A deterministic analysis of self-incompatibility alleles

A number of plant species have a self-incompatibility locus that prevents self-fertilization. We 'analyse a deterministic model with an arbitrary number of alleles. We prove that the only polymorphic equilibrium is the one for which all (heterozygous) genotypes are equally frequent, and we prove that all (initially) polymorphic populations converge to this equilibrium.     

Stability in Gilpin and Ayala's models of competition

Summary Simple and effective conditions for global stability in a class of models for m competing species are given. A numerical method is used to establish a large finite region of attraction for the feasible equilibrium in Gilpin and Ayala's model of two competing Drosophila populations.     

具有年龄结构的食蚜蝇-蚜虫捕食模型

现有的具有年龄结构的捕食-食饵模型总是假设只有成年捕食者捕食猎物,这与实际情况不符。建立了一个幼年捕食者捕食食饵的具有年龄结构的食蚜蝇-蚜虫模型,应用微分方程定性理论,讨论了系统平衡点及其稳定性:其中平衡点E1(0,0,0)为不稳定的;满足一定条件时,边界平衡点E2(K,0,0)及正平衡点E3(x*,y1*,y2*)为局部渐近稳定的;且应用一致持续生存理论得到了系统永久持续生存的条件,为有害生物综合治理提供了理论依据。     

Classical and resource-based competition: a unifying graphical approach

A graphical technique is given for determining the outcome of two species competition for two resources. This method is unifying in the sense that the graphical criterion leading to the various outcomes of competition are consistent across most of the spectrum of resource types (from those that fulfill the same growth needs to those that fulfill different needs) regardless of the classification method used, and the resulting graphs bear a striking resemblance to the well-known phase portraits for two species Lotka–Volterra competition. Our graphical method complements that of Tilman. Both include zero net growth isoclines. However, instead of using the consumption vectors at potential coexistence equilibria to determine input resource concentrations leading to specific competitive outcomes, we introduce curves bounding the feasible set (the set where the resource concentrations of any equilibrium solution must be located). The washout equilibrium (corresponding to the supply point) occurs at an intersection of curves defining the feasible set boundary. The resource concentrations of all other equilibria are found where zero net growth isoclines either intersect each other inside the feasible set or they intersect the feasible set boundary. A species has positive biomass at such an equilibrium only if its zero net growth isocline is involved in such an intersection. The competitive outcomes are then determined from the position of the single species equilibria, just as in the phase portrait analysis for classical competition (rather than from information at potential coexistence equilibria as in Tilman’s method).     

The evolution of resource partitioning in a multidimensional resource space

The evolution of resource partitioning in a multidimensional resource space is studied for two and three competing species. Optimal patterns of resource partitioning are determined by simultaneously maximizing the fitness of each species with respect to its own niche position, conditional on the positions of all other species. We find that there are only a finite number of possible solutions, and several of these may be optimal simultaneously. Some solutions of the three-species model involve partitioning along more resource axes than any solutions of the two-species model. The results are related to empirical resource partitioning phenomena in Anolis lizard populations.     

A non-ideal replacement for the Boyle van't Hoff equation

A non-ideal osmotic equilibrium equation is proposed as a replacement for the Boyle van’t Hoff equation to describe the equilibrium volume of a living cell as a function of external osmolality. Contrary to common understanding, the Boyle van’t Hoff equation is only thermodynamically correct for ideal, dilute solutions. However, the Boyle van’t Hoff equation is commonly used to determine the osmotically inactive fraction of the cell. This involves extrapolating to infinite osmolality, which violates the ideal, dilute solution constraint. It has been noted that the osmotically inactive fractions obtained from the Boyle van’t Hoff equation for human erythrocytes are markedly larger than measured values of the dry volume fraction of the cell. Using the new osmotic equilibrium equation to analyze experimental osmotic equilibrium data reduces the inferred osmotically inactive fraction of human erythrocytes by approximately 20%.     

Cost‐benefit analysis of acoustic recorders as a solution to sampling challenges experienced monitoring cryptic species

The inferences that can be made from any study are limited by the quality of the sampling design. By bad luck, when monitoring species that are difficult to detect (cryptic), sampling designs become dictated by what is feasible rather than what is desired. We calibrated and conducted a cost‐benefit analysis of four acoustic recorder options that were being considered as potential solutions to several sampling restrictions experienced while monitoring the Australasian bittern, a cryptic wetland bird. Such sampling restrictions are commonly experienced while monitoring many different endangered species, particularly those that are cryptic. The recorder options included mono and stereo devices, with two sound file processing options (visual and audible analysis). Recording devices provided call‐count data similar to those collected by field observers but at a fraction of the cost, which meant that “idealistic” sampling regimes, previously thought to be too expensive, became feasible for bitterns. Our study is one of the few to assess the monetary value of recording devices in the context of data quality, allowing trade‐offs (and potential solutions) commonly experienced while monitoring cryptic endangered species to be shown and compared more clearly. The ability to overcome challenges of monitoring cryptic species in this way increases research possibilities for data deficient species and is applicable to any species with similar monitoring challenges.     

The evolutionary history of Drosophila buzzatii. XXX. Mitochondrial DNA polymorphism in original and colonizing populations

Both original and colonizer populations of Drosophila buzzatii have been analyzed for mtDNA restriction polymorphisms. Most of the mtDNA nucleotide variation in original populations of NW Argentina can be explained by intrapopulation diversity and only a small fraction can be accounted for by between-population diversity. Similar results are obtained using either the estimated number of nucleotide substitutions per site or considering each restriction site as a locus. Colonizer populations of the Iberian Peninsula are monomorphic and show only the most common haplotype from the original populations. Under the infinite island model and assuming that populations are in equilibrium, fixation indices indicate enough gene flow to explain why the populations are not structured. Yet, the possibility exists that populations have not reached an equilibrium after a founder event at the end of the last Pleistocene glaciation. Tajima's test suggests that directional selection and/or a recent bottleneck could explain the present mtDNA differentiation. Considering the significant population structure found for the chromosomal and some allozyme polymorphisms, the among- population uniformity for mtDNA variability argues in favor of the chromosomal and some allozyme polymorphisms being adaptive.      

Metapopulation structure of the specialized herbivore Macrosiphoniella tanacetaria (Homoptera,Aphididae)

We investigated population dynamics, genetic diversity and spatial structure in the aphid species Macrosiphoniella tanacetaria, a specialist herbivore feeding on tansy, Tanacetum vulgare. Tansy plants (genets) consist of many shoots (ramets), and genets are grouped in sites. Thus, aphids feeding on tansy can cluster at the level of ramets, genets and sites. We studied aphid population dynamics in 1997 and 2001 and found that within sites: (i). at any time, aphids used only a fraction of the available ramets and genets; (ii). at the level of ramets, most aphid colonies survived only one week; (iii). at the level of genets, mean survival time was less than 4 weeks; and (iv). colonization and extinction events occurred throughout the season. We sampled aphids in seven sites in the Alsace region, France (4-45 km apart) and two sites in Germany in 1999 to study genetic structure within and between populations. Genetic analyses using nine microsatellite loci showed that: (i). genotypic variability was high, (ii). none of the populations was in Hardy-Weinberg equilibrium, (iii). heterozygote deficits and linkage disequilibria were frequent, and (iv). all populations were genetically differentiated, even at a small geographical scale. Renewed sampling of the Alsace sites in 2001 showed that three populations had become extinct and significant genetic changes had occurred in the remaining four populations. The frequencies of extinction and colonization events at several spatial scales suggest a hierarchical metapopulation structure for M. tanacetaria. Frequent population turnover and drift are likely causes for the genetic differentiation of M. tanacetaria populations.     

Global stability in two species interactions

Summary It is proved that sufficient conditions for global stability in a Lotka-Volterra model of a two species interactions are (i) the equilibrium is feasible, (ii) the equilibrium is locally stable and (iii) at the equilibrium each species sustains density dependent mortalities due to intraspecific interactions.     

Genetic structure of the genera Psorophora (Diptera: Culicidae) in Columbian and North American populations using isoenzymes and ITS2 sequences

Two, a priori, Psorophora columbiae and one, a priori, Ps. toltecum populations from Colombia were studied by means of eleven isoenzyme loci. The levels of genetic diversity, Hardy-Weinberg equilibrium, gene flow estimates, isolation by distance and genetic relationships among these three populations were studied and the results were as follows: 1. The gene diversity levels were high as well as very similar among the three populations indicating no differences between them. 2. Within each population and from a hierarchical standpoint several loci were not in Hardy-Weinberg equilibrium simultaneously by excess and defect of heterozygous. This could reflect that several natural selection forces are acting upon these mosquito populations. 3. The gene flow estimate for these populations showed the existence of this event between them. This agrees quite well with the fact that the three populations really belong to a single species. In addition, maximum parsimony analyses with 16 isoenzyme for several individuals from four Colombian and two United States Psorophora populations showed that effectively only one species was present in the Colombian area surveyed, and that this species is Ps. columbiae, which hardly contrast with that previously suggested by other authors.     

Allozyme Variation within and between Populations of Coreopsis latifolia (Asteraceae)

Abstract Enzyme electrophoresis was used to measure genetic variation in five populations of the rare diploid species Coreopsis latifolia which appears to be a relict taxon endemic to a small area of the southeastern United States. Gene diversity within the species as a whole is low compared to other species with similar ecological and life history traits. Also, gene diversity in C. latifolia is lower than nearly all other species of Coreopsis that have been examined. Larger populations contain significantly more variation at isozyme loci than do smaller populations. Populations of C. latifolia are deficient in heterozygotes relative to expected equilibrium values.     

A general theory of environmental noise in ecological food webs

We examine the effects of environmental noise on populations that are parts of simple two-species food webs. We assume that the species are strongly interacting and that one or the other population is affected by the noise signal. Further assuming that a stable equilibrium with positive population densities exists, we are able to perform a complete frequency analysis of the system. If only one of the populations is subject to noise, the relative noise response by both populations is fully determined by the sign of a single element of the Jacobian matrix. The analysis is readily extended to cases when both species are affected by noise or when the food web has more than two species. The general conclusion about relative responses to noise is then less unambiguous, but the power spectra describing the frequency composition of the population variabilities are nevertheless completely determined. These results are entirely independent on the exact nature of the interaction (i.e., predation, competition, mutualism) between the populations. The results show that the interpretation of the "color" of ecological time series (i.e., the frequency composition of population variability over time) may be complicated by species interactions. The propagation of noise signals through food webs and the importance of web structure for the expected response of all parts of the web to such signals is a challenging field for future studies.     

Niche based distribution modelling of an invasive alien plant: effects of population status, propagule pressure and invasion history

Forecasting the spatial spread of invasive species is important to inform management planning. Niche-based species distribution models offer a well-developed framework for assessing the potential range of species. However, these models assume equilibrium between the species’ distribution and its ecological requirements. During range expansion, invasive species are not in such equilibrium due to both dispersal limitation and frequent casual occurrence in sites unsuitable to persistent populations. In this article we use the example of the invasive annual plant Ambrosia artemisiifolia in Austria to evaluate if model accuracy can be enhanced in such non-equilibrium situations by taking account of propagule pressure and by restricting model calibration to naturalized populations. Moreover, we test if model accuracy increases during invasion history using distribution data from 1984 to 2005. The results suggest that models calibrated with naturalized populations are much more accurate than those based on the total set of records. Proxies of propagule pressure slightly but significantly improve goodness of fit, accuracy, and Type I and II error rates of models calibrated with all available records but have less consistent effects on models of naturalized populations. Model accuracy did not increase during the recent invasion history, probably because the species is still far from an equilibrium distribution. We conclude that even a coarse assessment of population status with records of invasive species delivers important information for predictive modelling and that proxies of propagule pressure should be included into such models at least during early to intermediate stages of the invasion history.     

Population structure and host-plant specialization in two Scaptodrosophila flower-breeding species

In contrast to phytophagous insect species, little attention has been paid to the possibility of host races in the Drosophilidae, although flower-breeding species, where courtship and mating take place on the flowers, are likely candidates. Two species of Scaptodrosophila, S. hibisci and S. aclinata, are restricted to flowers of Hibiscus species (section Furcaria), and the Furcaria specialization likely predated the separation of S. hibisci and S. aclinata. In all, 20 microsatellite loci were analysed in nine populations of S. hibisci and five of S. aclinata. For two pairs of S. hibisci populations in close proximity, but breeding on different Hibiscus species, differentiation between the populations of each of these pairs was similar to that between the populations that were from the same Hibiscus species, but geographically distant, suggesting the early stages of host-race formation. Genetic variability was significantly less in S. aclinata than in S. hibisci, suggesting greater drift effects in the former. However, of 253 alleles detected, 82 were present in both species, 160 in S. hibisci only and 11 in S. aclinata only, indicating that S. aclinata was derived from S. hibisci, following a strong bottleneck at the time of separation--possibly 40,000 years BP. Analyses and interpretation of Hardy-Weinberg equilibrium and F statistics needed to account for null alleles known to be present at eight loci in S. hibisci, and possibly present at other loci. The results emphasize the need for caution in studies where the presence of null alleles is inferred only from population data.     

A reaction-diffusion system of a predator-prey-mutualist model

Mutualism is part of many significant processes in nature. Mutualistic benefits arising from modification of predator-prey interactions involve interactions of at least three species. In this paper we investigate the Homogeneous Neumann problem and Dirichlet problem for a reaction-diffusion system of three species—a predator, a mutualist-prey, and a mutualist. The existence, uniqueness, and boundedness of the solution are established by means of the comparison principle and the monotonicity method. For the Neumann problem, we analyze the constant equilibrium solutions and their stability. For the Dirichlet problem, we prove the global asymptotic stability of the trivial equilibrium solution. Specifically, we study the existence and the asymptotic behavior of two nonconstant equilibrium solutions. The main method used in studying of the stability is the spectral analysis to the linearized operators. The O.D.E. problem for the same model was proposed and studied in [13]. Through our results, we can see the influences of the diffusion mechanism and the different boundary value conditions upon the asymptotic behavior of the populations.     

The struggle for life: III. A predator-prey chain

Ann species predator-prey chain is analyzed to determine what oscillations occur in population sizes. It is found that only the populations of the first and second species in the chain must necessarily oscillate around the point of equilibrium if they do not come to equilibrium. The other species may or may not oscillate.     

Studies on the physical state of water in living cells and model systems. X. The dependence of the equilibrium distribution coefficient of a solute in polarized water on the molecular weights of the solute: experimental confirmation of the "size rule" in model studies

The equilibrium distribution of 14 sugars, sugar alcohols, and other nonelectrolytes in solutions of polyethylene oxide (PEO) and of native and alkali-denatured bovine hemoglobin were studied over wide concentration ranges. The results show that the equilibrium concentrations of all the solutes studies are rectilinearly related to their external concentrations. This straight-line relationship demonstrates the existence of these solutes entirely or almost entirely in the aqueous phase of these systems. Therefore the slope of each of these straight lines equals the equilibrium distribution coefficient or q-value of the solute involved. In general, the q-values decrease with increasing molecule weights (M.W.) of the solutes in 15% solutions of PEO, 20% solutions of alkali-denatured hemoglobin (and in 18% gelatin) but not in 39% solution of native hemoglobin. In solutions of PEO, of alkali-denatured hemoglobin studied (and of gelatin) a fraction of the water (20% to 30%) appears to have solvency similar to that of normal liquid water. The experimental findings of M.W.-dependent solute exclusion were discussed in the light of four alternative theories that have been offered to explain this type of phenomena. Among these four theories only the polarized multilayer theory agrees with most, if not all the facts known.     

A sampling theory for local selection

We have examined a model of selection (local selection) in which successive favorable alleles enter into a population by displacing a random fraction of each of the preexisting alleles. When the distribution of fitness among newly arising favorable mutations is given by a power law, then the distribution of allele frequencies in the population converge to a Poisson-Dirichlet limit, and the sampling distribution of alleles is a Ewens distribution. This property leads to a convenient algorithm for simulating random equilibrium frequencies of alleles within samples. The model can also be interpreted in terms of species abundances when each invading species displaces a random fraction of each pre-existing species, or in terms of age structures in populations subjected to random catastrophes.