bridled nailtail wallaby (Onychogalea fraenata). Our particular translocation question is: if we have a set number of wallabies to translocate in each time period and two translocation sites, how many wallabies should we put at each site given the state of each population to maximise the benefit to the species? We model the translocated populations with first-order Markov chain stochastic population models, and use stochastic dynamic programming to determine the optimal management decisions. We look at two sites with different growth rates – one increasing and one decreasing – and compare the optimal strategies for two different objective functions. The first is a long-term persistence objective function, which maximises the persistence of translocated populations a large number of time steps after the end of the translocation program. The second maximises total population size at the end of the translocation program. Although these objective functions are similar, they generate surprisingly different optimal translocation strategies. When maximising the long-term persistence of the translocated populations, translocation decisions are not important as long as an increasing population is established. This indicates that site quality – rather than the number and timing of translocations – primarily determines the long-term persistence of populations. When maximising total population size, the optimal strategy is to add to the increasing population unless it is above a size where it is likely to reach its carrying capacity over the planning timeframe. As translocation decisions are important in fulfilling the objective, this objective function is more useful in creating practical advice for translocation managers. The discrepancy between the optimal strategies given by the two objectives demonstrates the importance of careful consideration when specifying the goals of a project. This observation applies not only to translocation programs, but any project where clear decision-making is needed.     

Leaf habit and woodiness regulate different leaf economy traits at a given nutrient supply

The large variation in the relationships between environmental factors and plant traits observed in natural communities exemplifies the alternative solutions that plants have developed in response to the same environmental limitations. Qualitative attributes, such as growth form, woodiness, and leaf habit can be used to approximate these alternative solutions. Here, we quantified the extent to which these attributes affect leaf trait values at a given resource supply level, using measured plant traits from 105 different species (254 observations) distributed across 50 sites in mesic to wet plant communities in The Netherlands. For each site, soil total N, soil total P, and water supply estimates were obtained by field measurements and modeling. Effects of growth forms, woodiness, and leaf habit on relations between leaf traits (SLA, specific leaf area; LNC, leaf nitrogen concentration; and LPC, leaf phosphorus concentration) vs. nutrient and water supply were quantified using maximum-likelihood methods and Bonferroni post hoc tests. The qualitative attributes explained 8-23% of the variance within sites in leaf traits vs. soil fertility relationships, and therefore they can potentially be used to make better predictions of global patterns of leaf traits in relation to nutrient supply. However, at a given soil fertility, the strength of the effect of each qualitative attribute was not the same for all leaf traits. These differences may imply a differential regulation of the leaf economy traits at a given nutrient supply, in which SLA and LPC seem to be regulated in accordance to changes in plant size and architecture while LNC seems to be primarily regulated at the leaf level by factors related to leaf longevity.     

On the use of growth rate parameters for projecting population sizes: Application to aphids

This paper extends the application of the cumulative size based mechanistic model, which has previously been shown to describe diverse aphid population size data well. The mechanistic model is reviewed with a focus on the explanatory role of the birth and death rate formulation. An analysis of two data sets, one on the mustard aphid and the other on the pecan aphid, indicates that multiple linear regression equations based on the estimated birth and death rate parameters alone account for nearly all (R² > 0.95) of the variability in two key population attributes, namely the peak count and the cumulative density. This indicates that population size variables may be projected directly from the growth rate parameters using linear equations. Such linear relationships based on the birth and death rate parameters are shown to hold also for certain generalized mechanistic models for which the analytical solution is not available. The birth and death rate coefficients, therefore, constitute a new succinct set of variables that could be included in the predictive modeling of aphid populations, as well as other insect and animal populations with local collapse which follow similar growth dynamics.     

A further contribution to the study of fish populations by capture-recapture experiments

In capture-recapture experiments, fish populations can be studied by two different sampling procedures. In both procedures, tagged fish are released on capture, but untagged fish are in one procedure released after tagging, in the second procedure they are retained. Using the two sampling techniques, Rafail (1971a,b) gave expressions for the estimation of an assumed constant (C) of proportionality between probabilities of capture of tagged to untagged fish which are simplified here to forms easier for calculation. The estimation of this constant (C) aids in estimation of abundance and mortality rates of untagged fish which are assumed to differ from those of tagged fish.     

"Mobbing" in Hawaiian Monk Seals (Monachus schauinslani): The Value of Simulation Modeling in the Absence of Apparently Crucial Data

Several small populations of Hawaiian monk seals ( Monachus schauinslani ) exhibit male-biased adult sex ratios and "mobbing," an aggressive behavior in which adult males injure and often kill adult females and immature seals of both sexes during mating attempts. Mobbing appears to be limiting the growth of some populations of this endangered species. The frequency of mobbing deaths appears to increase as a population's sex ratio becomes increasingly male-biased, although the exact relationship between these two variables (the mobbing response) is unknown. We developed a stochastic demographic model of a small Hawaiian monk seal population using several different assumptions about the mobbing response. We used the model to explore the origins of male-biased sex ratios in monk seal populations and to determine whether it was possible, given the lack of data on the mobbing response, to evaluate the probable effects of alternative management strategies to address the mobbing problem. Small populations (100 to 200 seals) and those with slower growth rates were more likely to develop male-biased adult sex ratios. Almost all of our modeling scenarios supported the immediate removal of males from populations where mobbing occurs. Our conclusions were relatively unaffected when the assumptions regarding the mobbing response were varied. Thus, a model was helpful even when apparently crucial data were unavailable.     

Spreading of oil on water in the surface-tension regime

The third stage of oil spreading on water, in which surface-tension force promotes spreading against the resisting viscous effect, is investigated using a similarity solution in combination with an integral boundary-layer technique to solve the unidirectional oil-spreading dynamics problem in the last stage of spreading. The thin layer is assumed to be supplied by oil from a bulk boundary. Using a constitutive equation for oil-film surface tension versus oil-film thickness, analytical solutions near the bulk boundary and near the edge are developed. Using the asymptotic solutions to initiate integration, the differential equations for the oil thickness, oil velocity, and boundary-layer profiles are integrated starting from the leading edge and bulk boundary, which after matching provide a complete solution. The results for the spreading-law prefactors are found to differ by about 10 % from published theoretical results using the same constitutive equation. Using an empirical constitutive equation for oil-film surface tension versus distance from the bulk boundary leads to a spreading-law prefactor that is in excellent agreement with the published experimental result and published theoretical work providing and using the same empirical constitutive equation.     

Role of climate and competitors in limiting fitness across range edges of an annual plant

It is often assumed that the geographic distributions of species match their climatic tolerances, but this assumption is not frequently tested. Moreover, few studies examine the relative importance of abiotic and biotic factors for limiting species ranges. We combined multiple approaches to assess the extent to which fitness of a widespread native annual legume, Chamaecrista fasciculata, decreases at and beyond its northern and western range edges, and how this is influenced by the presence of neighbors. First, we examined plant fitness and the effect of neighbors in natural populations at different geographic range locations for three years. Fitness decreased toward the northern range edge, but not the western edge. Neighbor removal had a consistently positive effect on seedpod production across all years and sites. Second, we established experimental populations at sites within the range, and at and beyond the northern and western range edges. We tracked individual fitness and recorded seedling recruitment in the following year (a complete generation) to estimate population growth rate. Individual fitness and population growth declined to near zero beyond both range edges, indicating that C. fasciculata with its present genetic composition will not establish in these regions, given conditions currently. We also carried out a neighbor removal treatment. Consistent with the natural populations, neighbors reduced seedpod production of reproductive adults. However, neighbors also increased early-season survival, and this positive effect early in life history resulted in a net positive effect of neighbors on lifetime fitness at most range locations. Our data show that the population growth rate of C. fasciculata includes values above replacement, and populations are well adapted to conditions up to the edge of the range, whereas the severely compromised fitness at sites beyond the edge precludes immediate establishment of populations and thereby impedes adaptation to these conditions.     

Photosynthate partitioning by phytoplankton in a New Zealand coastal upwelling system

A stimulation model of copepod population dynamics (development rate, fecundity, and mortality) was used to compute the predatory consumption necessary to control population growth in three dominant copepod species (Pseudocalanus sp., Paracalanus parvus, and Calanus finmarchicus) on Georges Bank, given observed seasonal cycles of copepod and predator populations. The model also calculated secondary production of each species. Copepod development rate and fecundity were functions of temperature while mortality was a function of predator abundance and consumption rate. Daily inputs of temperature and predator abundance (chaetognaths, ctenophores, and Centropages spp.) were derived from equations fit to field data. Model runs were made with various consumption rates until the model output matched observed copepod seasonal cycles. Computed consumption rates were low compared with published values from field and laboratory studies indicating that, even at conservative estimates of consumption, predators are able to control these copepod populations. Combined annual secondary production by the small copepod species, Pseudocalanus sp. and P. parvus, was nearly twice that of the larger C. finmarchicus with P. parvus having the highest total annual production.     

Diploid male production — a significant colony mortality factor in the fire ant Solenopsis invicta (Hymenoptera: Formicidae)

Summary Two forms of the fire ant, Solenopsis invicta, occur in North America; the monogyne form has colonies with a single functional queen while the polygyne form has colonies containing many functional queens. Field surveys indicate that diploid males are common in natural populations of the polygyne form but absent from monogyne populations, in contrast to laboratory data showing that similar frequencies of queens producing such males occur in the two types of populations. Our results show that mature monogyne colonies with adopted queens rear diploid males in the laboratory, so it is unlikely that the absence of these males from monogyne colonies in the field is due to discrimination against them by monogyne workers. On the other hand, incipient monogyne colonies that produce diploid males exhibit significantly higher mortality and significantly slower rates of growth (Figs. 1–3) than colonies producing workers only. These results suggest that the observed distribution of male diploidy in S. invicta can be explained by differential mortality of diploid male producing colonies of the two forms, with such colonies of the monogyne form experiencing 100% mortality early in development. The mortality differences due to this factor are shown to be related to the different social structures and modes of colony founding characterizing the two forms.     

Vertical distributions of Calanus finmarchicus and C. helgolandicus (Crustacea: Copepoda)

The vertical distributions of the spring populations of Calanus finmarchicus (Gunnerus) and C. helgolandicus Claus are described and compared. The differences we observed between the two species have probably confused the understanding of the vertical distribution and development of the populations of Calanus spp. in the shelf seas around the United Kingdom where the species occur together. The results imply that these two congeneric species have different behaviour patterns which minimise interspecific competition where the species have sympatric distributions. C. finmarchicus has its younger development stages overlying the older stages in the water column. In C. helgolandicus the converse is true; i. e., the majority of the populations of Stage I and II copepodites of the first spring generations are found below the thermocline. It is also suggested that the different behaviour patterns lead to different feeding regimes and strategies.JONSDAP Contribution No. 52