Estimating effective population size using RADseq: Effects of SNP selection and sample size

Effective population size (N_e) is a key parameter of population genetics. However, N_e remains challenging to estimate for natural populations as several factors are likely to bias estimates. These factors include sampling design, sequencing method, and data filtering. One issue inherent to the restriction site‐associated DNA sequencing (RADseq) protocol is missing data and SNP selection criteria (e.g., minimum minor allele frequency, number of SNPs). To evaluate the potential impact of SNP selection criteria on N_e estimates (Linkage Disequilibrium method) we used RADseq data for a nonmodel species, the thornback ray. In this data set, the inbreeding coefficient F_IS was positively correlated with the amount of missing data, implying data were missing nonrandomly. The precision of N_eestimates decreased with the number of SNPs. Mean N_e estimates (averaged across 50 random data sets with2000 SNPs) ranged between 237 and 1784. Increasing the percentage of missing data from 25% to 50% increased N_e estimates between 82% and 120%, while increasing the minor allele frequency (MAF) threshold from 0.01 to 0.1 decreased estimates between 71% and 75%. Considering these effects is important when interpreting RADseq data‐derived estimates of effective population size in empirical studies.     

Evaluation of absolute quantitation by nonlinear regression in probe-based real-time PCR

Background  

In real-time PCR data analysis, the cycle threshold (CT) method is currently the gold standard. This method is based on an assumption of equal PCR efficiency in all reactions, and precision may suffer if this condition is not met. Nonlinear regression analysis (NLR) or curve fitting has therefore been suggested as an alternative to the cycle threshold method for absolute quantitation. The advantages of NLR are that the individual sample efficiency is simulated by the model and that absolute quantitation is possible without a standard curve, releasing reaction wells for unknown samples. However, the calculation method has not been evaluated systematically and has not previously been applied to a TaqMan platform. Aim: To develop and evaluate an automated NLR algorithm capable of generating batch production regression analysis.     

Solvent‐Polarity‐Induced Active Layer Morphology Control in Crystalline Diketopyrrolopyrrole‐Based Low Band Gap Polymer Photovoltaics

Solvent effects on the morphology of diketopyrrolopyrrole (DPP)‐based low band gap polymer (PDPPBT):phenyl‐C71‐butyric acid methyl ester (PC₇₁BM) blends are studied systematically using a mixture of a non‐aromatic polar primary solvent with high boiling point (b.p.) secondary solvents of increasing polarities. An unfavorable solvent‐PC₇₁BM interaction, due to a polarity mismatch, leads to significantly different morphology, also affecting the growth process of polymer crystallites. Non‐aromatic polar solvent produces large PC₇₁BM aggregates that increase in size with the addition of non‐polar secondary solvents. The size scales of the aggregates decrease markedly when polar solvents are instead used as the secondary solvents. This processing method fundamentally changes the behavior of phase separation, creating a percolated fibrillar type network structure. Moreover, polar secondary solvents with lower vapor pressures reduce the interfibrillar distances that enhance the device performance even more. Power conversion efficiencies (PCE) of 0.03% to 5% are obtained, depending on the solvent system used.     

Why longer song elements are easier to detect: threshold level-duration functions in the Great Tit and comparison with human data

Our study estimates detection thresholds for tones of different durations and frequencies in Great Tits (Parus major) with operant procedures. We employ signals covering the duration and frequency range of communication signals of this species (40–1,010 ms; 2, 4, 6.3 kHz), and we measure threshold level-duration (TLD) function (relating threshold level to signal duration) in silence as well as under behaviorally relevant environmental noise conditions (urban noise, woodland noise). Detection thresholds decreased with increasing signal duration. Thresholds at any given duration were a function of signal frequency and were elevated in background noise, but the shape of Great Tit TLD functions was independent of signal frequency and background condition. To enable comparisons of our Great Tit data to those from other species, TLD functions were first fitted with a traditional leaky-integrator model. We then applied a probabilistic model to interpret the trade-off between signal amplitude and duration at threshold. Great Tit TLD functions exhibit features that are similar across species. The current results, however, cannot explain why Great Tits in noisy urban environments produce shorter song elements or faster songs than those in quieter woodland environments, as detection thresholds are lower for longer elements also under noisy conditions.     

Reproductive and developmental biology of Gonatocerus ashmeadi (Hymenoptera: Mymaridae), an egg parasitoid of Homalodisca coagulata (Hemiptera: Cicadellidae)

The reproductive and developmental biology of Gonatocerus ashmeadi Girault, a parasitoid of the glassy-winged sharpshooter Homalodisca coagulata (Say), was determined at five constant temperatures in the laboratory: 15; 20; 25; 30; 33 °C. At 30 °C, G. ashmeadi maintained the highest successful parasitism rates with 46.1% of parasitoid larvae surviving to adulthood. Lifetime fecundity was greatest at 25 °C and fell sharply as temperature either increased or decreased around 25 °C. Temperature had no effect on sex ratio of parasitoid offspring. Mean adult longevity was inversely related to temperature with a maximum of 20 days at 15 °C to a minimum of eight days at 33 °C. Developmental rates increased nonlinearly with increasing temperatures. Developmental rate data were fitted with the modified Logan model for oviposition to adult development times across each of the five experimental temperatures to determine optimal and upper lethal temperature thresholds. The lower developmental threshold estimated by the Logan model and linear regression were 1.10 and 7.16 °C, respectively. Linear regression of developmental rate for temperatures 15–30 °C indicated that 222 degree-days were required above a minimum threshold of 7.16 °C to complete development. A temperature of 37.6 °C was determined to be the upper development threshold with optimal development occurring at 30.5 °C. Demographic parameters were calculated and pseudo-replicates for intrinsic rate of increase (r_m), net reproductive rates (R_o), generation time (T_c), population doubling time (T_d), and finite rate of increase (λ) were generated using the bootstrap method. Mean bootstrap estimates of demographic parameters were compared across temperatures using ANOVA and nonlinear regression.     

Developmental times and life table statistics of Aulacorthum solani (Hemiptera: Aphididae) at six constant temperatures, with recommendations on the application of temperature-dependent development models

Aulacorthum solani (Kaltenbach) (known as foxglove aphid or glasshouse potato aphid) is a pest of increasing economic importance in several agricultural crops worldwide, including greenhouse vegetables and ornamentals. Developmental rates and age-specific life tables for a North American population of A. solani on pansy (Viola × wittrockiana) (Gams.) were determined at six constant temperatures, and comparisons were made to previous studies of A. solani from differing geographic regions and host crops. On pansy, A. solani developed fastest at 25°C, passing through the four nymphal instars in an average of 6.9 d. The highest intrinsic rates of population increase (0.410 and 0.445) and shortest population doubling times (1.69 and 1.56 d) were recorded at 20 and 25°C, respectively. Average total fecundity remained high from 10 to 20°C (74-68 nymphs/adult); a significant decrease to 39 nymphs/adult occurred at 25°C. For calculating developmental thresholds, we present here a method of adjusting the lower developmental threshold (t(min)) using estimates from nonlinear models to provide an improved estimate of the thermal constant (K, in degree-days). We also call attention to the necessity of using a simulation method to estimate the true upper developmental threshold (t(max)) and optimum developmental temperature (t(opt)) from the Lactin-2 model of temperature-dependent development.     

Trawl Selectivity Trials on the Deep-water Rose Shrimp (Parapenaeus longirostris) in Sicilian Waters

The selectivity of the traditional commercial bottom trawl net employed in Sicily to catch the Mediterranean deep-water rose shrimp, Parapenaeus longirostris, has been assessed. Two fishing campaigns were carried out in the Strait of Sicily and in the Southern Tyrrhenian Sea, using the covered cod-end method (mesh 20 mm vs. 31 mm). Of a total catch of 11,601 individuals, 23.4% escaped in the cover; the sample length structure from the Strait is unimodal, while that from the Tyrrhenian, polymodal. A logistic curve, fitted with a maximum likelihood criterion, has been used to model the selectivity data, in order to obtain the parameters CL_c50% (50% retention size), SR_75–25% (selection range) and SF (selection factor, i.e. CL_c50%/mesh). The two sets of data, besides a larger selection range for the Strait sample (5.2 mm vs. 2.3 mm), produced very similar estimates (retention sizes of 13.0 mm vs. 12.8 mm CL), fitting the logistic curve well. Almost no shrimp larger than 20 mm does escape from the cod-end; moreover, from the amount of damaged specimens found in the cover, even the evaded shrimps sustain a high fishing mortality. An increase of the present cod-end mesh opening, even above the size required by the EU bylaws (at present, 40 mm stretched) seems necessary for managing the fishery.     

Spatial variation in sensitivity as a factor in measurements of spatial summation of warmth and cold

Perception of cutaneous heating and cooling depends strongly on stimulus size. Although this dependence has been attributed solely to spatial summation, topographical variations in temperature sensitivity may also play a role. These variations, which differentially affect perception of small stimuli, may have led to overestimation of spatial summation. This possibility was investigated by measuring detection thresholds and perceived intensity for heating and cooling on the volar surface of the forearm using a multiple-thermode stimulus array. By keeping the array in place throughout each testing session we were able to measure threshold sensitivity and suprathreshold responsiveness at eight individual sites and for combinations of these sites having total stimulus areas of 0.64-5.12 cm². When spatial summation was calculated in the traditional way by averaging the data for all stimuli of each size, the results agreed closely with previous estimates of summation for warmth and cold. When calculations were based instead on the most sensitive test site for each stimulus size, estimates of summation were reduced by about two-thirds. This outcome indicates that the spatial heterogeneity of thermal sensitivity likely contributed to estimates of spatial summation reported in earlier psychophysical studies. A schematic model of cutaneous thermoreception is presented that shows how neural summation and the density of innervation may combine to produce the psychophysical effects of increasing stimulus size (spatial enhancement).     

Observations below multiple lower limits of quantification: How to estimate the mean and variance

Multiple lower limits of quantification (MLOQs) result if various laboratories are involved in the analysis of concentration data and some observations are too low to be quantified. For normally distributed data under MLOQs there exists only the multiple regression method of Helsel to estimate the mean and variance. We propose a simple imputation method and two new maximum likelihood estimation methods: the multiple truncated sample method and the multiple censored sample method. A simulation study is conducted to compare the performances of the newly introduced methods to Helsel's via the criteria root mean squared error (RMSE) and bias of the parameter estimates. Two and four lower limits of quantification (LLOQs), various amounts of unquantifiable observations and two sample sizes are studied. Furthermore, the robustness is investigated under model misspecification. The methods perform with decreasing accuracy for increasing rates of unquantified observations. Increasing sample sizes lead to smaller bias. There is almost no change in the performance between two and four LLOQs. The magnitude of the variance impairs the performance of all methods. For a smaller variance, the multiple censored sample method leads to superior estimates regarding the RMSE and bias, whereas Helsel's method is superior regarding the bias for a larger variance. Under model misspecification, Helsel's method was inferior to the other methods. Estimating the mean, the multiple censored sample method performed better, whereas the multiple truncated sample method performs best in estimating the variance. Summarizing, for a large sample size and normally distributed data we recommend to use Helsel's method. Otherwise, the multiple censored sample method should be used to obtain estimates of the mean and variance of data including MLOQs.     

An analysis of the relationship between solubility and stimulating effect in tarsal chemoreception

The rejection thresholds of the blowfly Phormia regina Meigen for a selected series of substituted aliphatic hydrocarbons have been determined and an analysis made of the effect on stimulation of increasing the number of like substitutions from one to two, of the interaction of different types of substituent, and of the position of the substituent in the molecule. The order of stimulating efficiency (reciprocal of rejection threshold) of the functional groups which have been studied is: Br > Cl ? CH₃ ? CHO > C=O > OH. There is a consistent decrease in stimulating effect following the introduction of a second hydroxyl group. The introduction of a second C=O has little effect. Introduction of a second halogen is generally followed by a decrease in threshold. Two different species of functional group, one of which tends to increase water solubility and the other to decrease it, tend to counter-balance each other. A single oxygen-containing functional group on the end of the molecule or two of these groups which are terminal reduce the stimulating effect less than when one or more of such groups are subterminal or located elsewhere within the molecule. Branching of the carbon chain decreases effectiveness. Sulfur and oxygen linkages also decrease effectiveness. In general, the length of the free alkyl group largely determines the stimulating effectiveness. Its power is modified to varying degrees by the nature of the attached polar groups. Of all chemical properties examined, solubility alone agrees consistently with the foregoing data. Threshold varies directly with the molar solubility of the compounds in water. The fact that the threshold values for individual compounds are frequently different from those which would be expected solely on the basis of the correlation between threshold and solubility in water suggests that other factors are also concerned in stimulation. These have not yet been identified.     

Overcoming the winner's curse: estimating penetrance parameters from case-control data

Genomewide association studies are now a widely used approach in the search for loci that affect complex traits. After detection of significant association, estimates of penetrance and allele-frequency parameters for the associated variant indicate the importance of that variant and facilitate the planning of replication studies. However, when these estimates are based on the original data used to detect the variant, the results are affected by an ascertainment bias known as the "winner's curse." The actual genetic effect is typically smaller than its estimate. This overestimation of the genetic effect may cause replication studies to fail because the necessary sample size is underestimated. Here, we present an approach that corrects for the ascertainment bias and generates an estimate of the frequency of a variant and its penetrance parameters. The method produces a point estimate and confidence region for the parameter estimates. We study the performance of this method using simulated data sets and show that it is possible to greatly reduce the bias in the parameter estimates, even when the original association study had low power. The uncertainty of the estimate decreases with increasing sample size, independent of the power of the original test for association. Finally, we show that application of the method to case-control data can improve the design of replication studies considerably.     

Quantitative trait locus mapping based on resampling in a vast maize testcross experiment and its relevance to quantitative genetics for complex traits

From simulation studies it is known that the allocation of experimental resources has a crucial effect on power of QTL detection as well as on accuracy and precision of QTL estimates. In this study, we used a very large experimental data set composed of 976 F(5) maize testcross progenies evaluated in 19 environments and cross-validation to assess the effect of sample size (N), number of test environments (E), and significance threshold on the number of detected QTL, the proportion of the genotypic variance explained by them, and the corresponding bias of estimates for grain yield, grain moisture, and plant height. In addition, we used computer simulations to compare the usefulness of two cross-validation schemes for obtaining unbiased estimates of QTL effects. The maximum, validated genotypic variance explained by QTL in this study was 52.3% for grain moisture despite the large number of detected QTL, thus confirming the infinitesimal model of quantitative genetics. In both simulated and experimental data, the effect of sample size on power of QTL detection as well as on accuracy and precision of QTL estimates was large. The number of detected QTL and the proportion of genotypic variance explained by QTL generally increased more with increasing N than with increasing E. The average bias of QTL estimates and its range were reduced by increasing N and E. Cross-validation performed well with respect to yielding asymptotically unbiased estimates of the genotypic variance explained by QTL. On the basis of our findings, recommendations for planning of QTL mapping experiments and allocation of experimental resources are given.     

Macular Pigment Optical Density Measured by Heterochromatic Modulation Photometry

Purpose

To psychophysically determine macular pigment optical density (MPOD) employing the heterochromatic modulation photometry (HMP) paradigm by estimating 460 nm absorption at central and peripheral retinal locations.

Methods

For the HMP measurements, two lights (B: 460 nm and R: 660 nm) were presented in a test field and were modulated in counterphase at medium or high frequencies. The contrasts of the two lights were varied in tandem to determine flicker detection thresholds. Detection thresholds were measured for different R:B modulation ratios. The modulation ratio with minimal sensitivity (maximal threshold) is the point of equiluminance. Measurements were performed in 25 normal subjects (11 male, 14 female; age: 30±11 years, mean ± sd) using an eight channel LED stimulator with Maxwellian view optics. The results were compared with those from two published techniques – one based on heterochromatic flicker photometry (Macular Densitometer) and the other on fundus reflectometry (MPR).

Results

We were able to estimate MPOD with HMP using a modified theoretical model that was fitted to the HMP data. The resultant MPOD_HMP values correlated significantly with the MPOD_MPR values and with the MPOD_HFP values obtained at 0.25° and 0.5° retinal eccentricity.

Conclusions

HMP is a flicker-based method with measurements taken at a constant mean chromaticity and luminance. The data can be well fit by a model that allows all data points to contribute to the photometric equality estimate. Therefore, we think that HMP may be a useful method for MPOD measurements, in basic and clinical vision experiments.     

Neglecting uncertainty behind Allee effect estimation may generate false predictions of population extinction risk

Estimation of extinction thresholds arising from Allee effects (Allee thresholds) and related probabilities of population extinction is notoriously difficult. One way is to analyze adequately parameterized population models. Traditionally, a point estimate is substituted for the Allee effect strength in such models. However, each point estimate entails an underlying uncertainty. We explore how accounting for this uncertainty affects the probability of population extinction, and show that this probability decreases sigmoidally with increasing population density, even in the absence of any stochasticity. Deviations from when only a point estimate of the Allee effect strength is used can be significant, unless stochasticity is added and the stochastic noise intensity is high. Significant deviations from when only a point estimate is used also occur when the Allee threshold and the environmental carrying capacity of the species are close enough one to another. We also show that the impact of the uncertainty in the Allee effect strength estimate increases as the Allee effect strength itself increases and decreases as the species recovery potential increases. This is not a good news, since we would like to preferentially and efficiently manage slowly recovering populations prone to strong Allee effects. Still, there is a way to come up with relatively good Allee threshold estimates. Besides an obvious option of collecting as many data as possible, the impact of the uncertainty can be mitigated by diversifying Allee effect experiments such that we put more emphasis on larger size groups. This is somewhat surprising, given that frequent complaints on the (im)possibility of detecting Allee effects concern difficulties in locating, observing and experimenting on rare populations. Our results extend current theory surrounding Allee effects and have broad ramifications for applied ecology.     

Publication bias in ecology and evolution: an empirical assessment using the 'trim and fill' method

Recent reviews of specific topics, such as the relationship between male attractiveness to females and fluctuating asymmetry or attractiveness and the expression of secondary sexual characters, suggest that publication bias might be a problem in ecology and evolution. In these cases, there is a significant negative correlation between the sample size of published studies and the magnitude or strength of the research findings (formally the ‘effect size’). If all studies that are conducted are equally likely to be published, irrespective of their findings, there should not be a directional relationship between effect size and sample size; only a decrease in the variance in effect size as sample size increases due to a reduction in sampling error. One interpretation of these reports of negative correlations is that studies with small sample sizes and weaker findings (smaller effect sizes) are less likely to be published. If the biological literature is systematically biased this could undermine the attempts of reviewers to summarise actual biology relationships by inflating estimates of average effect sizes. But how common is this problem? And does it really effect the general conclusions of literature reviews? Here, we examine data sets of effect sizes extracted from 40 peer‐reviewed, published meta‐analyses. We estimate how many studies are missing using the newly developed ‘trim and fill’ method. This method uses asymmetry in plots of effect size against sample size (‘funnel plots’) to detect ‘missing’ studies. For random‐effect models of meta‐analysis 38% (15/40) of data sets had a significant number of ‘missing’ studies. After correcting for potential publication bias, 21% (8/38) of weighted mean effects were no longer significantly greater than zero, and 15% (5/34) were no longer statistically robust when we used random‐effects models in a weighted meta‐analysis. The mean correlation between sample size and the magnitude of standardised effect size was also significantly negative (r_s=‐0.20, P < 0‐0001). Individual correlations were significantly negative (P < 0.10) in 35% (14/40) of cases. Publication bias may therefore effect the main conclusions of at least 15–21% of meta‐analyses. We suggest that future literature reviews assess the robustness of their main conclusions by correcting for potential publication bias using the ‘trim and fill’ method.     

Inferring Influenza Infection Attack Rate from Seroprevalence Data

Seroprevalence survey is the most practical method for accurately estimating infection attack rate (IAR) in an epidemic such as influenza. These studies typically entail selecting an arbitrary titer threshold for seropositivity (e.g. microneutralization [MN] 1∶40) and assuming the probability of seropositivity given infection (infection-seropositivity probability, ISP) is 100% or similar to that among clinical cases. We hypothesize that such conventions are not necessarily robust because different thresholds may result in different IAR estimates and serologic responses of clinical cases may not be representative. To illustrate our hypothesis, we used an age-structured transmission model to fully characterize the transmission dynamics and seroprevalence rises of 2009 influenza pandemic A/H1N1 (pdmH1N1) during its first wave in Hong Kong. We estimated that while 99% of pdmH1N1 infections became MN_1∶20 seropositive, only 72%, 62%, 58% and 34% of infections among age 3–12, 13–19, 20–29, 30–59 became MN_1∶40 seropositive, which was much lower than the 90%–100% observed among clinical cases. The fitted model was consistent with prevailing consensus on pdmH1N1 transmission characteristics (e.g. initial reproductive number of 1.28 and mean generation time of 2.4 days which were within the consensus range), hence our ISP estimates were consistent with the transmission dynamics and temporal buildup of population-level immunity. IAR estimates in influenza seroprevalence studies are sensitive to seropositivity thresholds and ISP adjustments which in current practice are mostly chosen based on conventions instead of systematic criteria. Our results thus highlighted the need for reexamining conventional practice to develop standards for analyzing influenza serologic data (e.g. real-time assessment of bias in ISP adjustments by evaluating the consistency of IAR across multiple thresholds and with mixture models), especially in the context of pandemics when robustness and comparability of IAR estimates are most needed for informing situational awareness and risk assessment. The same principles are broadly applicable for seroprevalence studies of other infectious disease outbreaks.     

Minimum required number of specimen records to develop accurate species distribution models

Species distribution models (SDMs) are widely used to predict the occurrence of species. Because SDMs generally use presence‐only data, validation of the predicted distribution and assessing model accuracy is challenging. Model performance depends on both sample size and species’ prevalence, being the fraction of the study area occupied by the species. Here, we present a novel method using simulated species to identify the minimum number of records required to generate accurate SDMs for taxa of different pre‐defined prevalence classes. We quantified model performance as a function of sample size and prevalence and found model performance to increase with increasing sample size under constant prevalence, and to decrease with increasing prevalence under constant sample size. The area under the curve (AUC) is commonly used as a measure of model performance. However, when applied to presence‐only data it is prevalence‐dependent and hence not an accurate performance index. Testing the AUC of an SDM for significant deviation from random performance provides a good alternative. We assessed the minimum number of records required to obtain good model performance for species of different prevalence classes in a virtual study area and in a real African study area. The lower limit depends on the species’ prevalence with absolute minimum sample sizes as low as 3 for narrow‐ranged and 13 for widespread species for our virtual study area which represents an ideal, balanced, orthogonal world. The lower limit of 3, however, is flawed by statistical artefacts related to modelling species with a prevalence below 0.1. In our African study area lower limits are higher, ranging from 14 for narrow‐ranged to 25 for widespread species. We advocate identifying the minimum sample size for any species distribution modelling by applying the novel method presented here, which is applicable to any taxonomic clade or group, study area or climate scenario.     

Spatial variation in sensitivity as a factor in measurements of spatial summation of warmth and cold

Perception of cutaneous heating and cooling depends strongly on stimulus size. Although this dependence has been attributed solely to spatial summation, topographical variations in temperature sensitivity may also play a role. These variations, which differentially affect perception of small stimuli, may have led to overestimation of spatial summation. This possibility was investigated by measuring detection thresholds and perceived intensity for heating and cooling on the volar surface of the forearm using a multiple-thermode stimulus array. By keeping the array in place throughout each testing session we were able to measure threshold sensitivity and suprathreshold responsiveness at eight individual sites and for combinations of these sites having total stimulus areas of 0.64-5.12 cm2. When spatial summation was calculated in the traditional way by averaging the data for all stimuli of each size, the results agreed closely with previous estimates of summation for warmth and cold. When calculations were based instead on the most sensitive test site for each stimulus size, estimates of summation were reduced by about two-thirds. This outcome indicates that the spatial heterogeneity of thermal sensitivity likely contributed to estimates of spatial summation reported in earlier psychophysical studies. A schematic model of cutaneous thermoreception is presented that shows how neural summation and the density of innervation may combine to produce the psychophysical effects of increasing stimulus size (spatial enhancement).     

Threshold effects observed in conformation changes induced by electric fields

Single-stranded polynucleotides are used as model systems for the investigation of conformational changes induced by electric fields. It is demonstrated that the single-strand helix–coil transition in poly(A), poly(dA), and poly(C) can be induced by application of high electric fields. The transition is measured by UV absorbance using polarized light at an angle of 54.8° with respect to the vector of the electric field and by electrodichroism. A linear increase of the absorbance, reflecting the helix-to-coil transition, is observed at increasing field strength. When ions are added to the polymer, electric fields do not induce conformation changes, unless a threshold value of the electric field strength E₀ is exceeded. At field strengths above this threshold, the degree of transition is a linear function of the increase in field strength. The threshold values E₀ show a linear increase with the logarithm of the ion concentration. Bivalent ions cause thresholds at much lower ion concentrations than mo-novalent ions. The shielding efficiency of ions is correlated to the binding affinity of these ions to the polymer. The conformation changes induced by the field and the existence of thresholds can be explained on the basis of dissociation field effects. Similar threshold effects may be expected for other macromolecules as well as for membrane structures and may be important in the regulation of bioelectricity.