The continuous smooth hockey stick: a newly proposed spawner‐recruitment model

Spawner‐recruit relationships are important components of fisheries management. The two most widely used models have been criticized for unsatisfactory fits and biologically unreasonable extrapolations. A simple hockey stick model has been shown to provide more robust predictions, however, this model is not widely used, possibly because the abrupt change from density‐dependence to density‐independence is unrealistic and the piecewise model is difficult to fit. Here I present a continuous two‐parameter model that resembles a smoothed hockey stick and provides parameter estimates similar to the piecewise hockey stick. The new model is easily parameterized with regular curve‐fitting routines.     

Relationship Between Fecal Pellet Counts and Snowshoe Hare Density in Western Wyoming

ABSTRACT Snowshoe hares (Lepus americanus) are an important prey species for Canada lynx (Lynx canadensis) and are considered critical for lynx population persistence. Determination of snowshoe hare distribution and abundance is needed by land management agencies for lynx conservation. An accepted approach for estimating snowshoe hare abundance is the use of fecal-pellet plot counts. Locally derived regression equations are preferred for accurate calibration of pellet counts to snowshoe hare density due to local differences in pellet deposition and decomposition. We used linear regression to examine correlations between snowshoe hare density, as determined by mark–recapture estimates, and pellet plot counts on both uncleared plots and annually cleared plots on the Bridger-Teton National Forest, western Wyoming, USA. We found significant correlations between snowshoe hare density estimates and fecal pellet counts for both uncleared and annually cleared pellet counts; however, the relationship was stronger (higher r) when using pellet counts from annually cleared plots. In addition, we found that adjusting the buffer size by omitting hard habitat edges (not used by hares) around trapping grids improved correlations between snowshoe hare density and fecal pellet counts for both uncleared plots and annually cleared plots. Though precision is sacrificed when using uncleared plots, they may be useful as a coarse index of habitat use by snowshoe hares. Our derived regression equations may be useful to identify important foraging habitat for Canada lynx in western Wyoming. Land managers responsible for conserving snowshoe hare habitat in western Wyoming may use these equations to monitor changes in hare populations among habitats and during prescribed management actions.     

Recruitment rates in forest plots: Gf estimates using growth rates and size distributions

1 In censuses of tree populations in permanent plots, short census intervals and small population size lead to uncertainty in the observed recruitment rate of a minimum size. Increasing the census interval, however, underestimates the rate because of unrecorded 'recruit and die' events.
2 We propose a new Gf procedure for estimation of recruitment rates. Recruitment rate per area is obtained by multiplication of the density in the smallest size class (f) and the average size growth rate in that class (G) divided by the width of the class. This procedure is valid when the size distribution of the population examined is continuous with size.
3 When tree size structure is negative‐exponentially distributed, as is often the case in natural rain forest populations, the Gf estimate of the recruitment rate for a given size class was least biased close to the midpoint size of this class.
4 Gf estimates agreed well with census estimates of recruitment rate from permanent plots in rain forests. A tendency for Gf estimates to be larger than census estimates disappeared when census estimates were corrected for mortality after recruitment.
5 The effects of plot size, census interval and variation in growth rate on estimates of recruitment rate were simulated using model populations. Small plot size caused substantially more among‐plot deviation for the census count of recruitment events than for the Gf estimate. The census recruitment rate also showed larger variation among plots for shorter intervals than the Gf estimate, which was independent of census interval. The Gf estimates were therefore more accurate than census counts in many situations. More than several tens of trees were needed in a size class to allow a reliable Gf estimates.     

Probability density function of successive intervals of a nonhomogeneous Poisson process under low-frequency conditions

The probability density function (pdf) of successive intervals of a truncated, nonhomogeneous Poisson process was examined under both low- and high-frequency conditions. In general, if the instantaneous rate contains a single frequency component, then the phase of this component is not represented in the interval pdf. However, if the instantaneous rate contains harmonically related components, with fundamental frequency of the same order as, or less than, the mean rate, then the phases of these components do appear in the interval pdf. Correction formulae for estimating synchronization indices under low-frequency conditions are derived.     

An evaluation of the sampling variation when estimating the population of Verticillium dahliae in field soil

This paper describes a study designed to find a reliable sampling procedure for estimating the population of Verticillium duhliue in field plots that would not be too demanding in terms of the time required to assay soil samples. In the soil under study, the amount of time needed to obtain reliable estimates of the inoculum density was reduced by taking the larger plot sizes in the range considered, generally taking more plots with fewer samples per plot, and mixing the samples within a plot before redividing for assaying.     

Local Renyi entropic profiles of DNA sequences

Background  

In a recent report the authors presented a new measure of continuous entropy for DNA sequences, which allows the estimation of their randomness level. The definition therein explored was based on the Rényi entropy of probability density estimation (pdf) using the Parzen's window method and applied to Chaos Game Representation/Universal Sequence Maps (CGR/USM). Subsequent work proposed a fractal pdf kernel as a more exact solution for the iterated map representation. This report extends the concepts of continuous entropy by defining DNA sequence entropic profiles using the new pdf estimations to refine the density estimation of motifs.     

Genetic sampling for estimating density of common species

Understanding population dynamics requires reliable estimates of population density, yet this basic information is often surprisingly difficult to obtain. With rare or difficult‐to‐capture species, genetic surveys from noninvasive collection of hair or scat has proved cost‐efficient for estimating densities. Here, we explored whether noninvasive genetic sampling (NGS) also offers promise for sampling a relatively common species, the snowshoe hare (Lepus americanus Erxleben, 1777), in comparison with traditional live trapping. We optimized a protocol for single‐session NGS sampling of hares. We compared spatial capture–recapture population estimates from live trapping to estimates derived from NGS, and assessed NGS costs. NGS provided population estimates similar to those derived from live trapping, but a higher density of sampling plots was required for NGS. The optimal NGS protocol for our study entailed deploying 160 sampling plots for 4 days and genotyping one pellet per plot. NGS laboratory costs ranged from approximately $670 to $3000 USD per field site. While live trapping does not incur laboratory costs, its field costs can be considerably higher than for NGS, especially when study sites are difficult to access. We conclude that NGS can work for common species, but that it will require field and laboratory pilot testing to develop cost‐effective sampling protocols.     

Density influences accuracy of model‐based estimates for a forest songbird

Golden‐cheeked Warblers (Setophaga chrysoparia) are endangered songbirds that breed exclusively in the Ashe juniper (Juniperus ashei) and oak (Quercus spp.) woodlands of central Texas. Despite being the focus of numerous studies, we still know little about the size of the range‐wide breeding population and how density varies across the spectrum of juniper co‐dominated woodlands. Models that have been tested and shown to be accurate are needed to help develop management and conservation guidelines. We evaluated the accuracy and bias of density estimates from binomial mixture models, the dependent double‐observer method, and distance sampling by comparing them to actual densities determined by intensive territory monitoring on plots in the Balcones Canyonlands Preserve, Austin, Texas. We found that the binomial mixture models consistently overestimated density by 1.1–3.2 times (actual density = 0.07–0.46 males/ha), and the other two models overestimated by 1.1–29.8 times at low density and underestimated by 0.5–0.9 times at high density plots (actual density = 0.01–0.46 males/ha). The magnitude of error for all models was greatest at sites with few or no birds (<0.15 males/ha), with model performance improving as actual density increased. These non‐linear relationships indicate a lack of sensitivity with respect to true changes in density. Until systematic evaluation demonstrates that models such as those we tested provide accurate and unbiased density estimates for a given species over space and time, we recommend additional field tests to validate model‐based estimates. Continued model validation and refinement of point‐count methods are needed until accurate estimates are obtained across the density spectrum for Golden‐cheeked Warblers and other songbird species.     

Statistical properties of ion channel records. Part II: estimation from the macroscopic current

Macroscopic ion channel current is the summation of the stochastic records of individual channel currents and therefore relates to their statistical properties. As a consequence of this relationship, it may be possible to derive certain statistical properties of single channel records or even generate some estimates of the records themselves from the macroscopic current when the direct measurement of single channel currents is not applicable. We present a procedure for generating the single channel records of an ion channel from its macroscopic current when the stochastic process of channel gating has the following two properties: (I) the open duration is independent of the time of opening event and has a single exponential probability density function (pdf), (II) all the channels have the same probability to open at time t. The application of this procedure is considered for cases where direct measurement of single channel records is difficult or impossible. First, the probability density function (pdf) of opening events, a statistical property of single channel records, is derived from the normalized macroscopic current and mean channel open duration. Second, it is shown that under the conditions (I) and (II), a non-stationary Markov model can represent the stochastic process of channel gating. Third, the non-stationary Markov model is calibrated using the results of the first step. The non-stationary formulation increases the model ability to generate a variety of different single channel records compared to common stationary Markov models. The model is then used to generate single channel records and to obtain other statistical properties of the records. Experimental single channel records of inactivating BK potassium channels are used to evaluate how accurately this procedure reconstructs measured single channel sweeps.     

CONSTANCY OF POPULATION PARAMETERS FOR LIFE-HISTORY AND FLORAL TRAITS IN RAPHANUS SATIVUS L. II. EFFECTS OF PLANTING DENSITY ON PHENOTYPE AND HERITABILITY ESTIMATES

To determine the effect of growing conditions on population parameters in wild radish, (Raphanus sativus L.: Brassicaceae), we replicated maternal and paternal half-sib families of seed across three planting densities in an experimental garden. A nested breeding design performed in the greenhouse produced 1,800 F₁ seeds sown in the garden. We recorded survivorship, measured phenotypic correlations among and estimated narrow-sense and broad-sense heritabilities (h²) of: days to germination, days to flowering, petal area, ovule number/flower, pollen production/flower, and modal pollen grain volume. Survivorship declined with increasing density, but the relative abundances of surviving families did not differ significantly among densities. Seeds in high-density plots germinated significantly faster than seeds sown in medium- or low-density plots, but they flowered significantly later. Plants in high-density plots had fewer ovules per flower than those in the other treatments. Petal area and pollen characters did not differ significantly among densities. Densities differed with respect to the number and sign of significant phenotypic correlations. Analyses of variance were conducted to detect additive genetic variance (V_a) of each trait in each density. At low density, there were significant paternal effects on flowering time and modal pollen grain volume; in medium-density plots, germination time, flowering time and ovule number exhibited significant paternal effects; in high-density plots, only pollen grain volume differed among paternal sibships. The ability to detect maternal effects on progeny phenotype also depended on density. Narrow-sense h² estimates differed markedly among density treatments for germination time, flowering time, ovule number and pollen grain volume. Maternal, paternal and error variance components were estimated for each trait and density to examine the sources of variation in narrow-sense h² across densities. Variance components did not change consistently across densities; each trait behaved differently. To provide qualitative estimates of genetic correlations between characters, correlation coefficients were estimated using paternal family means; these correlations also differed among densities. These results demonstrate that: a) planting density influences the magnitude of maternal and paternal effects on progeny phenotype, and of h² estimates, b) traits differ with respect to the density in which heritability is greatest, c) density affects the variance components that comprise heritability, but each trait behaves differently, and d) the response to selection on any target trait should result in different correlated responses of other traits, depending on density.     

Methods of Measuring the Proportions of Plant-Species Present in Forest and Their Effect on Estimates of Bird Preferences for Plant-Species

Stem density, basal area, vegetation cover and vegetation surface area were compared as measures of the proportions of plant species present in North Okarito Forest, South Westland, for use in determining bird preferences for plant species. In general, stem density estimates of the proportions of canopy species were about 10 times lower than basal area estimates. The converse was true for estimates of the proportions of sub- canopy and understorey species. The proportions estimated from vegetation cover and vegetation surface area were similar for most species, and were intermediate between the proportions estimated from stem density and basal area. However, in the upper forest tiers, vegetation cover gave lower estimates for the proportions of canopy species and higher estimates for the proportions of sub-canopy species than given by vegetation surface area. These differences affect calculation of bird preferences for plant species. We recommend vegetation surface area as a measure of the proportional availability of plant species to birds because it is appropriate to most birds in New Zealand forests, is likely to be more accurate than visual estimates of vegetation cover, and can be measured on the same plots separately for trunks, branches, foliage, and fruit.     

Alternate methods of representing single-channel data.

Clustering of dwell times in data from single-channel recordings, which is in excess of the value predicted from the probability density function (pdf) alone, provides restrictions on modeling schemes. Two methods, (a) the probability density function of the running median for groups of any size of sequential dwell times, and (b) the distribution of cumulative probabilities associated with dwell times separated by any lag, or the second cumulative probability distribution, are proposed as alternative representations of single-channel data; these methods are suitable for the detection of such clusters or modes. Simulation of three models with and without modes is done to test the efficacy of these methods. It is found that they often yield a better estimate of moding parameters than the methods of running mean pdf and autocorrelation.     

Estimating index of population trend by re-sampling techniques (jackknife and bootstrap) and its application to the life table study of rice leaf roller, Cnaphalocrocis medinalis (Lepidoptera: Pyralidae)

Taking a published natural population life table of rice leaf roller, Cnaphalocrocis medinalis (Lepidoptera: Pyralidae), as an example, we estimated the population trend index, I, via re‐sampling methods (jackknife and bootstrap), determined its statistical properties and illustrated the application of these methods in determining the control effectiveness of bio‐agents and chemical insecticides. Depending on the simulation outputs, the smoothed distribution pattern of the estimates of I by delete‐1 jackknife is visually distinguishable from the normal density, but the smoothed pattern produced by delete‐d jackknife, and logarithm‐transformed smoothed patterns produced by both empirical and parametric bootstraps, matched well the corresponding normal density. Thus, the estimates of I produced by delete‐1 jackknife were not used to determine the suppressive effect of wasps and insecticides. The 95% percent confidence intervals or the narrowest 95 percentiles and Z‐test criterion were employed to compare the effectiveness of Trichogramma japonicum Ashmead and insecticides (powder, 1.5% mevinphos + 3% alpha‐hexachloro cyclohexane) against the rice leaf roller based on the estimates of I produced by delete‐d jackknife and bootstrap techniques. At α= 0.05 level, there were statistical differences between wasp treatment and control, and between wasp and insecticide treatments, if the normality is ensured, or by the narrowest 95 percentiles. However, there is still no difference between insecticide treatment and control. By Z‐test criterion, wasp treatment is better than control and insecticide treatment with P‐value < 0.01. Insecticide treatment is similar to control with P‐value > 0.2 indicating that 95% confidence intervals procedure is more conservative. Although similar conclusions may be drawn by re‐sampling techniques, such as the delta method, about the suppressive effect of trichogramma and insecticides, the normality of the estimates can be checked and guaranteed, and the correlation among sequential life stages of rice leaf roller is also considered in the estimation. Judged by the P‐values from Z‐test, the delta method is more conservative.     

Comparison of pollen gene flow among four European beech (Fagus sylvatica L.) populations characterized by different management regimes

The study of the dispersal capability of a species can provide essential information for the management and conservation of its genetic variability. Comparison of gene flow rates among populations characterized by different management and evolutionary histories allows one to decipher the role of factors such as isolation and tree density on gene movements. We used two paternity analysis approaches and different strategies to handle the possible presence of genotyping errors to obtain robust estimates of pollen flow in four European beech (Fagus sylvatica L.) populations from Austria and France. In each country one of the two plots is located in an unmanaged forest; the other plots are managed with a shelterwood system and inside a colonization area (in Austria and France, respectively). The two paternity analysis approaches provided almost identical estimates of gene flow. In general, we found high pollen immigration (~75% of pollen from outside), with the exception of the plot from a highly isolated forest remnant (~50%). In the two unmanaged plots, the average within-population pollen dispersal distances (from 80 to 184 m) were higher than previously estimated for beech. From the comparison between the Austrian managed and unmanaged plots, that are only 500 m apart, we found no evidence that either gene flow or reproductive success distributions were significantly altered by forest management. The investigated phenotypic traits (crown area, height, diameter and flowering phenology) were not significantly related with male reproductive success. Shelterwood seems to have an effect on the distribution of within-population pollen dispersal distances. In the managed plot, pollen dispersal distances were shorter, possibly because adult tree density is three-fold (163 versus 57 trees per hectare) with respect to the unmanaged one.     

Data transformations for improved display and fitting of single-channel dwell time histograms.

A.L. Blatz and K.L. Magleby (1986a. J. Physiol. [Lond.]. 378:141-174) have demonstrated the usefulness of plotting histograms with a logarithmic time axis to display the distributions of dwell times from recordings of single ionic channels. We derive here the probability density function (pdf) corresponding to logarithmically binned histograms. Plotted on a logarithmic time scale the pdf is a peaked function with an invariant width; this and other properties of the pdf, coupled with a variance-stabilizing (square root) transformation for the ordinate, greatly simplify the interpretation and manual fitting of distributions containing multiple exponential components. We have also examined the statistical errors in estimation, by the maximum-likelihood method, of kinetic parameters from logarithmically binned data. Using binned data greatly accelerates the fitting procedure and introduces significant errors only for bins spaced more widely than 8-16 per decade.     

Computing a population budget from sequentially sacrificed,replicated cultures

When a population budget must be obtained from censuses based on replicated, sacrificed cultures, it is difficult to obtain estimates of transition probabilities and of the errors of such estimates, because there is no logical basis for pairing successive census counts. In a study of this nature estimating a population budget of immature stages of the housefly, the problem was solved by a randomization treatment of the original census results obtained at two densities. One hundred randomly generated census matrices over all census times for each density were smoothed to remove the effects of sampling error and a population budget constructed according to defined rules. Transition probabilities computed from the population budget were plotted on triangular coordinate paper and mean probabilities, 95% confidence regions for these means, and 95% equal frequency ellipses computed. All computations and the graphing of the results were carried out on a digital computer. The computer program, available from the authors, is written in FORTRAN IV and could be easily modified for similar studies.     

PROBLEMS WITH SAMPLING DESERT TORTOISES: A SIMULATION ANALYSIS BASED ON FIELD DATA

Abstract: The desert tortoise (Gopherus agassizii) was listed as a U.S. threatened species in 1990 based largely on population declines inferred from mark-recapture surveys of 2.59-km² (1-mi²) plots. Since then, several census methods have been proposed and tested, but all methods still pose logistical or statistical difficulties. We conducted computer simulations using actual tortoise location data from 2 1-mi² plot surveys in southern California, USA, to identify strengths and weaknesses of current sampling strategies. We considered tortoise population estimates based on these plots as “truth” and then tested various sampling methods based on sampling smaller plots or transect lines passing through the mile squares. Data were analyzed using Schnabel's mark-recapture estimate and program CAPTURE. Experimental subsampling with replacement of the 1-mi² data using 1-km² and 0.25-km² plot boundaries produced data sets of smaller plot sizes, which we compared to estimates from the 1-mi² plots. We also tested distance sampling by saturating a 1-mi² site with computer simulated transect lines, once again evaluating bias in density estimates. Subsampling estimates from 1-km² plots did not differ significantly from the estimates derived at 1-mi². The 0.25-km² subsamples significantly overestimated population sizes, chiefly because too few recaptures were made. Distance sampling simulations were biased 80% of the time and had high coefficient of variation to density ratios. Furthermore, a prospective power analysis suggested limited ability to detect population declines as high as 50%. We concluded that poor performance and bias of both sampling procedures was driven by insufficient sample size, suggesting that all efforts must be directed to increasing numbers found in order to produce reliable results. Our results suggest that present methods may not be capable of accurately estimating desert tortoise populations.     

Reptation theory of ion channel gating.

Reptation theory is a highly successful approach for describing polymer dynamics in entangled systems. In turn, this molecular process is the basis of viscoelasticity. We apply a modified version of reptation dynamics to develop an actual physical model of ion channel gating. We show that at times longer than microseconds these dynamics predict an alpha-helix-screw motion for the amphipathic protein segment that partially lines the channel pore. Such motion has been implicated in several molecular mechanics studies of both voltage-gated and transmitter-gated channels. The experimental probability density function (pdf) for this process follows t-3/2 which has been observed in several experimental systems. Reptation theory predicts that channel gating will occur on the millisecond time scale and this is consistent with experimental results from single-channel recording. We examine the consequences of reptation over random barriers and we show that, to first order, the pdf remains unchanged. In the case of a charged helix undergoing reptation in the presence of a transmembrane potential we show that the tail of the pdf will be exponential. We provide a list of practical experimental predictions to test the validity of this physical theory.     

Sequential interval histogram analysis of non-stationary neuronal spike trains

The spike interval histogram, a commonly used tool for the analysis of neuronal spike trains, is evaluated as a statistical estimator of the probability density function (pdf) ofinterspike intervals. Using a mean square error criterion, it is concluded that a Parzen convolution estimate of the pdf is superior to the conventional histogram procedure. The Parzen estimate using a Gaussian weighting function reduces the number of intervals required to achieve a given error by a factor of 5–10. The Parzen estimation procedure has been implemented in the sequential interval histogram (SQIH) procedure for analysis of non-stationary spike trains. Segments of the spike train are defined using a moving window and the pdf for each segment is estimated sequentially. The procedure which we have found most practical is interactive with the user and utlizes the theoretical results of the error analysis as guidelines for the evolution of an estimation strategy. The SQIH procedure appears useful both as a criterion for stationarity and as a means to characterize non-stationary activity.Portions of this work were presented at the Symposium on Computer Technology in Neuroscience Research, West Virginia University Medical Center, Morgantown, West Virginia, USA, April, 1975.     

A simple alternative to line transects of nests for estimating orangutan densities

We conducted a validation of the line transect technique to estimate densities of orangutan (Pongo pygmaeus) nests in a Bornean swamp forest, and compared these results with density estimates based on nest counts in plots and on female home ranges. First, we examined the accuracy of the line transect method. We found that the densities based on a pass in both directions of two experienced pairs of observers was 27% below a combined sample based on transect walks by eight pairs of observers, suggesting that regular line-transect densities may seriously underestimate true densities. Second, we compared these results with those obtained by nest counts in 0.2-ha plots. This method produced an estimated 15.24 nests/ha, as compared to 10.0 and 10.9, respectively, by two experienced pairs of observers who walked a line transect in both directions. Third, we estimated orangutan densities based on female home range size and overlap and the proportion of females in the population, which produced a density of 4.25–4.5 individuals/km² . Converting nest densities into orangutan densities, using locally estimated parameters for nest production rate and proportion of nest builders in the population, we found that density estimates based on the line transect results of the most experienced pairs on a double pass were 2.82 and 3.08 orangutans/km², based on the combined line transect data are 4.04, and based on plot counts are 4.30. In this swamp forest, plot counts therefore give more accurate estimates than do line transects. We recommend that this new method be evaluated in other forest types as well.