Linear discrete population models with two time scales in fast changing environments II: non-autonomous case

As the result of the complexity inherent in nature, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often deal with models for structured populations in which individuals are classified regarding their age, size, activity or location, and this structuring of the population leads to high dimensional systems. In many instances, the dynamics of the system is controlled by processes whose time scales are very different from each other. Aggregation techniques take advantage of this situation to build a low dimensional reduced system from which behavior we can approximate the dynamics of the complex original system.In this work we extend aggregation techniques to the case of time dependent discrete population models with two time scales where both the fast and the slow processes are allowed to change at their own characteristic time scale, generalizing the results of previous studies. We propose a non-autonomous model with two time scales, construct an aggregated model and give relationship between the variables governing the original and the reduced systems. We also explore how the properties of strong and weak ergodicity, regarding the capacity of the system to forget initial conditions, of the original system can be studied in terms of the reduced system.     

Coexistence of two types on a single resource in discrete time

Armstrong and McGehee (1980) have shown that two species modeled in continuous time can coexist on a single resource provided that one species oscillates autonomously. This paper demonstrates the parallel result in discrete time. I consider a deterministic model of two asexual types in a single patch competing for a single resource, and show that such systems generically produce oscillatory coexistence or bistability if one of the types displays periodic or chaotic behavior in isolation. The conditions for coexistence or bistability are derived in terms of the convexity of the functions describing fitness as a function of resource availability. I also analyze whether or not a stable type, a type with a stable equilibrium population size when considered in isolation, can invade a periodic orbit of an unstable type, and show that the same convexity condition distinguishes these two cases. The widely considered exponential or Ricker model for population dynamics lies on the boundary between the two cases and is highly degenerate in this context.     

A threshold theorem for the general epidemic in discrete time

Summary A theorem, analogous to the continuous time Threshold Theorem of Kermack and McKendrick, is proved for a certain discrete time epidemic model. This model, in contrast to its continuous time analogue, leads to some solutions in which the total population of susceptibles may become infected in a finite time.     

Automatic reconstruction of molecular and genetic networks from discrete time series data

We apply a mathematical algorithm which processes discrete time series data to generate a complete list of Petri net structures containing the minimal number of nodes required to reproduce the data set. The completeness of the list as guaranteed by a mathematical proof allows to define a minimal set of experiments required to discriminate between alternative network structures. This in principle allows to prove all possible minimal network structures by disproving all alternative candidate structures. The dynamic behaviour of the networks in terms of a switching rule for the transitions of the Petri net is part of the result. In addition to network reconstruction, the algorithm can be used to determine how many yet undetected components at least must be involved in a certain process. The algorithm also reveals all alternative structural modifications of a network that are required to generate a predefined behaviour.     

Generation time and the stability of sex-determining alleles in oyster populations as deduced using a gene-based population dynamics model

Crassostrea oysters are protandrous hermaphrodites. Sex is thought to be determined by a single gene with a dominant male allele M and a recessive protandrous allele F, such that FF animals are protandrous and MF animals are permanent males. We investigate the possibility that a reduction in generation time, brought about for example by disease, might jeopardize retention of the M allele. Simulations show that MF males have a significantly lessened lifetime fecundity when generation time declines. The allele frequency of the M allele declines and eventually the M allele is lost. The probability of loss is modulated by population abundance. As abundance increases, the probability of M allele loss declines. Simulations suggest that stabilization of the female-to-male ratio when generation time is long is the dominant function of the M allele. As generation time shortens, the raison d’être for the M allele also fades as mortality usurps the stabilizing role. Disease and exploitation have shortened oyster generation time: one consequence may be to jeopardize retention of the M allele. Two alternative genetic bases for protandry also provide stable sex ratios when generation time is long; an F-dominant protandric allele and protandry restricted to the MF heterozygote. In both cases, simulations show that FF individuals become rare in the population at high abundance and/or long generation time. Protandry restricted to the MF heterozygote maintains sex ratio stability over a wider range of generation times and abundances than the alternatives, suggesting that sex determination based on a male-dominant allele (MM/MF) may not be the optimal solution to the genetic basis for protandry in Crassostrea.     

A note on the estimation of selective values from recaptures of marked animals when selection pressures remain constant over time

An equation is given for the estimation of selective values from data obtained by mark-recapture experiments, assuming that selective pressures remain constant while the experiments are carried out. The equation does not have an explicit solution but can readily be solved using a trial-and-error method. The use of the equation is illustrated on some data reported byKettlewell et al. (1969) from an experiment involving typica and edda morphs of the moth Amathes glareosa. It is found that the edda morph apparently had a selective advantage of about 12% per day compared to the typica morph and that this is significantly different from zero. Using another methodKettlewell concluded that the selective advantage of the edda morph was only 7% and that this was not statistically significant.     

Mean labor time of a leaf

The mean labor time of a leaf (hour/day^–1) is defined as the ratio of mean daily photosynthetic rate of a leaf (D_a; molm^–2day^–1) to the mean value of potential hourly photosynthetic rate (6060A_max mol m^–2h^–1) of the leaf. A model was proposed to estimate mean labor time of leaves. Mean labor time was obtained as the product of 24 (hours/day^–1) and the four effects, each of which reduces production of a leaf: diel change in light (Diel Effect), reduction in light during cloudy and rainy days (Cloudy Effect), shading on the focal leaves (Shading Effect), and midday and afternoon depression in photosynthesis (Depression Effect). These four effects were estimated for open grown saplings of alder (Alnus sieboldiana), by measuring instantaneous photosynthetic rate and photon flux density above each leaf. The potential daily photosynthetic rate calculated from diel light condition in a clear day was 46.5% of hypothetical daily photosynthetic rate where maximum instantaneous photosynthetic rate was assumed to last throughout the life of the leaf (Diel Effect). The average of the daily photosynthetic rate considering clear, cloudy and rainy days was 79.7% of the clear day (Cloudy Effect). The photosynthetic rate estimated from light condition on the leaf was 85.6% of that in the open site (Shading Effect). Midday depression reduced the daily photosynthetic rate to 72.1% of the potential daily photosynthetic rate (Depression Effect). The product of the four effects multiplied by 24h gave the estimate of mean labor time of leaves to be approximately 5.5 (h/day^–1).     

Divergence time of the two regional medaka populations in Japan as a new time scale for comparative genomics of vertebrates

The southern and northern Japanese populations of the medaka fish provide useful tools to gain insights into the comparative genomics and speciation of vertebrates, because they can breed to produce healthy and fertile offspring despite their highly divergent genetic backgrounds compared with those of human–chimpanzee. Comparative genomics analysis has suggested that such large genetic differences between the two populations are caused by higher molecular evolutionary rates among the medakas than those of the hominids. The argument, however, was based on the assumption that the two Japanese populations diverged approximately at the same time (4.0–4.7 Myr ago) as the human–chimpanzee lineage (5.0–6.0 Myr ago). This can be misleading, because the divergence time of the two populations was calculated based on estimated, extremely higher molecular evolutionary rates of other fishes with an implicit assumption of a global molecular clock. Here we show that our estimate, based on a Bayesian relaxed molecular-clock analysis of whole mitogenome sequences from 72 ray-finned fishes (including 14 medakas), is about four times older than that of the previous study (18 Myr). This remarkably older estimate can be reconciled with the vicariant events of the Japanese archipelago, and the resulting rates of molecular evolution are almost identical between the medaka and hominid lineages. Our results further highlight the fact that reproductive isolation may not evolve despite a long period of geographical isolation.     

Ecogeographical distribution of HMW glutenin alleles in populations of the wild tetraploid wheat Triticum turgidum var. dicoccoides

Summary Polymorphism of high molecular weight (HMW) glutenin subunits in 466 accessions of the wild tetraploid wheat Triticum turgidum var. dicoccoides in Israel was characterized with regard to the ecogeographical distribution of the HMW glutenin alleles, both between and within 22 populations, and along transects in a single population. While some populations were monomorphic for all the HMW glutenin loci, namely, Glu-A1-1, Glu-A1-2, Glu-B1-1 and Glu-B1-2, others contained up to four alleles per locus. Intrapopulation variability could be predicted by the geographical distribution: marginal populations tended to be more uniform than those at the center of distribution. The various HMW glutenin alleles tended to be clustered, both at a regional level and within a single population along transects of collection. It is suggested that this clustering is due to selection pressures acting both at a regional and at a microenvironmental level. This was confirmed by the significant correlations found between the MW of subunits encoded by Glu-A1-1 and the populations' altitude, average temperature and rainfall. The possible selective values of seed storage proteins are discussed.     

The reliability of approximate reduction techniques in population models with two time scales

As a result of the complexity inherent in some natural systems, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often find multiregional models for structured populations in which individuals are classified regarding their age and their spatial location. Dealing with such structured populations leads to high dimensional models. Moreover, in many instances the dynamics of the system is controlled by processes whose time scales are very different from each other. For example, in multiregional models migration is often a fast process in comparison to the growth of the population.Approximate reduction techniques take advantage of the presence of different time scales in a system to introduce approximations that allow one to transform the original system into a simpler low dimensional system. In this way, the dynamics of the original system can be approximated in terms of that of the reduced system. This work deals with the study of that approximation. In particular, we work with a non-autonomous discrete time model previously presented in the literature and obtain different bounds for the error we incur when we describe the dynamics of the original system in terms of the reduced one.The results are illustrated by some numerical simulations corresponding to the reduction of a Leslie type model for a population structured in two age classes and living in a two patch system.     

Effects of habitat size and quality on equilibrium density and extinction time of Sorex araneus populations

1. The effects of changes in habitat size and quality on the expected population density and the expected time to extinction of Sorex araneus are studied by means of mathematical models that incorporate demographic stochasticity.
2. Habitat size is characterized by the number of territories, while habitat quality is represented by the expected number of offspring produced during the lifetime of an individual.
3. The expected population density of S. araneus is shown to be mainly influenced by the habitat size. The expected time to extinction of S. araneus populations due to demographic stochasticity, on the other hand, is much more affected by the habitat quality.
4. In a more general setting we demonstrate that, irrespective of the actual species under consideration, the likelihood of extinction as a consequence of demographic stochasticity is more effectively countered by increasing the reproductive success and survival of individuals then by increasing total population size.     

Identification of two new alleles, IGHV3-23*04 and IGHJ6*04, and the complete sequence of the IGHV3-h pseudogene in the human immunoglobulin locus and their prevalences in Danish Caucasians

More than 100 variable (V), 27 diversity (D), and six joining (J) genes are encoded in the human heavy chain locus, and many of these genes exists in different allelic forms. The number of genes and the allelic differences help to create diversity in the immunoglobulin receptors, a key feature of the adaptive immune system. We here report the identification of two novel and seemingly functional alleles of human heavy chain genes. The variable IGHV3-23*04 allele is found with an allele frequency of 0.21 amongst Danish Caucasians, whereas the novel joining IGHJ6*04 allele is rare (allele frequency 0.02). We also report the full sequence of IGHV3-h. The gene exists in two allelic forms but is only found in 58% of the Danish Caucasians studied. The methionine translation initiation codon is mutated, ATG→AAG, and we therefore propose that the gene is a pseudogene incapable of being translated.     

Assembly and selective "in synthesis" labeling of quenched fluorogenic protease substrates

Because impaired cellular protease activities are linked to many diseases, such as cancer, inflammation, neurodegeneration, and infection, internally quenched fluorescent peptides have recently been developed as tools for analyzing the specificities of these enzymes. Here we report convenient and cost-effective approaches for the selective "in synthesis" assembly of such substrate peptides for protease assays. Fluorescein and Dabcyl groups were covalently and selectively attached during synthesis to epsilon-amino groups of internal lysines. Functionality was then tested by digestion with leucine aminopeptidase, chymotrypsin, and microsomal vesicles. All peptides proved to be appropriate substrates of the enzymes tested and of the endogenous peptidases in the microsomal vesicles. In summary, we describe an innovative and cheap method to develop completely functional quenched fluorescent peptides that are usable in specific detection of individual proteases, in particular aminopeptidases, in both in vitro and in vivo systems.     

The impact of selective logging on forest structure and tenrec populations in western Madagascar

Summary This paper reports on possible effects of selective logging on vegetation structure and its consequences for two tenrec species in a dry forest in western Madagascar. On a small scale semi-mechanized logging of less than 10 m³ per ha alters forest structure significantly. However on a large scale most of these changes are smaller than the variation of forest structure due to natural causes. The most profound ecological effect of logging is a reduction in the number of woody species in the regenerating cohort of trees. Potential longterm consequences of this feature are discussed. Microhabitat variables influencing the habitat utilization of two tenrec species,Echinops telfairi andTenrec ecaudatus, were identified in an area of unlogged forest. The conclusions derived from this analysis were then tested in other parts of the forest which had been modified by selective logging. Logging of the extent described above slightly impairs habitats forE. telfairi but has no effect onT. ecaudatus. Though the latter species is hunted extensively in the logged areas, loggingper se does not threaten the survival of either species.

---

Résumé Cette étude met en évidence quelques effets de l'exploitation séléctive de la forêt sur la structure de la végétation et les conséquences pour deux espèces de tenrecs dans une forêt sèche à l'ouest de Madagascar. Dans un domaine limité, l'exploitation de bois de moins de 10 m³ par ha change considérablement la structure de la forêt. Mais si on considère une échelle plus grande, ces effets sont inférieurs à la variabilité naturelle. L'effet le plus grave de l'exploitation forestière sélective est la reduction du nombre d'espèces végétales ligneuses dans le processus de regénération naturelle de la forêt. Quelques conséquences possibles de cette réduction pour les animaux sont discutées. Quelques caractères distinctifs de la végétation qui influencent l'utilisation de l'habitat par deux espèces de tenrec,Echinops telfairi etTenrec ecaudatus, ont été identifiés dans une partie de la forêt qui n'a pas encore été exploitée. Les conclusions de cette analyse sont vérifiées dans une autre partie de la forêt qui a été modifiée par l'exploitation du bois. L'exploitation forestière sélective du bois détériore légèrement l'habitat pourE. telfairi, mais elle n'a pas d'effets remarquables surT. ecaudatus. L'exploitation sélective du bois favorise la chasse par l'ouverture de chemins d'accès. La chasse deT. ecaudatus est particulièrement intense, mais cependant ni l'une ni l'autre des espèces de tenrec considérées ne sont en danger d'extinction par cette form d'exploitationper se.

     

Frequencies of plasma protease inhibitor alleles in Australian horse breeds and the recognition of two new alleles

Investigation of the plasma protease inhibitor system (Pi) in the Arabian and quarter horse breeds and re-examination of the standardbred breed resulted in the recognition of two new Pi alleles, designated E and L2. PiE is rare and has been found in only three quarter horses. In contrast, PiL2 is relatively common in the standardbred (0.107) and allowed subdivision of PiL into PiL and PiL2. Splitting of PiL resulted in an exclusion probability (PE) of 0.649 for the standardbred Pi system. Frequencies of the Pi genes have now been determined for four breeds (thoroughbred, standardbred, quarter horse and Arabian) of horses in Australia.     

Residence time and exposure time of sinking phytoplankton in the euphotic layer

The residence time of a sinking particle in the euphotic layer is usually defined as the time taken by this particle to reach for the first time the bottom of the euphotic layer. According to this definition, the concept of residence time does not take into account the fact that many cells leaving the euphotic layer at some time can re-enter the euphotic layer at a later time. Therefore, the exposure time in the surface layer, i.e. the total time spent by the particles in the euphotic layer irrespective of their possible excursions outside the surface layer, is a more relevant concept to diagnose the effect of diffusion on the survival of phytoplankton cells sinking through the water column.While increasing the diffusion coefficient can induce both a decrease or an increase of the residence time, the exposure time in the euphotic layer increases monotonically with the diffusion coefficient, at least when the settling velocity does not increase with depth. Turbulence is therefore shown to increase the total time spent by phytoplankton cells in the euphotic layer.The generalization of the concept of exposure time to take into account the variations of the light intensity with depth or the functional response of phytoplankton cells to irradiance leads to the definition of the concepts of light exposure and effective light exposure. The former provides a measure of the total light energy received by the cells during their cycling through the water column while the latter diagnose the potential growth rate.The exposure time, the light exposure and the effective light exposure can all be computed as the solution of a differential problem that generalizes the adjoint approach introduced by Delhez et al. (2004) for the residence time. A general analytical solution of the 1D steady-state version of this equation is derived from which the properties of the different diagnostic tools can be obtained.