A stochastic computer model for simulating population growth

A model is described for investigating the interactions of age-specific birth and death rates, age distribution and density-governing factors determining the growth form of single-species populations. It employs Monte Carlo techniques to simulate the births and deaths of individuals while density-governing factors are represented by simple algebraic equations relating survival and fecundity to population density. In all respects the model's behavior agrees with the results of more conventional mathematical approaches, including the logistic model andLotka's Law, which predicts a relationship betwen age-specific rates, rate of increase and age distribution. Situations involving exponential growth, three different age-independent density functions affecting survival, three affecting fecundity and their nine combinations were tested. The one function meeting the assumptions of the logistic model produced a logistic growth curve embodying the correct values or r_m and K. The others generated sigmoid curves to which arbitrary logistic curves could be fitted with varying success. Because of populational time lags, two of the functions affecting fecundity produced overshoots and damped oscillations during the initial approach to the steady state. The general behavior of age-dependent density functions is briefly explored and a complex example is described that produces population fluctuations by an egg cannibalism mechanism similar to that found in the flour beetle Tribolium. The model is free of inherent time lags found in other discrete time models yet these may be easily introduced. Because it manipulates separate individuals, the model may be combined readily with the Monte Carlo simulation models of population genetics to study eco-genetic phenomena.     

Precise feeding of probiotics in the treatment of edwardsiellosis by accurate estimation of <Emphasis Type="Italic">Edwardsiella tarda</Emphasis>

Edwardsiella tarda is one of the leading fish pathogens for the aquaculture industry. To realize efficient disease control of edwardsiellosis, a predictive model for E. tarda in seawater was developed. The modified logistic model was used to regress the growth curves of E. tarda JN at five different temperatures (range from 10 to 30 °C) and four organic nutrient concentrations (range from 5 to 40 mg l^?1 measured by chemical oxygen demand (COD)). The modeling effects of temperature and COD on the specific growth rate (μ) were developed by square-root model and saturation-growth rate model, respectively. The growth model was validated in turbot aquaculture tanks by estimating the dynamics of inoculated E. tarda. The accurate feeding of probiotic Bacillus pumilus strain H2 was calculated based on the estimation of E. tarda. Results showed that the logistic model produced a good fit to the growth curves of E. tarda JN (average R²?=?0.962). The overall predictions based on above models agreed well with the growth curve of E. tarda JN observed by plate counting in the validation tests (average Af?=?1.16; average Bf?=?1.32). The use of predicted amount of B. pumilus (5.66 log CFU ml^?1) successfully prevent the deterioration of disease for turbot with 13.3% mortality rate in a recirculating aquaculture system (RAS), while the feeding of 0 and 3.0 log CFU ml^?1 of B. pumilus resulted in 53.7 and 75.3% of turbot mortality rate, respectively. In conclusion, accurate estimation of E. tarda realized the precise feeding of probiotics, which successfully prevent the rapid progression of the edwardsiellosis.     

Refractive index of uranyl-treated bacterial cytoplasm as related to ribonucleic-acid content and growth rate

After fixation and treatment with uranyl acetate solutions, the refractive index (n _D) of the cytoplasm ofCorynebacterium bovis varies with substrate-dependent growth rate and RNA content. The effect, which presumably is due to quantitative binding of uranyl ions by RNA, permits a measurement of the growth rate of single cells in a single-species system by interference microscopy. Temperature-induced changes in growth rate are not reflected in changes ofn _D or RNA content.     

Mathematical modelling to centre low tidal volumes following acute lung injury: A study with biologically variable ventilation

Background

With biologically variable ventilation [BVV – using a computer-controller to add breath-to-breath variability to respiratory frequency (f) and tidal volume (V_T)] gas exchange and respiratory mechanics were compared using the ARDSNet low V_T algorithm (Control) versus an approach using mathematical modelling to individually optimise V_T at the point of maximal compliance change on the convex portion of the inspiratory pressure-volume (P-V) curve (Experimental).

Methods

Pigs (n = 22) received pentothal/midazolam anaesthesia, oleic acid lung injury, then inspiratory P-V curve fitting to the four-parameter logistic Venegas equation F(P) = a + b[1 + e^-(P-c)/d]^-1 where: a = volume at lower asymptote, b = the vital capacity or the total change in volume between the lower and upper asymptotes, c = pressure at the inflection point and d = index related to linear compliance. Both groups received BVV with gas exchange and respiratory mechanics measured hourly for 5 hrs. Postmortem bronchoalveolar fluid was analysed for interleukin-8 (IL-8).

Results

All P-V curves fit the Venegas equation (R² > 0.995). Control V_T averaged 7.4 ± 0.4 mL/kg as compared to Experimental 9.5 ± 1.6 mL/kg (range 6.6 – 10.8 mL/kg; p < 0.05). Variable V_Ts were within the convex portion of the P-V curve. In such circumstances, Jensen''s inequality states "if F(P) is a convex function defined on an interval (r, s), and if P is a random variable taking values in (r, s), then the average or expected value (E) of F(P); E(F(P)) > F(E(P))." In both groups the inequality applied, since F(P) defines volume in the Venegas equation and (P) pressure and the range of V_Ts varied within the convex interval for individual P-V curves. Over 5 hrs, there were no significant differences between groups in minute ventilation, airway pressure, blood gases, haemodynamics, respiratory compliance or IL-8 concentrations.

Conclusion

No difference between groups is a consequence of BVV occurring on the convex interval for individualised Venegas P-V curves in all experiments irrespective of group. Jensen''s inequality provides theoretical proof of why a variable ventilatory approach is advantageous under these circumstances. When using BVV, with V_T centred by Venegas P-V curve analysis at the point of maximal compliance change, some leeway in low V_T settings beyond ARDSNet protocols may be possible in acute lung injury. This study also shows that in this model, the standard ARDSNet algorithm assures ventilation occurs on the convex portion of the P-V curve.     

Life tables for worker honeybees

Life tables for worker honeybees covering all life span, and those for adults, were prepared for three seasonal cohorts, June bees, July bees and wintering bees. Survivorship curves for June and July bees show a convex type being exceptional for insects, with relatively high mortality at egg and feeding larval stages and at later adult stage after most bees became potential foragers. Adult longevity greatly lengthens in Winteriing bees and survivorship curve drops approximately with the same rate. A remarkable similarity of survivorship curves for men and honeybees was demonstrated, apparently due to highly developed social care in both. Some comments were given on mortality factors. The importance of life tables for population researches was shown by applying our result to the population growth curve made byBodenheimer , based upon the data byNolan . At the asymptote of the uncorrected curve, the ratio of total population estimated by uncorrected curve to that by corrected curve reaches about 3∶2.     

Asymptotic behavior of some stochastic difference equation population models

We consider a general class of Markov population models formulated as stochastic difference equations. The population density is shown to converge either to 0, to +, or to a unique stationary distribution concentrated on (0, +), depending on the signs of the mean log growth rates near 0 and +. These results are applied to the Watkinson-MacDonald bottleneck model of annual plants with a seedbank, extended to allow for random environmental fluctuations and competition among co-occurring species. We obtain criteria for long-term persistence of single-species populations, and for coexistence of two competing species, and the biological significance of the criteria is discussed. The lamentably few applications to the problem at hand of classical limit-theory for Markov chains are surveyed.     

Measurement of Fitness and Its Components in Six Laboratory Strains of DROSOPHILA MELANOGASTER

Six laboratory strains of Drosophila melanogaster were used to measure "net fitness" and its components by interspecific competition with D. hydei using 100 experimental populations. The "total competitive ability," an estimate of net fitness measured in these competition experiments, was tightly correlated with another measure of net fitness, the population size, in single-species experiments (phenotypic correlation r_p = 0.675 and genotypic correlation r_g = 0.997). Other components of fitness were also measured simultaneously, and the correlation with the net fitness was calculated. The very high correlation between two measurements of net fitness and lower correlations between net fitness and components of fitness suggests that these net fitness measures are more reliable estimates of the "real net fitness" than the components of fitness.     

Competition and information

Reconsideration of the logistic equation and of its expansion to the special and general Volterra competition equations in terms of mass/energy in phase-space, shows that information on the phase-spatial conditions of resource and consumers determines specific population parameters which, in turn, decide on coexistence and extinction.Thus, introduction ofInformation as a separate and independent biophysical parameter, in analogy, and in addition, to Force in Classical Physics, is necessary. This allows for quantification of informational effects on resource flows and population numbers. As such, different population growth dN/dt during a competitive exclusion process, is theeffect of competition, and not itscause.It is found that species recognition of self and ignorance of other consumers and of their phase-spatial conditions of resource supplies stabilizes coexistence, while excess information on competitors and on resource supplies destabilizes community structure. These findings are particularly relevant for the speciesHomo sapiens.Among other, apparently disparate population phenomena, Information as a causative parameter also resolves the controversy of complexity and stability in biological systems.     

Natural selection and population density-feedback II. The evolution of functional response curves

The nature of the functional response may be qualitatively understood as follows. Sigmoid responses to one food type may arise, in the presence of alternate foods, as a result of optimal feeding and foraging behavior. Sigmoid curves resulting from this cause I term class A curves. The same curve may also arise in the absence of alternate foods as a result of learning, individual variations in the level of food density at which predators begin feeding, or training effects. The latter I have termed class B curves. At very high food densities, a drop in food intake per predator might occur because of the tendency for predators to take easily found and captured items first and to become more selective when food is very common. Such “dome-shaped” curves have been found in the laboratory but should be rare in nature. Computer simulation of a three trophic-level system, using the phenotypic selection model of Emlen, indicates that natural selection acting on prey should encourage sigmoidality in the predator's class B functional response, at least in disturbed environments. The opposite force arises from selection acting on predators. However, given the magnitudes of growth efficiencies (see Eq. (8), it appears that at least for terrestrial vertebrates, selection on prey species is more important than selection on predators for determining functional responses. Accordingly, prey-predator systems occupying highly variable environments are expected to show more marked type III (class B) curves than systems in more stable areas. Finally, the role of functional response for prey-predator stability is discussed. Class A (alternate food) responses may result in population control for prey in multiple prey systems. Peterman and Pikitch have modeled systems in which type III functional response by predators, in systems where predation varies independently of prey, may lead to double equilibria. This picture is clouded, however, when predator populations are interactive with their food, though double equilibria are still possible (J. M. Emlen, 1984, “Population Biology: The Coevolution of Population Dynamics and Behavior,” Macmillan, New York, in press).     

Fast seedling root growth leads to competitive superiority of invasive plants

The competitive superiority of invasive plants plays a key role in the process of plant invasions, enabling invasive plants to overcome the resistance of local plant communities. Fast aboveground growth and high densities lead to the competitive superiority of invasive species in the competition for light. However, little is understood of the role belowground root competition may play in invasion. We conducted an experiment to test the effect of root growth on the performance of an invasive shrub Cassia alata, a naturalized, non-invasive shrub Corchorus capsularis, and a native shrub Desmodium reticulatum. We compared seedling growth of the three species and their competitive ability in situ. The roots of the C. alata seedlings grew much faster than those of C. capsularis and D. reticulatum during the entire growth period although C. alata had shorter shoots than D. reticulatum. Furthermore, C. alata showed an apparent competition advantage compared to the other two species as evidenced by less biomass reduction in intraspecific competition and higher competitive effects in interspecific competition. Our study reveals that fast seedling root growth may be important in explaining the competitive advantages of invasive plants. Future studies should pay more attention to the belowground traits of invasive plants, the trade-off between shoot and root growth, and the role of root competition in affecting the population dynamics of invasive plants and the structures of invaded communities.     

Evolutionary entropy predicts the outcome of selection: Competition for resources that vary in abundance and diversity

Competition between individuals for resources which are limited and diverse in composition is the ultimate driving force of evolution. Classical studies of this event contend that the outcome is a deterministic process predicted by the growth rate of the competing types—a tenet called the Malthusian selection principle. Recent studies of competition indicate that the dynamics of selection is a stochastic process, regulated by the population size, the abundance and diversity of the resource, and predicted by evolutionary entropy—a statistical parameter which characterizes the rate at which the population returns to the steady state condition after a random endogenous or exogenous perturbation. This tenet, which we will call the entropic selection principle entails the following relations:

• (a)When resources are constant, limited and diverse, variants with higher entropy will have a selective advantage and increase in frequency.
• (b)When resources undergo large variations in abundance and are singular, variants with lower entropy will have a selective advantage and increase in frequency.

This article delineates the analytic, computational and empirical support for this tenet. We show moreover that the Malthusian selection principle, a cornerstone of classical evolutionary genetics, is the limit, as population size and resource abundance tends to infinity of the entropic selection principle. The Malthusian tenet is an approximation to the entropic selection principle—an approximation whose validity increases with increasing population size and increasing resource abundance. Evolutionary entropy is a generic concept that characterizes the interaction dynamics of metabolic entities at several levels of biological organization: cellular, organismic and ecological. Accordingly, the entropic selection principle represents a general rule for explaining the processes of adaptation and evolution at each of these levels.     

Effects of Host Interspecific Interaction in the <Emphasis Type="Italic">Maculinea</Emphasis>–<Emphasis Type="Italic">Myrmica</Emphasis> Parasite–Host System

A model of interspecific host competition in a system with one parasite (butterfly—Maculinea) and multiple potential hosts (ants—Myrmica) is presented. Results indicate that host interspecific competition increases the occurrence of multiple host behaviour in Maculinea natural populations but decreases the ability of the parasite populations to adapt to the most abundant host species. These qualitative predictions were compared with data on host specificity, with good agreement. Analysis of the data also indicates that Maculinea teleius and Maculinea arion respond differently to changes in relative host abundances. Maculinea teleius shows a larger fraction of sites where it displays multiple host behaviour and a larger fraction of sites where the niches of the hosts overlap. In some instances, Maculinea teleius is adapted to Myrmica hosts that are present in lower frequencies. Maculinea arion is locally more host-specific and occurs at sites where host interspecific competition is unlikely and is more frequently adapted to the most abundant host species.     

Modeling Surface Growth of Escherichia coli on Agar Plates

Surface growth of Escherichia coli cells on a membrane filter placed on a nutrient agar plate under various conditions was studied with a mathematical model. The surface growth of bacterial cells showed a sigmoidal curve with time on a semilogarithmic plot. To describe it, a new logistic model that we presented earlier (H.Fujikawa et al., Food Microbiol. 21:501-509, 2004) was modified. Growth curves at various constant temperatures (10 to 34°C) were successfully described with the modified model (model III). Model III gave better predictions of the rate constant of growth and the lag period than a modified Gompertz model and the Baranyi model. Using the parameter values of model III at the constant temperatures, surface growth at various temperatures was successfully predicted. Surface growth curves at various initial cell numbers were also sigmoidal and converged to the same maximum cell numbers at the stationary phase. Surface growth curves at various nutrient levels were also sigmoidal. The maximum cell number and the rate of growth were lower as the nutrient level decreased. The surface growth curve was the same as that in a liquid, except for the large curvature at the deceleration period. These curves were also well described with model III. The pattern of increase in the ATP content of cells grown on a surface was sigmoidal, similar to that for cell growth. We discovered several characteristics of the surface growth of bacterial cells under various growth conditions and examined the applicability of our model to describe these growth curves.     

Condition and size of damselflies: a field study of food limitation

Summary Based on evidence from field manipulations, several authors have recently suggested that interference competition among larval odonates reduces individual growth rates and biomass by reducing foraging rates. This study was designed to test the effects of food shortage on condition (relative mass per unit head width) of larval Ischnura verticalis (Odonata: Coenagrionidae) under laboratory conditions and to use these results to estimate the degree of food shortage of larvae under naturally occurring field conditions. In the laboratory, there were marked differences in condition of larvae fed diets ranging from ad libitum feeding with worms to ad libitum feeding with Daphnia 1 day out of every 8. Condition of larvae collected from May through October from 17 different sites in southern Ontario indicated that, for most of the year, larvae had conditions similar to those fed ad libitum with Daphnia in the laboratory. There was no evidence that larval condition was related to population density. Condition of larvae in most sites during July was similar to that of larvae fed poor diets in the laboratory. It is unlikely that the low conditions were due to competition as there were no correlations with density across sites and population densities during July were at their lowest. Adult head widths showed a seasonal decline from mid June to the end of the flight season. There was no evidence that head widths were related to population density although there was some evidence that head widths of males were positively related to larval condition. My results do not support the hypothesis that competition is important in affecting foraging rates and subsequent development of larvae. Contrasts between my results and other studies may stem from difficulties with the interpretation of field experiments, that densities in my study may have been low due to fish predation, and/or that I. verticalis larvae are slow moving relative to other larvae and thus less likely to interact.     

Fast versus slow growing tuna species: age,growth, and implications for population dynamics and fisheries management

Growth models describe the change in length or weight as a function of age. Growth curves in tunas can take different forms from relatively simple von Bertalanffy growth curves (Atlantic bluefin, albacore tunas) to more complex two- or three-stanza growth curves (yellowfin, bigeye, skipjack, southern bluefin tunas). We reviewed the growth of the principal market tunas (albacore, bigeye, skipjack, yellowfin and the three bluefin tuna species) in all oceans to ascertain the different growth rates among tuna species and their implications for population productivity and resilience. Tunas are among the fastest-growing of all fishes. Compared to other species, tunas exhibit rapid growth (i.e., relatively high K) and achieve large body sizes (i.e., high L _∞ ). A comparison of their growth functions reveals that tunas have evolved different growth strategies. Tunas attain asymptotic sizes (L _∞ ), ranging from 75 cm FL (skipjack tuna) to 400 cm FL (Atlantic bluefin tuna), and reach L _∞ at different rates (K), varying from 0.95 year^?1 (skipjack tuna) to 0.05 year^?1 (Atlantic bluefin tuna). Skipjack tuna (followed by yellowfin tuna) is considered the “fastest growing” species of all tunas. Growth characteristics have important implications for population dynamics and fisheries management outcomes since tunas, and other fish species, with faster growth rates generally support higher estimates of Maximum Sustainable Yield (MSY) than species with slower growth rates.     

两种异养性鞭毛虫实验种群数量动态的比较研究

1999年4－8月从武昌东湖PFU样本中分离纯化了两种异养性鞭毛虫,对四种不同浓度Ceraphyl培养液中的种群增长进行了比较研究,结果表明这两种异养性鞭毛虫种群的数量动态显著不同,聚滴虫在四种浓度Ceraphyl培养液中均呈逻辑斯谛增长;而舞行波豆虫在四种浓度Ceraphyl培养液中的增长曲线均为抛物线。拟合组建了种群增长方程,并论证了方程可信度及其参数的生态学意义。     

Effects of density-restricted food encounter on some single-level competition models

A family of two-species competition models in which density-restricted rates of food enounter are explicitly incorporated generates the following results:

1. 1. Sigmoidal growth. A new model for sigmoidal single-species growth is produced, but one whose inflection point always falls below half the carrying capacity.

2. 2. Comparison with simpler models. In models having shared and exclusive resources, the one or two stable nodes of simpler models may no longer occur in the first quadrant. Such models can simulate how one species by consuming enough overlapping resource can cause another species, unable to maintain itself on its exclusive resources, to go extinct. In models for interspecific interference competition (resource competition purely intraspecific), one or even two more intersections of the zero-isoclines may occur, or the isoclines may intersect once, but with different relative slopes than in the simpler models.

3. 3. Alternative communities. A new model is produced for alternative communities. Conditions for this situation, phrased in terms of parameters measuring feeding and competitive abilities, are rather narrow.

     

Conquerors or exiles? Impact of interference competition among invasive Ponto-Caspian gammarideans on their dispersal rates

Ponto-Caspian gammarids have invaded European waters, affecting local communities by predation and competition. Their ranges and dispersal rates vary across Europe, which may result from their interspecific interactions, accelerating or reducing migrations. We checked this hypothesis by testing interference competition among co-occurring invaders: Dikerogammarus villosus, D. haemobaphes and Pontogammarus robustoides. We used 140-cm long tanks (gravel substratum), divided into seven compartments. We introduced 25 “residents” into the outermost compartment, separated with a barrier. After 1 h, we introduced 25 “intruders”. After the next 1 h, we removed the barrier and the gammarids dispersed in the tank. After 4 or 20 h, we counted the gammarids in the compartments. We tested all pairwise species combinations and single-species controls. Dikerogammarus villosus displaced other species (P. robustoides only after 4 h) and reduced its own motility after 20 h in their presence. Pontogammarus robustoides stimulated the short-time migrations of D. villosus intruders and of D. haemobaphes. As P. robustoides migrated spontaneously much more than Dikerogammarus spp., its impact decreased after longer time. Dikerogammarus haemobaphes stimulated the short-time movement of P. robustoides intruders but reduced the long-time relocation of this species. In general, gammarid dispersal increased in the presence of stronger competitors (D. villosus and P. robustoides, especially residents) and decreased in response to weaker competitors (D. haemobaphes). Thus, competitive interactions may affect dispersal of invasive gammarids and contribute to the fastest spread of the weakest competitor, D. haemobaphes observed in the field, whereas the strongest species, D. villosus was the latest newcomer in many novel areas.     

Efficient FPT Algorithms for (Strict) Compatibility of Unrooted Phylogenetic Trees

In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species X; these relationships are often depicted via a phylogenetic tree—a tree having its leaves labeled bijectively by elements of X and without degree-2 nodes—called the “species tree.” One common approach for reconstructing a species tree consists in first constructing several phylogenetic trees from primary data (e.g., DNA sequences originating from some species in X), and then constructing a single phylogenetic tree maximizing the “concordance” with the input trees. The obtained tree is our estimation of the species tree and, when the input trees are defined on overlapping—but not identical—sets of labels, is called “supertree.” In this paper, we focus on two problems that are central when combining phylogenetic trees into a supertree: the compatibility and the strict compatibility problems for unrooted phylogenetic trees. These problems are strongly related, respectively, to the notions of “containing as a minor” and “containing as a topological minor” in the graph community. Both problems are known to be fixed parameter tractable in the number of input trees k, by using their expressibility in monadic second-order logic and a reduction to graphs of bounded treewidth. Motivated by the fact that the dependency on k of these algorithms is prohibitively large, we give the first explicit dynamic programming algorithms for solving these problems, both running in time \(2^{O(k^2)} \cdot n\), where n is the total size of the input.