Nuclear androdioecy and gynodioecy

We formulate two single-locus Mendelian models, one for androdioecy and the other one for gynodioecy, each with 3 parameters: t the male (female) fertility rate of males (females) to hermaphrodites, s the fraction of the progeny derived from selfing; and g the fitness of inbreeders. Each model is expressed as a transformation of a 3 dimensional zygotic algebra, which we interpret as a rational map of the projective plane. We then study the dynamics for the evolution of each reproductive system; and compare our results with similar published models. In this process, we introduce a general concept of fitness and list some of its properties, obtaining a relative measure of population growth, computable as an eigenvalue of a mixed mating transformation for a population in equilibrium. Our results concur with previous models of the evolution of androdioecy and gynodioecy regarding the threshold values above which the sexual polymophism is stable, although the previous models assume constant the fraction of ovules from hermaphrodites that are self pollinated, while we assume constant the fraction of the progeny derived from selfing. A stable androdioecy requires more stringent conditions than a stable gynodioecy if the amount of pollen used for selfing is negligible in comparison with the total amount of pollen produced by hermaphrodites. Otherwise, both models are identical. We show explicitly that the genotype fitnesses depend linearly on their frequencies. Simulations show that any population not at equilibrium always converges to the equilibrium point of higher fitness. However, at intermediate steps, the fitness function occasionally decreases.     

On the concept of attractor for community-dynamical processes II: the case of structured populations

In Part I of this paper Jacobs and Metz (2003) extended the concept of the Conley-Ruelle, or chain, attractor in a way relevant to unstructured community ecological models. Their modified theory incorporated the facts that certain parts of the boundary of the state space correspond to the situation of at least one species being extinct and that an extinct species can not be rescued by noise. In this part we extend the theory to communities of physiologically structured populations. One difference between the structured and unstructured cases is that a structured population may be doomed to extinction and not rescuable by any biologically relevant noise before actual extinction has taken place. Another difference is that in the structured case we have to use different topologies to define continuity of orbits and to measure noise. Biologically meaningful noise is furthermore related to the linear structure of the community state space. The construction of extinction preserving chain attractors developed in this paper takes all these points into account.     

Stability of the replicator equation for a single species with a multi-dimensional continuous trait space

The replicator equation model for the evolution of individual behaviors in a single species with a multi-dimensional continuous trait space is developed as a dynamics on the set of probability measures. Stability of monomorphisms in this model using the weak topology is compared to more traditional methods of adaptive dynamics. For quadratic fitness functions and initial normal trait distributions, it is shown that the multi-dimensional continuously stable strategy (CSS) of adaptive dynamics is often relevant for predicting stability of the measure-theoretic model but may be too strong in general. For general fitness functions and trait distributions, the CSS is related to dominance solvability which can be used to characterize local stability for a large class of trait distributions that have no gaps in their supports whereas the stronger neighborhood invader strategy (NIS) concept is needed if the supports are arbitrary.     

Mutual exclusion versus coexistence for discrete competitive systems

Using discrete competition models where the density dependent growth functions are either all exponential or all rational, notwithstanding the complex interactions of the species, we establish an exclusion principle. Moreover, in a 2-species discrete competition model where the growth functions are exponential and rational, an example is given illustrating coexistence when our conditions are satisfied. We obtain an exclusion principle for this 2-species model for some choice of parameters.Research partially supported by funds provided by a Science and Education Grant to the USDA-Forest Service, Southeastern Forest Experiment Station, Population Genetics of Forest Trees Research Unit, Raleigh, North Carolina     

Comparison of deterministic and stochastic SIS and SIR models in discrete time

The dynamics of deterministic and stochastic discrete-time epidemic models are analyzed and compared. The discrete-time stochastic models are Markov chains, approximations to the continuous-time models. Models of SIS and SIR type with constant population size and general force of infection are analyzed, then a more general SIS model with variable population size is analyzed. In the deterministic models, the value of the basic reproductive number R0 determines persistence or extinction of the disease. If R0 < 1, the disease is eliminated, whereas if R0 > 1, the disease persists in the population. Since all stochastic models considered in this paper have finite state spaces with at least one absorbing state, ultimate disease extinction is certain regardless of the value of R0. However, in some cases, the time until disease extinction may be very long. In these cases, if the probability distribution is conditioned on non-extinction, then when R0 > 1, there exists a quasi-stationary probability distribution whose mean agrees with deterministic endemic equilibrium. The expected duration of the epidemic is investigated numerically.     

Diversity–productivity relationships in two ecologically realistic rarity–extinction scenarios

To develop a better understanding of how biodiversity loss and productivity are related, we need to consider ecologically realistic rarity (i.e. reduced evenness and increased dominance) and extinction (i.e. reduced richness) scenarios. Furthermore, we need to identify and better understand the factors that influence species and community yielding behaviors because the general conditions for overyielding are the same as those for coexistence. We established experimental tallgrass prairie plots in Iowa to determine how two ecologically realistic rarity–extinction scenarios influenced aboveground net primary productivity (ANPP) and disassembly. Equal‐mass seedlings of six tallgrass prairie species were transplanted into field plots to establish realistic declining species evenness (high, medium, low) and richness (4, 1) treatments. Across declining evenness treatments, the relative abundance of the ubiquitous tall species Andropogon gerardii increased, the relative abundance of the tall species Salvia azurea was constant, and the relative abundance of two short (dissimilar height scenario) or two tall species (tall scenario) decreased. Monocultures of Andropogon represented a continuation of this trend until there was complete dominance by Andropogon and extinction of all other species. Our treatments also allowed us to test if variation in plant height contributes to the complementarity effect. Niche partitioning in plant height was not positively related to complementarity. The effects of declining species evenness and richness on the diversity–productivity relationship were different for these two ecologically realistic rarity–extinction scenarios. Specifically, as diversity declined across treatments, ANPP and the selection effects decreased in tall communities, but not in dissimilar communities. Additionally, differences between these two scenarios revealed that decreased species yielding behavior is associated with two tallgrass prairie extinction risk factors, rarity and short height. The differences between these scenarios demonstrate the importance of incorporating the known patterns of diversity declines into future studies.     

Convergence of multilocus systems under weak epistasis or weak selection

 The convergence of multilocus systems under viability selection with constant fitnesses is investigated. Generations are discrete and nonoverlapping; the monoecious population mates at random. The number of multiallelic loci, the linkage map, dominance, and epistasis are arbitrary. It is proved that if epistasis or selection is sufficiently weak (and satisfies a certain nondegeneracy assumption whose genericity we establish), then there is always convergence to some equilibrium point. In particular, cycling cannot occur. The behavior of the mean fitness and some other aspects of the dynamics are also analyzed. Received: 15 November 1997 / Revised version: 25 May 1998     

Population viability analysis of Saxifraga cotyledon,a perennial plant with semelparous rosettes

The aim with this study was to analyse the population dynamics ofSaxifraga cotyledon, a rare, long lived herb, withsemelparous rosettes. In Sweden, S. cotyledon grows infragmented habitats at high altitude and is classified as vulnerable accordingto the IUCN system. From a five year demographical study we estimatedpopulationgrowth rates and extinction risks for one small and one large subpopulation. Inthe small subpopulation deterministic matrix simulations showed largevariation,with two transitions projecting negative and two projecting positive populationgrowth. The large subpopulation also showed large variation, but all yearlytransitions projected positive population growth. In both subpopulationssurvival and growth contributed more than twice as much to population growthrates than did sexual reproduction, vegetative reproduction and the seed bankall taken together. In stochastic simulations the maximum likelihood growthestimator waslarger than 1 for both subpopulations. None of the two subpopulations sufferfrom high extinction rates and although the effect of demographic stochasticityincrease extinction risk in small populations it is enough with 70 individualsfor a viable population of S. cotyledon. Hence, for thestudied population of S. cotyledon, rareness per se is nota good indicator of vulnerability.     

“Gomori-positive” neurosecretion in the rat after deafferentation of the medial basal hypothalamus

A portion of the "Gomori-positive" peptidergic neurosecretory (NS) cells in the paraventricular and especially in the supraoptic and postoptic nuclei degenerate three weeks after deafferentation of the medial basal hypothalamus. Most of the remaining NS cells show signs of high activity. Regenerating NS fibres form "muffs" around the blood vessels laterally from the lesion; some of them enter the "isolated" area or persist there if a thin layer of the brain tissue is left somewhere untouched under the basal end of the cut. The regenerating NS fibres are also found outside the nervous tissue: within the scar tissue, in the proliferating connective tissue of the brain sheet below the basal end of the cut and in the mantel plexus area. The NS fibres make close contact with blood vessels invading or penetrating the vascular wall. It is suggested that peptide neurohormones discharged from the "Gomori-positive" NS terminals enter the general blood circulation as well as the portal blood at the site of these newly formed axovasal contacts. It is supposed that under these conditions monoaminergic terminals do not discharge monoamines because no stimulation of monoamine-producing NS cells occurs with deafferentation.     

Permanence of discrete-time Kolmogorov systems for two species and saturated fixed points

This paper considers the dynamics of a discrete-time Kolmogorov system for two-species populations. In particular, permanence of the system is considered. Permanence is one of the concepts to describe the species coexistence. By using the method of an average Liapunov function, we have found a simple sufficient condition for permanence of the system. That is, nonexistence of saturated boundary fixed points is enough for permanence of the system under some appropriate convexity or concavity properties for the population growth rate functions. Numerical investigations show that for the system with population growth rate functions without such properties, the nonexistence of saturated boundary fixed points is not sufficient for permanence, actually a boundary periodic orbit or a chaotic orbit can be attractive despite the existence of a stable coexistence fixed point. This result implies, in particular, that existence of a stable coexistence fixed point is not sufficient for permanence.     

Effects of dominance on the probability of fixation of a mutant allele

We consider whether the fixation probability of an allele in a two-allele diploid system is always a monotonic function of the selective advantage of the allele. We show that while this conjecture is correct for intermediate dominance, it is not correct in general for either overdominant or underdominant alleles, and that for some parameter ranges the fixation probability can initially decrease and then increase as a function of the amount of selection. We have partial results that characterize the ranges of parameters for which this happens.      

When does the variance of replicator fitness decrease?

For the general replicator dynamics with regular relative advantage functions (having non-singular Jacobian and symmetrized Jacobian), it will be shown that the variance of marginal fitness of the replicators strictly decreases along each trajectory of the replicator dynamics near an interior rest point if and only if this rest point is a regular evolutionarily stable state.     

The nature of extinction

The phenomenon of species extinction raises more and more concern among ecologists facing the actual crisis of biodiversity. Scientific investigations of the causes and effects of extinction must be completed by a philosophical analysis of the concept of extinction that aims to clarify the meanings of the term 'extinction' and to analyse modalities, criteria and degrees of extinction. We will focus our attention on the apparent paradox of the possible 'resurrection' of species in the near future with the help of genetic biotechnology and cloning techniques. The ontological background of the extinction concept is analysed in relation to the idea of species as classes. We will also show that there is no simple analogy between death and species extinction, and develop a conceptualist and dualistic system of supra-individual entities (species vs. population), supported by an instrumentalist approach to genetic manipulations which transform species into interactive kinds, which can go extinct and be recreated.     

Estimation of local extinction rates when species detectability covaries with extinction probability: is it a problem?

Estimating the rate of change of the composition of communities is of direct interest to address many fundamental and applied questions in ecology. One methodological problem is that it is hard to detect all the species present in a community. Nichols et al. presented an estimator of the local extinction rate that takes into account species probability of detection, but little information is available on its performance. However, they predicted that if a covariance between species detection probability and local extinction rate exists in a community, the estimator of local extinction rate complement would be positively biased.
Here, we show, using simulations over a wide range of parameters that the estimator performs reasonably well. The bias induced by biological factors appears relatively weak. The most important factor enhancing the performance (bias and precision) of the local extinction rate complement estimator is sampling effort. Interestingly, a potentially important biological bias, such as the covariance effect, improves the estimation for small sampling efforts, without inducing a supplementary overestimation when these sampling efforts are high. In the field, all species are rarely detectable so we recommend the use of such estimators that take into account heterogeneity in species detection probability when estimating vital rates responsible for community changes.     

Alternative splicing generates a CaM kinase IIβ isoform in myocardium that targets the sarcoplasmic reticulum through a putative αKAP and regulates GAPDH

In the postgenomic era the elucidation of the physiological function of genes has become the rate-limiting step in the quest to understand the development and function of living organisms. Double-stranded RNA (dsRNA) interferes with gene expression in various species, a phenomenon known as RNA interference (RNAi). We show here that RNAi is also effective in modifying gene expression in neural stem cell differentiation. The progenitor cells were obtained from E14 mouse embryonic forebrain and maintained using N-2 medium containing basic fibroblast growth factor (bFGF), epidermal growth factor (EGF) and B27.A gene (NM017084.1) was previously discovered and validated to express obviously differently between differentiated and undifferentiated neural stem cells in our laboratory. Here we report a long double-stranded RNA to knock out or knock down this gene. The results demonstrated that following RNAi inhibition of expression of the NM017084.1 gene, the differentiation of neural stem cells is accelerated. Thus the NM017084.1 gene may play a pivotal role in the process of differentiation of neural stem cells.     

Evolution of cooperation in patchy habitat under patch decay and isolation

The spatial version of Prisoners Dilemma (PD) is studied, which incorporates habitat decay through change in the mortality parameter and habitat isolation through change in the colonization coefficient. We found four kinds of evolutionary results, which are affected profoundly by the elements of the payoff matrix and the ratio of the colonization coefficient to the mortality parameter: population extinction, a pure cooperator population, coexistence of cooperators and defectors, and a pure defector population. First, the parameter region of cooperation (pure cooperator and coexistence region) shrinks with an increase in the cooperative cost, and that of defection extends. The increase in cooperative reward makes the cooperative region extend and the defector region become small. Second, the cooperative reward can compensate for the extinction risk due to habitat destruction and allow a population to survive even if the colonization coefficient is smaller than the mortality parameter. Third, although habitat destruction (including decay and isolation) increase the extinction risk of a population, moderate external power can push the evolution of cooperation ahead of population extinction, and even make a completely cooperative world come into being. Finally, for certain values of elements of the payoff matrix, the population suffering habitat destruction can maintain a stable population size by regulating the frequencies of cooperators and defectors. This implies that the multi-behavior strategy within a population may be a mechanism to defend against the influences of a changing environment.     

Community structure and the evolution of aposematic coloration

Studies on the evolution of aposematic coloration (prey coloration advertising for unpalatability) have mainly focused on predator psychology in simplified single-prey species systems. We chose, instead, to model population dynamics on the community level. We studied the invasion by an aposematic phenotype in the presence and absence of another prey species. The single-prey and two-prey models differed in two major ways. First, with two prey species the invasion was possible only with a weak aposematic signal, whereas with a single prey species there was no such an upper limit for signal strength. Second, with a single prey species, increase of the aposematic phenotype always resulted in rapid extinction of the predator. Resource value and growth rate of the alternative prey species affected the invasion. These results suggest that community structure is an important determinant of the conditions for invasion of aposematism, and may have contributed to its initial evolution.     

Dedifferentiated variants of a rat hepatoma: analysis by cell hybridization

Two independent dedifferentiated variants, H5 and FaoflC2, derived from the Reuber H35 hepatoma, produce trans-acting diffusible substances(s) that extinguish the expression of liver-specific proteins when hybridized with a well-differentiated cell line of the same origin (Fao and Fu5-5, respectively). H5 x Fao hybrids show total and stable extinction of four liver functions and clonal variability in the expression of three others. FaoflC2 x Fu5-5 hybrids are initially flat (like FaoflC2 cells), and die in glucose-free medium where survival requires expression of hepatic gluconeogenic enzymes, but then evolve to hepatoma-like and finally round morphology; these latter cells express all liver functions analyzed including the gluconeogenic enzymes. Two exceptional clones that remained flat long enough for complete analysis showed extinction of all hepatic functions not expressed by FaoflC2 cells. We conclude that this transitory extinction reflects the action and then loss of extinguishing factor(s) contributed by FaoflC2. When crossed with BW1-J mouse hepatoma cells. FaoflC2 causes stable extinction of mouse aldolase B. We propose that production of extinguishing factor(s) is the rule for dedifferentiated variants.     

Anthropogenic extinction threats and future loss of evolutionary history in reef corals

Extinction always results in loss of phylogenetic diversity (PD), but phylogenetically selective extinctions have long been thought to disproportionately reduce PD. Recent simulations show that tree shapes also play an important role in determining the magnitude of PD loss, potentially offsetting the effects of clustered extinctions. While patterns of PD loss under different extinction scenarios are becoming well characterized in model phylogenies, analyses of real clades that often have unbalanced tree shapes remain scarce, particularly for marine organisms. Here, we use a fossil‐calibrated phylogeny of all living scleractinian reef corals in conjunction with IUCN data on extinction vulnerabilities to quantify how loss of species in different threat categories will affect the PD of this group. Our analyses reveal that predicted PD loss in corals varies substantially among different threats, with extinctions due to bleaching and disease having the largest negative effects on PD. In general, more phylogenetically clustered extinctions lead to larger losses of PD in corals, but there are notable exceptions; extinction of rare corals from distantly‐related old and unique lineages can also result in substantial PD loss. Thus our results show that loss of PD in reef corals is dependent on both tree shape and the nature of extinction threats.     

Competition and coexistence in regional habitats

Habitat heterogeneity plays a key role in the dynamics and structures of communities. In this article, a two-species metapopulation model that includes local competitive dynamics is analyzed to study the population dynamics of two competing species in spatially structured habitats. When local stochastic extinction can be ignored, there are, as in Lotka-Volterra equations, four outcomes of interspecific competition in this model. The outcomes of competition depend on the competitive intensity between the competing pairs. An inferior competitor and a superior competitor, or two strongly competing species, can never stably coexist, whereas two weak competitors (even if they are very similar species) may coexist over the long term in such environments. Local stochastic extinction may greatly affect the outcomes of interspecific competition. Two competing species can or cannot stably coexist depending not only on the competitive intensity between the competing pairs but also on their precompetitive distributions. Two weak competitors that have similar precompetitive distributions can always regionally coexist. Two strongly competing species that competitively exclude each other in more stable habitats may be able to stably coexist in highly heterogenous environments if they have similar precompetitive distributions. There is also a chance for an inferior competitor to coexist regionally or even to exclude a superior competitor when the superior competitor has a narrow precompetitive distribution and the inferior competitor has a wide precompetitive distribution.