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1.
Different types of the Logistic model are constructed based on a simple assumption that the microbial populations are all
composed of homogeneous members and consequently, the condition of design for the initial value of these models has to be
rather limited in the case of N(t
0)=N
0. Therefore, these models cannot distinguish the dynamic behavior of the populations possessing the same N
0 from heterogeneous phases. In fact, only a certain ratio of the cells in a population is dividing at any moment during growth
progress, termed as θ, and thus, dN / dt not only depends on N, but also on θ. So θ is a necessary element for the condition design of the initial value. Unfortunately, this idea has long been neglected in
widely used growth models. However, combining together the two factors (N
0 and θ) into the initial value often leads to the complexity in the mathematical solution. This difficulty can be overcome by using
instantaneous rates (V
inst) to express growth progress. Previous studies in our laboratory suggested that the V
inst curve of the bacterial populations all showed a Guassian function shape and thus, the different growth phases can be reasonably
distinguished. In the present study, the Gaussian distribution function was transformed approximately into an analytical form
(
Yi = ae[ - 0.5( \fracxi - x0 b )2 ] Y_i = \alpha e^{\left[ { - 0.5\left( {\frac{{x_i - x_0 }}{b}} \right)^2 } \right]}
) that can be conveniently used to evaluate the growth parameters and in this way the intrinsic growth behavior of a bacterial
species growing in heterogeneous phases can be estimated. In addition, a new method has been proposed, in this case, the lag
period and the double time for a bacterial population can also be reasonably evaluated. This approach proposed could thus
be expected to reveal important insight of bacterial population growth. Some aspects in modeling population growth are also
discussed. 相似文献
2.
According to the instantaneous growth rate (dN/dt) of E. coli CVCC249 growing in batch culture, the entire growth progress was distinguished into four phases: accelerating growth phase,
constant growth phase, decelerating growth phase and declining phase, in each of which obvious variation in physiological
and biochemical properties was detected, including total DNA, total protein, and MTT-dehydrogenase activity, etc., that led
to difference in their antibiotic susceptivity. Antibiotic susceptivity of the population sampled from each phase was tested
by Concentration-killing Curve (CKC) approach following the formula N=N
0/{1+exp[r·(x-BC
50)]}, showing as normal distribution at the individual cell level for an internal population, in which the median bactericidal
concentration BC
50 represents the mean level of susceptivity, while the bactericidal span BC
1−99=(2lnN
0)/r indicates the variation degree of the antibiotic susceptivity. Furthermore, tested by CKC approach, the antibiotic susceptivity
of E. coli CVCC249 population in each physiological phase to gentamicin or enoxacin was various: susceptivity of the population in the
constant growth phase and declining phase all increased compared with that in the accelerating growth phase for gentamicin
but declined for enoxacin. The primary investigations revealed that the physiological phase should be taken into account in
the context of antibiotic susceptivity and research into antimicrobial mechanism. However there are few reports concerned
with this study. Further research using different kinds of antibiotics with synchronized continuous culture of different bacterial
strains is required.
Supported by the Natural Science Foundation of Shandong Province, China (Grant No. Y2005C58), the Natural Key Technology R&D
Program of China (Grant No. 2006BAK02A03-6) and the Youth Scientific Research Foundation of Shandong Academy of Agricultural
Science (2005YQ035) 相似文献
3.
Stephen J. Merrill 《Journal of mathematical biology》1984,20(3):305-320
The probability of tumor extinction due to the action of cytotoxic cell populations is investigated by several one dimensional
stochastic models of the population growth and elimination processes of a tumor. The several models are made necessary by
the nonlinearity of the processes and the different parameter ranges explored.
The deterministic form of the model is
where γ0, k′6 and k
1 are positive constants. The parameter of most import is
which determines the stability of the T = 0 equilibrium. With an initial tumor size of one, a (linear) branching process is used to estimate the extinction probability.
However, in the case λ = 0 when the linearization of the deterministic model gives no information (T = 0 is actually unstable) the branching model is unsatisfactory. This makes necessary the utilization of a density-dependent
branching process to approximate the population. Through scaling a diffusion limit is reached which enables one to again compute
the probability of extinction. For populations away from one a sequence of density-dependent jump Markov processes are approximated
by a sequence of diffusion processes. In limiting cases, the estimates of extinction correspond to that computed from the
original branching process. Table 1 summarizes the results. 相似文献
4.
Effect of physiological heterogeneity of <Emphasis Type="Italic">E. coli</Emphasis> population on antibiotic susceptivity test
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According to the instantaneous growth rate (dN/dt) of E. coli CVCC249 growing in batch culture, the entire growth progress was distinguished into four phases: accelerating growth phase,
constant growth phase, decelerating growth phase and declining phase, in each of which obvious variation in physiological
and biochemical properties was detected, including total DNA, total protein, and MTT-dehydrogenase activity, etc., that led
to difference in their antibiotic susceptivity. Antibiotic susceptivity of the population sampled from each phase was tested
by Concentration-killing Curve (CKC) approach following the formula N=N
0/{1+exp[r·(x-BC
50)]}, showing as normal distribution at the individual cell level for an internal population, in which the median bactericidal
concentration BC
50 represents the mean level of susceptivity, while the bactericidal span BC
1−99=(2lnN
0)/r indicates the variation degree of the antibiotic susceptivity. Furthermore, tested by CKC approach, the antibiotic susceptivity
of E. coli CVCC249 population in each physiological phase to gentamicin or enoxacin was various: susceptivity of the population in the
constant growth phase and declining phase all increased compared with that in the accelerating growth phase for gentamicin
but declined for enoxacin. The primary investigations revealed that the physiological phase should be taken into account in
the context of antibiotic susceptivity and research into antimicrobial mechanism. However there are few reports concerned
with this study. Further research using different kinds of antibiotics with synchronized continuous culture of different bacterial
strains is required. 相似文献
5.
Barbara Hefti-Gautschi Monika Pfunder Lukas Jenni Verena Keller Hans Ellegren 《Conservation Genetics》2009,10(1):87-99
The conservation status of small breeding areas of the Goosander (Mergus merganser merganser) in Central Europe is unclear. Geographic isolation of these areas suggests restricted gene flow to and from large North-European
populations. On the other hand, migrating Goosanders from northern Europe join the Central European breeding population for
wintering. To evaluate the conservation status of the small breeding areas we assessed the genetic structure of M. merganser populations in Europe by examining two nuclear marker systems (microsatellites and Single Nucleotide Polymorphisms, SNP)
and mitochondrial (mtDNA) control region sequence variation for Goosanders in 11 sampling areas representing three of five
distinct breeding areas and two subspecies (M. m. merganser and M. m. americanus). Overall population differentiation estimates including both subspecies were high, both based on mtDNA () and nuclear markers (θ
ST = 0.219; 95% CI 0.088–0.398, SNP and microsatellites combined). Within Europe, mtDNA revealed a strong overall () and significant pairwise population differentiation between almost all comparisons. In contrast, both nuclear marker systems
combined revealed only a small overall genetic differentiation (θ
ST = 0.022; 95% CI 0.003–0.041). The strong genetic differentiation based on female-inherited mtDNA but not on biparentally
inherited nuclear markers can be explained by sex-biased dispersal and strong female philopatry. Therefore, small breeding
areas in Europe are endangered despite large male-mediated gene-flow, because when these populations decline, only males—but
due to strong philopatry not females—can be efficiently supplemented by migration from the large North European populations.
We therefore propose to manage the small breeding areas independently and to strengthen conservation efforts for this species
in Central Europe. 相似文献
6.
Albert Getabu 《Hydrobiologia》1992,232(1):91-97
Length-frequency data collected from fish landings in the Kenya waters of Lake Victoria were used to estimate the growth parameters,
total mortality rate and growth performance index in Oreochromis niloticus. The asymptotic length, (L
∞) and the ratio of the total mortality rate (Z) to the growth constant (K), were estimated to be 64.6 cm and 3.219 respectively. K was 0.254 y-1, Z was 0.818 y-1 and the growth performance index θ′ = Log10
K + 2 log10
L∞ = 3.025, which is rather high as compared to other tilapia populations in natural waters. 相似文献
7.
Founder group size is of prime importance in tree breeding programs. We determined whether sampling 20-plus trees for breeding
in Allanblackia floribunda, a tropical forest tree species that has been recently enrolled in tree improvement program for fruit and seed production,
would affect neutral genetic diversity and inbreeding level in both breeding and production populations. Using eight informative
microsatellite loci, we: (a) assessed the nuclear genetic diversity of ten natural populations, and of the breeding population
in the humid forest zone of Cameroon; (b) investigated temporal effective-size fluctuations in A. floribunda natural populations, with a view to identifying the role of past demographic events in the genetic structure of the studied
species; and (c) tested the hypothesis that genetic diversity in a founder group of 20 individuals is not different from that
existing in the wild. The eight loci were variable. High levels of genetic diversity (A = 4.96; H
E = 0.59) and moderate differentiation (R
ST = 0.061) were found within and among populations in wild stands. High genetic distances existed between populations
( \textaverage chord distance = 0.\text2769 ±0.00\text554 ) \left( {{\text{average chord distance}} = 0.{\text{2769}} \pm 0.00{\text{554}}} \right) . Eight of the ten surveyed populations showed signs of deviation from mutation-drift equilibrium, suggesting Pleistocene
population bottlenecks and fluctuations in effective population size. Mantel tests did not reveal any relationships between
genetic and geographic distances. A neighbor-joining dendrogram showed a population structure that could be explained by historical
factors. The hypothesis tested has been accepted. However, a slight increase in inbreeding was observed in the breeding population. 相似文献
8.
Archna Suman A. K. Shrivastava Asha Gaur Pushpa Singh J. Singh R. L. Yadav 《Plant Growth Regulation》2008,54(1):1-11
The nitrogen fixing bacterial endophytes Gluconacetobacter diazotrophicus and Herbaspirillum spp. have been proposed to benefit sugarcane (Saccaharum spp. hybrids) growth. Variable populations of these endophytes exist depending upon ontogenic and climatic variations as
well. This study investigates the effect of variable chemical nitrogen application in soil on the population of endophytic
diazotrophs, acetylene reduction ability of excised roots, plant N-nutrient use efficiency and probable interactions among
different parameters in eight commercial sugarcane varieties of subtropical India. Recovery efficiency (RE), agronomic efficiency
(AE), partial factor productivity (PFP) and physiologic efficiency (PE) indicators were used for accounting N-nutrient use
efficiency. The population of G. diazotrophicus was more at N75 compared to N0 and N150, whereas Herbaspirillum population increased from N0 to N150. ARA was positively correlated with Gluconacetobacter population in rhizosphere and root, whereas it had poor correlation with Herbaspirillum population. Positive correlation of RE and AE with ARA of roots, Gluconacetobacter and Herbaspirillum populations in roots and stems indicate their positive contribution in total nitrogen uptake by the plant per kg of N applied.
Average PFP was 808.9 at N75 compared to 408.7 at N150 indicating that N was utilized efficiently at low N input status in sugarcane. Strong positive correlations of AE75 (agronomic efficiency from 75 kg N ha−1 to 150 kg N ha−1) with N-uptake (r
2 = 0.615), cane yield (r
2 = 0.758) and PFP (r
2 = 0.758) and other parameters compared to AE (agronomic efficiency from 0 kg N ha−1 to 75 kg N ha−1 or 150 kg N ha−1) correlations with N-uptake (r
2 = 0.111), cane yield (r
2 = 0.368) and PFP (r
2 = 0.190) indicated that the AE of sugarcane was strongly directed towards producing more cane yield per unit of N fertilizer
once the sugarcane plant has established using initial dose of nitrogen and thus AE75 seems to be a more appropriate indicator for accounting N-nutrient use efficiency in sugarcane. 相似文献
9.
G. D. Reunova I. L. Kats T. I. Muzarok Cheng T. P. Nguen T. T. Dang Yu. N. Zhuravlev 《Russian Journal of Genetics》2012,48(3):291-301
Genetic variability in ten populations of wild-growing ginseng was assessed using AFLP markers with the application of fragment
analysis on a genetic analyzer. The variation indices were high in the populations (P = 55.68%, H
S = 0.1891) and for the species (P = 99.65%; H
S = 0.2857). Considerable and statistically significant population differentiation was demonstrated (θB = 0.363; Bayesian approach, “full model”; F
ST = 0.36, AMOVA). The results of AMOVA and Bayesian analysis indicate that 64.46% of variability is found within the populations.
Mantel test showed no correlation between the genetic and geographic distances among the populations (r = −0.174; p = 0.817). Hierarchical AMOVA and analysis of genetic relationships based on Euclidean distances (NJ, PCoA, and MST) identified
two divergent population groups of ginseng. Low gene flow between these groups (N
m = 0.4) suggests their demographic independence. In accordance to the concept of evolutionary significant units (ESU), these
population groups, in terms of the strategy and tactics for conservation and management of natural resources, should be treated
as management units (MUs). The MS tree topology suggests recolonization of southern Sikhote-Alin by ginseng along two directions,
from south and west. 相似文献
10.
Population growth rate (λ) and its components (adult survival, local recruitment, immigration and their relative contributions to λ) were studied in the declining willow tit Parus montanus in Northern Finland. Capture–recapture models for open populations were used to estimate the population parameters and their process variation. Adult survival was fairly high with low variation (0.593, CV=0.067). As expected, local recruitment was lower and more variable (0.063, CV=0.610). During the 12-year study, the population growth rate averaged to one
(0.988, CV=0.197; calculated as However, if the present processes continue, population projections show that the population is likely to decline. There was considerable temporal variation in the relative contributions of demographic parameters to λ. In all years, adult survival had the highest relative contribution (mean 64%) to the population growth rate and it was the least variable trait. Immigration had a higher relative contribution (22%) to λ than local recruitment (14%). Based on the results for the contributions to λ, the main conservation concern for willow tits is adult survival. Due to low variation, adult survival may be difficult to enhance, but at least it should be prevented from declining. High stochasticity in local recruitment and immigration is probably an inherent characteristic of highly seasonal environments, making these traits difficult to address for conservation practices. 相似文献
11.
Summary A Monte Carlo simulation is proposed to study the dynamics of helper T-cells (N
H) and viral (N
V) populations in an immune response model relevant to HIV. Cellular states are binary variables and the interactions are described
by logical expressions. Viral population shows a nonmonotonic growth before reaching a constant value while helper T-cells
grow to a constant after a relaxation/reaction time. Initially, the population of helper cells grows with time with a power-law,
N
H ∼t
β, before reaching the steady-state; the growth exponent β increases systematically (β ≈ 1 – 2) with the mutation rate (P
mut≈0.1–0.4). The critical recovery time (t
c) increases exponentially with the viral mutation, t
c≈Ae
αP
mut
, with α=4.52±0.29 in low mutation regime and α=15.21±1.41 in high mutation regime. The equilibrium population of helper T-cell
declines slowly with P
mut and collapses at ∼ 0.40; the viral population exhibits a reverse trend, i.e., a slow increase before the burst around the
same mutation regime. 相似文献
12.
Interactions between microbial growth and substrate degradation are important in determining the performance of trickle-bed
bioreactors (TBB), especially when salt is added to reduce biomass formation in order to alleviate media clogging. This study
was aimed at quantifying salinity effects on bacterial growth and substrate degradation, and at acquiring kinetic information
in order to improve the design and operation of TBB. Experiment works began by cultivating a mixed culture in a chemostat
reactor receiving artificial influent containing a mixture of benzene, toluene, and xylene (BTX), followed by using the enrichment
culture to degrade the individual BTX substrates under a particular salinity, which ranged 0–50 g l−1 in batch mode. Then, the measured concentrations of biomass and residual substrate versus time were analyzed with the microbial
kinetics; moreover, the obtained microbial kinetic constants under various salinities were modeled using noncompetitive inhibition
kinetics. For the three substrates the observed bacterial yields appeared to be decreased from 0.51–0.74 to 0.20–0.22 mg mg−1 and the maximum specific rate of substrate utilization,
declined from 0.25–0.42 to 0.07–0.11 h−1, as the salinity increased from 0 to 50 NaCl g l−1. The NaCl acted as noncompetitive inhibitor, where the modeling inhibitions of the coefficients, K
T(S), were 22.7–29.7 g l−1 for substrate degradation and K
T(μ), 13.0–19.0 g l−1, for biomass formation. The calculated ratios for the bacterial maintenance rate, m
S, to
further indicated that the percentage energy spent on maintenance increased from 19–24 to 86–91% as salinity level increased
from 0 to 50 g l−1. These results revealed that the bacterial growth was more inhibited than substrate degradation by the BTX oxidizers under
the tested salinity levels. The findings from this study demonstrate the potential of applying NaCl salt to control excessive
biomass formation in biotrickling filters. 相似文献
13.
Environmental factors that induce spatial heterogeneity of stomatal conductance, g
s, called stomatal patchiness, also reduce the photochemical capacity of CO2 fixation, yet current methods cannot distinguish between the relative effect of stomatal patchiness and biochemical limitations
on photosynthetic capacity. We evaluate effects of stomatal patchiness and the biochemical capacity of CO2 fixation on the sensitivity of net photosynthetic rate (P
N) to stomatal conductance (g
s), θ (θ = δP
N/g
s). A qualitative model shows that stomatal patchiness increases the sensitivity θ while reduced biochemical capacity of CO2 fixation lowers θ. We used this feature to distinguish between stomatal patchiness and mesophyll impairments in the photochemistry
of CO2 fixation. We compared gas exchange of sunflower (Helianthus annuus L.) plants grown in a growth chamber and fed abscisic acid, ABA (10−5 M), for 10 d with control plants (-ABA). P
N and g
s oscillated more frequently in ABA-treated than in control plants when the leaves were placed into the leaf chamber and exposed
to a dry atmosphere. When compared with the initial CO2 response measured at the beginning of the treatment (day zero), both ABA and control leaves showed reduced P
N at particular sub-stomatal CO2 concentration (c
i) during the oscillations. A lower reduction of P
N at particular g
s indicated overestimation of c
i due to stomatal patchiness and/or omitted cuticular conductance, g
c. The initial period of damp oscillation was characterised by inhibition of chloroplast processes while stomatal patchiness
prevailed at the steady state of gas exchange. The sensitivity θ remained at the original pre-treatment values at high g
s in both ABA and control plants. At low g
s, θ decreased in ABA-treated plants indicating an ABA-induced impairment of chloroplast processes. In control plants, g
c neglected in the calculation of g
s was the likely reason for apparent depression of photosynthesis at low g
s.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
14.
Interaction of maturation delay and nonlinear birth in population and epidemic models 总被引:16,自引:0,他引:16
A population with birth rate function B(N) N and linear death rate for the adult stage is assumed to have a maturation delay T>0. Thus the growth equation N′(t)=B(N(t−T)) N(t−T) e−
d
1
T−dN(t) governs the adult population, with the death rate in previous life stages d
1≧0. Standard assumptions are made on B(N) so that a unique equilibrium N
e
exists. When B(N) N is not monotone, the delay T can qualitatively change the dynamics. For some fixed values of the parameters with d
1>0, as T increases the equilibrium N
e
can switch from being stable to unstable (with numerically observed periodic solutions) and then back to stable. When disease
that does not cause death is introduced into the population, a threshold parameter R
0 is identified. When R
0<1, the disease dies out; when R
0>1, the disease remains endemic, either tending to an equilibrium value or oscillating about this value. Numerical simulations
indicate that oscillations can also be induced by disease related death in a model with maturation delay.
Received: 2 November 1998 / Revised version: 26 February 1999 相似文献
15.
Konstantin V. Krutovsky John Bradley St. Clair Robert Saich Valerie D. Hipkins David B. Neale 《Tree Genetics & Genomes》2009,5(4):641-658
Characterizing population structure using neutral markers is an important first step in association genetic studies in order
to avoid false associations between phenotypes and genotypes that may arise from non-selective demographic factors. Population
structure was studied in a wide sample of ∼1,300 coastal Douglas-fir [Pseudotsuga menziesii (Mirb.) Franco var. menziesii] trees from Washington and Oregon. This sample is being used for association mapping between cold hardiness and phenology
phenotypes and single-nucleotide polymorphisms in adaptive-trait candidate genes. All trees were genotyped for 25 allozyme
and six simple sequence repeat (SSR) markers using individual megagametophytes. Population structure analysis was done separately
for allozyme and SSR markers, as well as for both datasets combined. The parameter of genetic differentiation (θ or F
ST) was standardized to take into account high within-population variation in the SSR loci and to allow comparison with allozyme
loci. Genetic distance between populations was positively and significantly correlated with geographic distance, and weak
but significant clinal variation was found for a few alleles. Although the STRUCTURE simulation analysis inferred the same
number of populations as used in this study and as based on previous analysis of quantitative adaptive trait variation, clustering
among populations was not significant. In general, results indicated weak differentiation among populations for both allozyme
and SSR loci (θ
s = 0.006–0.059). The lack of pronounced population subdivision in the studied area should facilitate association mapping in
this experimental population, but we recommend taking the STRUCTURE analysis and population assignments for individual trees
(Q-matrix) into account in association mapping. 相似文献
16.
Commiphora wightii is a medicinally important endangered species endemic to the Thar Desert of Rajasthan, India and adjoining areas of Pakistan.
The populations of this species are declining sharply because of its extensive use as a natural herb. Random amplified polymorphic
DNA analysis was conducted to find the genetic variation among 7 populations of C. wightii. Of the 100 random primers screened, 44 primers yielded 220 loci. Statistical analysis indicated low genetic diversity (H
pop = 0.0958; I = 0.1498; mean polymorphic loci = 14.28%), and high genetic differentiation among the populations (G
ST = 0.3990; AMOVA Φ
ST of 0.3390; Bayesian θ
(II) = 0.3002). The low genetic diversity may be due to geographic isolation and restricted gene flow (N
m = 0.7533) between the fragmented populations. Unsustainable utilization of the plant has fragmented the population continuum
which served the purpose of genetic exchange between populations. Mantel’s test was performed which revealed a highly significant
positive correlation between genetic and geographic distance (r
2 = 0.614, P = 0.023) among the populations studied. Low variation can also be attributed to poor seed setting and the slow growth pattern
of the species, which is also an apomict. In UPGMA dendrogram the Commiphora wightii samples were divided into two major and one minor cluster. These findings can serve as a guide to preserving the genetic
resources of this medicinal plant species. 相似文献
17.
Jan E. Janečka M. E. Tewes L. L. Laack L. I. GrassmanJr A. M. Haines R. L. Honeycutt 《Conservation Genetics》2008,9(4):869-878
Threatened populations are vulnerable to the effects of genetic drift and inbreeding, particularly when gene flow is low and
the effective population size is small. Estimates of effective population size (N
e
) provide important information on the status of endangered populations that have experienced severe fragmentation and serve
as indicators of genetic viability. Genetic data from microsatellite loci were used to estimate N
e
for the 2 remaining populations of the endangered ocelot (Leopardus pardalis albescens) occurring in the United States. Several methods were used to calculate N
e
, resulting in estimates ranging from N
e
= 8.0 (95% CI: 3.2–23.1) to 13.9 (95% CI: 7.7–25.1) for the population located at the Laguna Atascosa Wildlife Refuge in
Cameron County, Texas. The ocelot population in Willacy County, Texas, had N
e
estimates of 2.9 (95% CI: 1.7–5.6) and 3.1 (95% CI: 1.9–13.5), respectively. Estimates of N
e
in both populations were below the critical value recommended for short-term viability. 相似文献
18.
Ernesto Trucco 《Bulletin of mathematical biology》1954,16(4):279-316
This paper is based on N. Rashevsky's theory of imitative behavior, the underlying idea being that performance of one reaction
by a given individual produces an increased stimulation (or tendency) toward the same reaction in other individuals. For simplicity,
consideration is limited to cases in which each individual may choose only between two (or two main categories of) reactions,
denoted byA andB in the following. However, upon suggestion from Dr. Rashevsky and certainly in better agreement with actual facts, the strength
of imitative interaction is assumed to vary from individual to individual. More precisely, if Ψi denotes the additional excitation caused by imitation in theith individual,PAi the probability for performance of reactionA, andPBi the probability for performance of reactionB by theith individual, we postulate that
where the constants α
ik
′
and β
ik
′
(coefficients of imitative interaction) measure the amount of imitative influence exerted by thekth individual upon theith,N being the total number of individuals in the population. The term — αi Ψi accounts for the spontaneous decay of excitation, and the quantities α
ik
′
and α
ik
′
are assumed to benon-negative. The expressions forPAi andPBi are obtained from H. D. Landahl's theory of conflicting stimuli; they depend non-linearly on the values Ψi.
It is implicit in this formulation that the theory can only be applied if the frequency of contacts between individuals is
not too small. Some further shortcomings and limitations of the model are outlined, and the discussion includes suggestions
for reinterpretation and improvement of the theory.
If all the quantities α
ik
′
and α
ik
′
have the same value, sayA, we return to the case treated by Rashevsky (and Landau, 1950); these authors, however, replace the sums in the equation
above by integrals, which automatically restricts the validity of their results to very large values ofN. Their work may therefore be characterized by the assumption of uniform interaction in large populations. Our equations,
on the other hand, are applicable even to very small groups, and therein lies one of their main advantages.
In this paper the mathematical properties of the non-linear system of equations above are studied with particular reference
to the existence and stability of steady states [dΨi/dt ≡ 0;, i = 1 , 2, . . . N].
A sufficient condition for the existence of only one stable steady state is derived. It may be formulated roughly by stating
that all the coefficients of interaction should be sufficiently small. It that is not the case, there may exist a greater
number of stationary states. In particular, two of them (called “extremal”) have the following properties: they arestable and such that the average number of individuals in the group performing one or the other reaction is the largest (or smallest)
possible as compared with the other steady states. Hence the situation is qualitatively similar to that found by Rashevsky
and Landau.Quantitatively, however, important differences may arise, depending on the nature of the matrix specifying the interaction.
A stable state may be approached through damped oscillations, but this effect is important only if the damping is sufficiently
small for the oscillations to become practically observable. Little information could be obtained on this point, due to mathematical
difficulties.
As mentioned above, the most interesting applications of this theory will be with respect to small populations or to populations
partitioned into subgroups with varying amounts of imitative interaction within as well as between groups. 相似文献
19.
Miguel A. Pérez-Farrera Andrew P. Vovides Pablo Octavio-Aguilar Jorge González-Astorga Jesús de la Cruz-Rodríguez Rigoberto Hernández -Jonapá Susana Maza Villalobos-Méndez 《Plant Ecology》2006,187(1):97-108
The cycad Ceratozamia mirandae is endemic to Chiapas, Mexico. Demographic studies were made in two of its populations in the Sepultura Biosphere Reserve under different conservation conditions; in the nucleus zone “Tres Picos” (conserved) and buffer zone “La Sombra” (disturbed and under management). Spatial distribution of C. mirandae was aggregated, showed a clumped local distribution on shallow soils on steep slopes and male and female cones appear to be synchronous in both populations. The population structure was of type I (Bongers) for both sites. Individuals between the sites showed differences in growth pattern. The oldest plants (80–90 cm tall) were estimated to be about 490 years at “La Sombra”. The finite growth rate () in the buffer zone population showed a tendency for decrease whilst in the nucleus zone this estimate remained stable. The highest elasticity values lied in the transition of the first three classes of the “La Sombra” population, in “Tres Picos” this corresponded to adult plants between 20 and 30 cm tall. Given the above, it is proposed that in the nucleus zone, reproductive adults should be of highest conservation priority, whereas in the buffer zone seedling reintroduction should be carried out regularly until the population increases. We recommend an IUCN Red List category of Vulnerable (VU C, 2a), largely due to difficult-to-control destructive annual forest fires that occur in this Reserve. 相似文献
20.
S. J. Knapp J. L. Holloway W. C. Bridges B. H. Liu 《TAG. Theoretical and applied genetics. Theoretische und angewandte Genetik》1995,91(1):74-81
The development of efficient methods for amplifying random DNA sequences by the polymerase chain reaction has created the basis for mapping virtually unlimited numbers of mixed-phase dominant DNA markers in one population. Although dominant markers can be efficiently mapped using many different kinds of matings, recombination frequencies and locus orders are often mis-estimated from repulsion F2 matings. The major problem with these matings, apart from excessive sampling errors of recombination frequency () estimates, is the bias of the maximum-likelihood estimator (MLE) of (
ML).
when the observed frequency of double-recessive phenotypes is 0 and the observed frequency of double-dominant phenotypes is less than 2/3 — the bias for those samples is — . We used simulation to estimate the mean bias of
ML. Mean bias is a function of n and and decreases as n increases. Valid maps of dominant markers can be built by using sub-sets of markers linked in coupling, thereby creating male and feamle coupling maps, as long as the maps are fairly dense (about 5 cM) — the sampling errors of increase as increases for coupling linkages and are equal to those for backcross matings when =0. The use of F2 matings for mapping dominant markers is not necessarily proscribed because they yield twice as many useful markers as a backcross population, albeit in two maps, for the same number of DNA extractions and PCR assays; however, dominant markers can be more effeciently exploited by using doubled-haploid, recombinant-inbred, or other inbred populations. 相似文献