A statistical model of the reproduction of aphids

1. The logistic function has been generally used to describe the reproductive process of a “population” of animal. However, this model can not give us any information about the reproductive process of “individuals” in the population. In this study a statistical model on the basis of the reproduction of individuals of barley aphid is presented to find the proportion of the mature individuals, the heterogeneity in reproductive ability of the aphids, etc.
2. The model is constructed as follows:
3. The probability that j insects are found on a plant at time t₀ is represented as Q(j).
4. The probability that h individuals of j have reproductive ability, say, mature individuals, in the period t₀ to t₁ is represented as B(h/j)=_jC_hw^h(1−w)^j−h, where w is the proportion of mature individuals.
5. In a population with a homogeneous reproductive ability, the probability that each parent lays i offspring in the period t₀ to t₁ is represented as P(i/m)=e^−mmⁱ/i!, where m is mean. And, in a population, m changes according to the gamma distribution. Hence the probability that a parent lays i offspring between t₀ and t₁ is represented as , where p and k are parameters of negative binomial distribution. The probability that h parents on a plant lays s offspring is represented as .
6. From the assumptions mentioned above, the probability that s offspring are to be found at time t₁ on a plant with the original j individuals at time t₀ is represented by
7. The experimental populations were demonstrated to fit well to the model.

     

A model of the plant-to-plant movement of aphids I. Description of the model

The plant-to-plant movement of insects in one of the factors determining the distribution of individuals in insect populations. In this report the movement of barley aphids was analyzed by a statistical model. The model is represented as the convolution of three probability functions:

1. The probability that s individuals are found on a plant at time t₀:Q(s);
2. The probability that i individuals leave the plant and remain on the ground from time t₀ to t₁:_sC_ipⁱq^s−i and p+q=1, where p and q are the proportions of individuals which do not leave a plant and which leave it once or more, respectively;
3. The probability that j individuals climb a plant between time t₀ to t₁ and stay there at time t₁:e^−λλ^j/λ^!, where λ is the mean of the individuals.

The probability that l individuals are located on a plant at time t₁ is represented by the following equation It was shown by simple experiments that the experimental populations were well fitted to the model.     

Tolerance regions with segmented fermentation processes

Many microbial fermentation processes exhibit different phases (e.g. adaption phase, main growth phase, main production phase). The process variables e.g. the biomass vary randomly about their mean. The experimentalist is interested to know the break points of the different phases, and a tolerance region, i.e. a range of possible values of the process variable that can be considered as normal. This paper deals with statistical methods for determining break points and tolerance regions.List of Symbols a _i intercept in phasei - b _i specific growth rate in phasei - e _t deviation of a measurement in timet - tEX expectation of variableX - r number of phases of fermentation - T _i break point of phaseit - t _ij time of measurementj in phasei - t _n–2.1–/2 quantile oft distribution - Y(t) logarithm of measurement at timet Greek Letters 1 – cover probability of tolerance region - 1 – part covered by the tolerance region - ² variance ofe _t - (·) standard normal distribution - quantile of chisquare distribution     

Comparison of models for subtractive and shunting lateral-inhibition in receptor-neuron fields

Summary Two types of neuronal lateral inhibition in one-dimensional fields of receptors and neurons are considered. The first type, which has been demonstrated in the eye of Limulus, is called subtractive inhibition (SI): it assumes that neuronal activity depends on the difference between the total excitation and inhibition. The second type is called shunting inhibition (SHI): it assumes that inhibitory influences cause a shunting of a portion of the excitation-produced depolarizing current. Consideration of the shunting model is dictated by its considerable physiological plausibility. The actions of SI and SHI, examined for a variety of coupling conditions and time-stationary positive inputs, are shown to be markedly different. The results indicate that SI is most suited for obtaining (1) a linearity between input and output, (2) a contrasting effect that does not depend on the presence of input discontinuities, and (3) contrasting whose degree is independent of input amplitude. SI is especially useful if coupling coefficients can be varied to accommodate the various input form functions or if, for fixed coupling coefficients, the class of input form functions is limited. On the other hand SHI appears most suited for obtaining (1) a nonlinear input-output relation, (2) a relative contrasting only of discontinuities, and (3) a dependence of the contrasting upon input amplitude.List of Main Symbols a coupling coefficient for neighboring units, also called coupling amplitude - V _j output of receptor number j - i _j generator current of neuron number j - g inhibitory function for subtractive inhibition - h inhibitory function for shunting inhibition - v ₂/v ₁ [applies to two-unit case] - N _k neuron number k - I _k total source current produced by excitatory influences on N _k - G _k conductance for source current not shunted (with shunting inhibition) - i portion of source current shunted as a result of inhibition - m number of inhibitory influences [in Eq. (1)] - G _kj conductance of inhibitory shunt path j for neuron N _k - q number of receptors - n number of neurons - R _j receptor number j - x distance - y(x) input stimulus to receptors - y _j =y(x _j ) input stimulus to receptor R _j - v _j v_j for v _j 0, zero otherwise - a _kj G _kj /v _j , inhibitory coupling coefficient for forward shunting inhibition [refer to Eq. (2)] - b _kj excitatory coupling coefficient for contribution to source current of neuron N _k by receptor R _j [refer to Eq. (3)] - i _j i _j for i _j 0, zero otherwise - c _kj G _kj /i _j , inhibitory coupling coefficient for backward shunting inhibition [refer to Eq. (4)] - â _kj inhibitory coupling coefficient for forward subtractive inhibition [refer to Eq. (5)] - _kj inhibitory coupling coefficient for backward subtractive inhibition [refer to Eq. (6)] - y(x _j )=Af(x _j ) sensory input function - A input amplitude - f(x _j ) sensory input form function, also called a sensory image - i(x _j ) generator current output of neuron Nj which is located at x=x _j - y (y ₁, y ₂, ..., y _n), a column vector - i (i ₁, i ₂, ..., i _n), a column vector, also called generator current configuration - a an n by n matrix having a _kj as the term in the k-th row, j-th column - U the unit matrix - d ¦k-j¦, separation between neurons N _k and N _j - a a _kj for d=1, called coupling amplitude - SI subtractive inhibition - SHI shunting inhibition - FSI forward subtractive inhibition - BSI backward subtractive inhibition - FSHI forward shunting inhibition - BSHI backward shunting inhibition - s i/i ₅₁ = (s ₁, s ₂, ..., s _n), normalized generator current vector, also called normalized generator current configuration - s _j i _j/i ₅₁, normalized generator current of neuron N _j - f(x) continuous input form function of which f(x _j ) is a sampled version - ^p f(x)/x ^p p-th order derivative of f(x)     

Is the Voltage Gate of Connexins CO<Subscript>2</Subscript>-sensitive? Cx45 Channels and Inhibition of Calmodulin Expression

The sensitivity of Cx45 channels to CO₂, transjunctional voltage (V _j) and inhibition of calmodulin (CaM) expression was tested in oocytes by dual voltage clamp. Cx45 channels are very sensitive to V _j and close with V _j preferentially by the slow gate, likely to be the same as the chemical gate. With a CO₂-induced drop in junctional conductance (G _j), both the speed of V _j-dependent inactivation of junctional current (I _j) and V _j sensitivity increased. With 40-mV V _j-pulses, the of single exponential I _j decay reversibly decreased by 40% during CO₂ application, and G_{j steady state}/G_{j peak} decreased multiphasically, indicating that both kinetics and V _j sensitivity of chemical/slow V _j gating are altered by changes in [H⁺]_i and/or [Ca²⁺]_i. CaM expression was inhibited with oligonucleotides antisense to CaM mRNA. With 15 min CO₂, relative junctional conductance (G _jt/G _jt0) dropped to 0% in controls, but only by 17% in CaM-antisense oocytes. Similarly, V _j sensitivity was significantly lessened in CaM-antisense oocytes. The data indicate that both the speed and sensitivity of V _j-dependent inactivation of the junctional current of Cx45 channels are affected by CO₂ application, and that CaM plays a key role in channel gating.     

Determination of thermodynamic functions from scanning calorimetry data. II. For the system that includes self-dissociation / association process

The basic relations between the molar fractions and the scanning calorimetry data for the system that includes self-dissociation/association process such as are presented, where m_i is the stoichiometric coefficient of the ith state A_i. The relations are described for each state j as where f_j(T) is the molar fraction function of state j and ΔH_j(T) is the difference enthalpy function of the system referred to the state j, which can be obtained by scanning calorimetry; R is the gas constant; and T is the absolute temperature. By these relations, scanning calorimetry data can be deconvoluted in order to determine the thermodynamic functions by means of single and double deconvolution. The concentration dependence of the data is analyzed by a method presented in this paper. The nonlinear least squares fitting method for the determination of the functions is discussed. For an example of the application of this method to the actual scanning calorimetry data, thermodynamic data of multistate thermal transition of Vibrio parahaemolyticus hemolysin are analyzed.     

Inference for an age-dependent,multitype branching-process model of mast cells

We consider an age-dependent, multitype model for the growth of mast cells in culture. After a colony of cells is established by an initiator type, the two possible types of cells are resting and proliferative. Using novel inferential procedures, we estimate the generation-time distribution and the offspring distribution of proliferative cells, and the waiting-time distribution of resting cells.List of Notations B _i cumulative distribution function for the time until branching of a cell of type i - b _i probability density function for the time until branching of a cell of type i - b _i b _i (1–D _i ) - D _i cumulative distribution function for the time until death of a cell of type i - d _i probability density function for the time until death of a cell of type i - probability density function of a gamma distribution - G _i cumulative distribution function for the lifetime of a cell of type i - G _1*2 Convolution of G ₁ and G ₂ - ¯G _i 1–G _i - g _i probability density function for the lifetime of a cell of type i - L _i likelihood of a history of type i - m average number of proliferative daughters produced by dividing cells - M _ij (t) the expected number of type-j cells in a colony at time t if that colony began at time 0 with one type-i cell - M _i+ (t) M _i0 (t) + M _i 1(t) + M _i 2(t) - p _rs probability that a dividing cell produces r proliferative and s resting daughters - t _i times defining colony histories. See IV.2.1 - T ₀ time to division of an initiator cell - T ₁, T ₂ times from birth to division of the two daughters of an initiator cell - T ₍₁₎, T ₍₂₎ order statistics of T ₁ and T ₂ - minimum value of a gamma distribution - scale parameter of a gamma distribution or of an exponential distribution - probability per unit time of death for proliferative and resting cells - _rs expected value of p _rs when there is heterogeneity - shape parameter of a gamma distribution     

Evaluation of the state of soil microbial communities in two types of Siberian forest ecosystems

Microbial respiration and biomass were evaluated in soils of the Ermak Tree Nursery and Pogorel’skii Forest under different coniferous species. The degree of disturbance of each biocenosis was determined from the metabolic coefficient (qCO₂). The microbial investigation demonstrated a lower resistance to ecological factors of the tree nursery biocenosis as compared to those of the Pogorel’skii Forest.     

Ion exchange properties of plant root cell walls

Acid-base properties and the swelling capacity of wheat, lupin and pea root cell walls were investigated. Roots of seedlings and green plants of different age were analysed by the potentiometric method. The ion exchange capacity (S _i) and the swelling coefficient (K ^cw) of root cell walls were estimated at various pH values (from 2 to 12) and at different ionic strength (between 0.3 and 1000 mM). To analyse the polysigmoid titration curves pH_i = f (S _i), the Gregor's equation was employed. It was shown that the Gregor's model fits well the experimental data. The total number of the cation exchange (S _t ^cat) and the anion exchange (S _t ^an) groups were determined in the root cell walls. The number of the functional group of each type (S ^j) was estimated, and the corresponding values of pK _a ^j were calculated. It was shown that for all types of cation exchangeable groups arranged in the cell wall structure the acid properties are enhanced by the increasing concentration of electrolyte. For each ionogenic group the coefficients of Helfferich's equation [pK _a ^j = f (C ^K+)] were determined. It was found that the swelling of root cell walls changes with pH, C ^K+ and strongly depends on plant species. Within the experimental pH and C ^K+ range the swelling coefficient changes as follows: lupin > pea > wheat. The obtained results show that for the plant species under investigation the differences in the swelling coefficients originate from (a) the differences in the cross-linking degrees of polymeric chains arranged in the cell wall structure, (b) the differences in the number of carboxyl groups and (c) the differences in the total number of functional groups. Based on the estimated swelling coefficients in water it could be inferred that for wheat the cross-linking degree of the polymeric chains in the root cell walls is higher than those for lupin or pea. It has been emphasized that the calculated parameters (S ^j, pK _a ^j, K ^cw), the equation {pK _a ^j = f (C^K+)} and the dependencies {K ^cw = f (C^K+, pH)} allow to estimate quantitatively the changes in the ion exchange capacity of the root cell walls in response to the changes in an ionic composition of an outer solution. The results of these estimations allow to suggest that (a) the root apoplast is a compartment where the accumulation of cations takes place during the first stage of cation uptake from an outer medium, and (b) the accumulation degree is defined by pH and ionic composition of an outer solution. On the basis of the literature review and the results of the present experimental study it was proposed that the changes in the cell wall swelling in response to variances of environmental or experimental conditions could lead to a change of the water flow through a root apoplast. It has been supported that there is direct relationship between the swelling of root cell walls and the water flow within the plant root apoplast.     

A new proposal for measurement of the adjusted mean crowding through consideration of size variability in habitat units

The mean crowding has previously been measured under the assumption that all quadrats or habitat units have the same size, even though the actual habitat units such as seeds or leaves are generally variable in size. A new index, ‘adjusted mean crowding’, which is adjusted for this variability can be given as where Q is the total number of habitat units in the whole area, x_j the number of individuals in the jth habitat unit, and a_j is defined as the ‘relative size’ of the jth habitat unit, i.e. a_y=y_y/(∑y_j/Q) where y_j is the actually measured size of the jth habitat unit. It is expected that and for the uniform distribution and the random distribution ‘per unit size’, respectively. The comparison between and regressions ( analysis) for the egg distribution pattern of Callosobruchus chinensis or C. maculatus proved that the regression is biased by a positive correlation between the egg number per seed and seed size rather than by a density-dependent change in the ovipositional behavior.     

Qualitative effects of patchy stomatal conductance distribution features on gas-exchange calculations

The qualitative influence of patchy stomatal conductance distributions on the values of photosynthesis (A) and intercellular CO₂ concentration (c_i) as determined by gas-exchange measurements were investigated using computer modelling. Gas-exchange measurements were simulated for different conductance distributions by modelling photosynthesis explicitly for each patch, summing these rates, and inferring c_i from a diffusion equation. Qualitative relationships are presented between conductance distribution features and the difference between assimilation rates measured for patchy and homogeneous leaves at the same c_i (A_p and A_h, respectively). These data show that, although most conductance distributions have little effect on the value of A measured for a given c_i, some distribution features (which we have termed ‘bimodality’, ‘position’, ‘skewness’ and ‘range’) play a key role in controlling the magnitude of these effects. Distributions that are more nearly bimodal, span regions of lower conductance, are right-skewed, or have broader conductance ranges are associated with larger effects on the A(c_i) relationship. To clarify our mathematical analysis and illustrate some of the trends it predicts, we present conductance distributions and gas-exchange data from leaves of Malus dolgo var. Spring Snow Dial were treated with ABA. The results are discussed in the light of recent controversy over the effect of patchy stomatal conductance on gas-exchange data.     

Modifications of current properties by expression of a foreign potassium channel gene in Xenopus embryonic cells

The pH-sensitivity of transepithelial K⁺ transport was studied in vitro in isolated vestibular dark cell epithelium from the gerbil ampulla. The cytosolic pH (pH _iwas measured microfluorometrically with the pH-sensitive dye 2,7-bicarboxyethyl-5(6)-carboxyfluorescein (BCECF) and the equivalent short-circuit current (I _sc), which is a measure for transepithelial K⁺ secretion, was calculated from measurements of the transepithelial voltage (V _t)and the transepithelial resistance (R _t) in a micro-Ussing chamber. All experiments were conducted in virtually HCO ₃ ^– -free solutions. Under control conditions, pH _iwas 7.01±0.04 (n=18), V _twas 9.1±0.5 mV, R _t16.7±0.09 cm², and I _sc was 587±30 A/cm² (n=49). Addition of 20 mm propionate^– caused a biphasic effect involving an initial acidification of pH _i, increase in V _tand I _sc and decrease in R _tand a subsequent alkalinization of pH _i, decrease of V _tand increase of R _t. Removal of propionate^– caused a transient effect involving an alkalinization of pH _i, a decrease of V _tand I _sc and an increase in R _t. pH _iin the presence of propionate^– exceeded pH _iunder control conditions. Effects of propionate ^– on V _t, R _tand I _sc were significantly larger when propionate^– was applied to the basolateral side rather than to the apical side of the epithelium. The pH _i-sensitivityof I _sc between pH 6.8 and 7.5 was –1089 A/(cm² · pH-unit) suggesting that K⁺ secretion ceases at about pH _i7.6. Acidification of the extracellular pH (pH _o)caused an increase of V _tand I _sc and a decrease of R _tmost likely due to acidification of pH _i. Effects were significantly larger when the extracellular acidification was applied to the basolateral side rather than to the apical side of the epithelium. The pH _osensitivity of I _sc between pH 7.4 and 6.4 was –155 A/(cm² · pH unit). These results demonstrate that transepithelial K⁺ transport is sensitive to pH _iand pH _oand that vestibular dark cells contain propionate^– uptake mechanism. Further, the data suggest that cytosolic acidification activates and that cytosolic alkalinization inactivates the slowly activating K⁺ channel (I _sK)in the apical membrane. Whether the effect of pH _ion the I _sK channel is a direct or indirect effect remains to be determined.The authors wish to thank Drs. Daniel C. Marcus, Zhjiun Shen and Hiroshi Sunose for helpful discussions. This work was supported by grants NIH-R29-DC01098 and NIH-R01-DC00212.     

Optimal and central-place foraging theory applied to a desert harvester ant,Pogonomyrmex californicus

Summary Certain predictions of optimal- and central place-foraging theory were tested on the desert harvester ant, Pogonomyrmex californicus. Colonies were offered three different sizes of oat seed and found to maximize net energy intake (ei) over time (t _i ) by harvesting the seed sizes with the highest e _i /t _i rank. Two aspects of t _i were measured that were assumed constant in previous studies. The handling components of t _i (time required to manipulate the seed and travel time back to the colony with the food) were measured and found to be positively correlated with seed size. The manipulation success rate (the percentage of handled seeds successfully picked up) decreased with increased seed size. These results point out how important it is to measure all parameters of e _i /t _i rather than to assume constancy with both prey type and foraging distance. The relative abundance of less preferred food types was important in determining the proportion of preferred types in the diet. The food supply of eight colonies was manipulated experimentally over a 25-day period. Four deprived colonies were constrained within aluminum enclosures to prevented foraging. The remaining four satiated colonies were given food ad libitum. The niche breadths of the treated colonies were then compared to controls, but found not to differ significantly. Seed baits were offered at three distances from the colony to test whether selectivity increased with disance. Contrary to theoretical predictions, all colonies harcested about the same proportion of each seed size at each distance.     

Packed-bed immobilized enzyme reactors for complex processes

Utilization of enzymic reactors for biotechnological-biomedical applications is currently developing at a sustained pace.Our present study concentrates on development of procedures for describing the performance of devices where enzyme-catalyzed reactions between two substrates take place, and for the rational design and optimization of the reactors considered. Within this context, an analytical model was developed for immobilized enzyme packed-bed reactors; it takes into account internal diffusion limitations for the cosubstrates, and hydrodynamic backmixing effects. In order to overcome the complex mathematical problems involved, the compartmental analysis approach was employed.Using this model, performance was simulated for various configurations of the enzymic unit, i.e. from a continuously operated stirred tank reactor (CSTR) to an essentially plug flow type. In addition, an experimental method is described for quantitatively assessing the backmixing effects prevailing in the reactor.The procedures established also provide the ground for further developments, particularly for systems where, in parallel to the enzymic reaction, additional processes (e. g. complexation) take place.List of Symbols C _j,i mM Concentration of substrate j in the pores of stage - iD _j cm²/s Internal (pore) diffusion coefficient of substrate j; defined in Eq. (7) - D _e cm²/s Axial dispersion diffusion coefficient - D _j, cm²/s cm²/s Bulk diffusion coefficient for substrate j - E mM Enzyme concentration inside the catalytic pores - J _j,immol/s/cm² Net flux of substrate j taking place from the bulk of stage i into the corresponding pores; defined in Eq. (6) - K _m,1, K _m,2 mM Michaelis-Menten constants for cosubstrates 1 and 2, respectively - k s ^–1 Catalytic constant - k _s cm/s Catalytic constant - n Total number of elementary stages in the reactor - Q cm³/s Volumetric flow rate throught the reactor - r cm Radius of the pore - R _j,i mM/s Reaction rate of substrate j in stage i, in terms of volumetric units - S cm² Internal surface of a pore - S _j,0 mM Concentration of substrate j in the reactor feed - S _j,i–1, S _j,i mM Concentration of substrate j in the bulk phase leaving stages i — 1 and i, respectivley - V _i cm³ Total volume of stage i (bulk phase + pore phase + inert solid carrier) - V cm³ Total volume of the reactor - V _m ^* mmol/s/cm² Maximal reaction rate in terms of surface units; defined in Eq. (8) - V _m mM/s Maximal reaction rate in terms of volumetric units; defined in Eq. (8) - V _p cm³ Volume of one pore - y cm Axial coordinate of the pores - y ₀ cm Depth of the pores - Z cm Axial coordinate of the reactor - Z ₀ cm Length of the reactor - ₁ Dimensionless parameter; defined in Eq. (27) - ₂ Dimensionless parameter; defined in Eq. (27) - ₁ Dimensionless parameter; defined in Eq. (27) - ₂ Dimensionless parameter; defined in Eq. (27) - Ratio between the radius of the enzyme molecule and the radius of the pore (dimensionless) - V₁ Dimensionless parameter; defined in Eq. (21) - v₂ Dimensionless parameter; defined in Eq. (21) - Q Volumetric packing density of catalytic particles (dimensionless) - Ø Porosity of the catalytic particles (dimensionless) - Ø Dimensionless concentration of substrate j in pores of stage i; defined in Eq. (16) - _j,i-1,_j,i Dimensionless concentration of substrate j in the bulk phase of stage i; defined in Eq. (18) - Dimensionless position; defined in Eq. (16) - ² s² Variance; defined in Eq. (33) - Mean residence time in the reactor; defined in Eq. (33)     

Multiple-channel conductance states and voltage regulation of embryonic chick cardiac gap junctions

Summary We used the double whole-cell voltage-clamp technique on ventricle cell pairs isolated from 7-day chick heart to measure the conductance of their gap junctions (G _j) and junctional channels ( _j) with a steady-state voltage difference (V _j) applied across the junction. Currents were recorded from single gap junction channels (i _j) as symmetrical rectangular signals of equal size and opposite sign in the two cells, and _j was measured from i _j/V _j. We observed channel openings at six reproducible conductance levels with means of 42.6, 80.7, 119.6, 157.7, 200.4 and 240.3 pS. More than half of all openings were to the 80-and 160-pS conductance levels. The probability that a high conductance event (e.g., 160 or 240 pS) results from the random simultaneous opening of several 40-pS channels is small, based on their frequency of occurrence and on the prevalence of shifts between small and large conductance states with no intervening 40-pS steps. Our results are consistent with three models of embryonic cardiac gap junction channel configuration: a homogeneous population of 40-pS channels that can open cooperatively in groups of up to six; a single population of large channels with a maximal conductance near 240 pS and five smaller substates; or several different channel types, each with its own conductance. G _j was determined from the junctional current (I _j) elicited by rectangular pulses of applied transjunctional voltage as I _j/V _j. It was highest near 0 V _j and was progressively reduced by application of V _j between 20 and 80 mV or –20 and –80 mV. In response to increases in V _j, G _j decayed in a voltage-and timedependent fashion. After a 6-sec holding period at 0 V _j, the initial conductance (G _init) measured immediately after the onset of an 80-mV step in V _j was nearly the same as that measured by a 10-mV prepulse. However, during 6-sec pulses of V _j>±20 mV, G _j declined over several seconds from G _init to a steady-state value (G _ss). At potentials greater than ±20 mV the current decay could be fit with biexponential curves with the slow decay time constant ( ₂) 5–20 times longer than ₁. For the response to a step to 80 mV V _j, for example, ₁=127 msec and ₂=2.6 sec. The rate of current decay in response to smaller positive or negative steps in V _j was slower, the magnitude of the decline was smaller, and the ratio ₂/ ₁ decreased. The relationship between G _init and V _j was approximately linear between 0 and 80 mV or –80 mV. whereas the relationship between G _ss and V _j was nonlinear beyond ±20 mV. Upon returning to 0 V _j, G _j recovered with a biexponential time course, reaching its maximal value after several seconds; recovery time constants after a step in V _j from 80 to 0 mV were 225 msec and 1.9 sec. In the resting state, at low junctional voltage, high conductance channel activity (160–240 pS) is favored. Voltage-dependent decline of G _j results in part from a shift from high to lower conductance states.We thank Ms. B.J. Duke for technical assistance and for preparation of the cell cultures and Drs. L.J. DeFelice and D. Eaton for stimulating and helpful discussions of the results.     

Identifying ‘climate keystone species’ as a tool for conserving ecological communities under climate change

Aim

Climate change affects ecological communities via impacts on species. The community's response to climate change can be represented as the temporal trend in a climate-related functional property that is quantified using a relevant functional trait. Noteworthy, some species influence this response in the community more strongly than others.

Innovation

Leveraging on the concept of keystone species, we propose that species with a strong effect on the community's functional response to climate change beyond their relative abundance can be considered as ‘climate keystone species’. We develop a stepwise tool to determine species' effects on a community's climate response and identify climate keystone species. We quantify the species-specific effect by measuring the difference in the community's climate response with and without the species. Next, we identify climate keystone species as those with a strong residual effect after weighting with their relative abundances in the community.

Main Conclusions

To illustrate the use of the stepwise tool with empirical data, we identify climate keystone species that have a strong effect on the change in the average temperature niche in North American bird communities over time and find the identification tool ecologically relevant. Identification of climate keystone species can serve as an additional conservation method to efficiently protect ecological communities and, in turn, the ecosystem functions they provide.     

Malthusian parameters,reproductive values and change under selection in self fertilizing age-structured populations

A population, reproducing wholly by selfing, is assumed to be observed at times . Individuals between x–1 and x units of age at time t are said to be in age class x at that time. The rate of increase in the long run of individuals of type A_iAj is denoted by m_ij+1=m_ji+1. For each genotype there is also a set of reproductive values, corresponding to all age classes and genotypes of individuals having descendants of that genotype. Then, if the number of individuals of each sort of ancestor is multiplied by its reproductive value and the products are summed, the result is the total value, which is V_ij(t) for genotype A_iAj. Then V_ij(t+1)–V_ij(t) is equal to m_ijV_ij(t), where m_ij is the Malthusian parameter for A_iAj. Furthermore, if the mean and variance at time t of the m_ijs, weighted by their corresponding reproductive values, are respectively (t) and _m²(t), then m¯(t+1)–m¯(t)=_m²(t)/(1+m¯(t)).     

The rate of convergence of a generalized stable population

In an age-structured population that grows exponentially, each age groupP _i(t) at periodt is asymptotically equivalent tox ₀ ^t for some positive number x₀. In this paper we show that the speed at which the ith age group reaches its exponential state of equilibrium can be measured by the rate at which the ratio v_i(t)=P_i(t)/p_i(t–1) converges tox ₀. The age specific rate of convergence is determined by considering a quantityr satisfyingv _i(t)-x ₀ ¦ r ^t whent is large;R _i=Infr (over all initial populations,r satisfying the above inequality) is the R-factor used in numerical analysis to measure the rate at which the sequencev _i (t) converges tox ₀;S _i =- In R_i is then defined as the rate of convergence to stability of the ith age group. The case of constant net maternity rates is studied in detail; in this contextS ₀ is compared to the population entropyH, which was proposed by Tuljapurkar (1982) as a measure of the rate of convergence to stability.     

The problem of nonstationary ion fluxes in excitable membranes

Time-dependent electrodiffusion through a membrane is analysed within a simple model treating the boundary-layers in a consistent manner. It is shown that time-independent reversal potentials for the ion fluxes exist only under steady-state conditions. We argue that this result holds very generally. Therefore nonstationary effects like ion storage and depletion inside the membrane should not contribute to the phenomena of excitability.Glossary of Symbols A _mv [V] functional cf. Equation (3) - C membrane capacitance - d one half the thickness of the membrane - F[V] functional cf. Equation (1) - g _i electrochemical potential inside membrane - g _i electrochemical potentials outside membrane at x ±d, respectively - i (index) refers to i-th ionic species - J electric current across membrane - j = j ^} = j ^< current density measured by external electrodes - j _i (x) current density inside membrane in x-direction - j _i ^inst(x) instantaneous current density - J _i ^stat steady-state current density - k Boltzmann constant - m (index) is used in Sec. 2 to denote the independent diffusion currents - n ^< ionic strength of electrolyte at x = - - n _i density of ions inside membrane - n _i density of ions outside membrane at x = ±, respectively - Q charge per unit area of boundary layers at x ± d, respectively - Q ₀ fixed charge per unit area of membrane - q elementary charge - q _i ionic charges - T temperature - it time - V membrane potential (= (-)-()) - V _i Nernst potential - V potential drops inside boundary layers (can be neglected, see Appendix II) - V ^± potential steps at x = ± d, cf. Equation (29) - V ₀ = V ^–-V ⁺ - w _i activation energy inside membrane - x spatial coordinate perpendicular to membrane - y, z spatial coordinates parallel to membrane - dielecric constant - ₀ dielectric constant of electrolyte solution ( 80) - _m dielectric constant of membrane ( 5) - (x) electrostatic potential - charge density of boundary layers - ⁰ fixed charge density inside membrane - spatial average, cf. Equation (12)     

A testcross procedure for selecting exotic strains to improve pure-line cultivars in predominantly self-fertilizing species

Methods for identifying germplasm carrying alleles with the potential to improve a particular single-cross hybrid have been proposed and discussed in recent years. There is a need for similar methods to be used in breeding crops for which pure-line cultivars, rather than hybrids, are the goal. The objective of this research was to develop a method to identify germplasm lines with the potential to contribute favorable alleles not present in a specified pure line or set of pure lines. Given a set of adapted pure lines (A ₁, A ₂ ..., A _m) to be improved and a set of germplasm lines (P ₁ P ₂ ..., P _f), the procedure consists of producing all f x m possible hybrids and evaluating them along with the parents. The testcross statistic T _ij is defined by T _ij=(F _ij–A _j)+(1–) (F _ij–P _i), where A _j, P _i, and F _ij represent the performance of thej ^th adapted line, the i ^th germplasm line, and their hybrid, respectively. The statistic is the mean value of T _ij over all adapted parents A _j. If =(1/2)(1+d), where d = the mean degree of dominance, then T _ij measures the potential for alleles from P _i to improve A _j and measures the potential for alleles from P _i to improve the set A ₁, A ₂ ..., A _m. Use of data on soybean and peanut hybrids published by other researchers suggests that the value assumed for d has little effect on the P _i chosen. The ability of the T _ij and statistics to identify germplasm strains carrying rare favorable alleles should be assessed in empirical studies.Joint contribution: OARDC (Journal Articale No. 161-94), USDAARS, Iowa Agriculture and Home Economics Expriment Station (Journal Paper No. J-16109; Project 2985), and Agreculture and Agri-Food Canada. Salaries and research support for S. K. St. Martin Provided by state and federal funds appropriated to the Ohio Agricultural Research and Development Center, Ohio State University