Estimation of the density of a clustered point pattern using a distance method

Distance-based methods use point-to-point distances or random-location-to-point distances in a cloud of points to estimate characteristics of the point pattern. One such characteristics is the density of points. The difficulty with distance-based density estimators is that their distribution depends on the spatial pattern of points. In particular, the distribution of distances is untractable for usual clustered patterns, that are often observed in natural systems. Here, we propose a density estimator for clustered patterns, based on the random-location-to-pth-point distance X _p . An approximate expression for the distribution function, F _p , of X _p was obtained by identifying the first two moments of the count of individuals in disks for a given point process with the first two moments of a negative binomial distribution. The approximate expression of F _p was then used to derive a maximum-likelihood estimator of the intensity of the point process. The quality of the approximation of F _p was assessed for homogeneous Poisson processes (for which the expression of F _p is exact) and for Matérn processes. The intensity estimator based on Matérn processes was then used to estimate tree density in a tree savanna in Mali, and it compared favorably with six robust estimators found in the literature.     

Use of Coarse‐Resolution Models of Species’ Distributions to Guide Local Conservation Inferences

Abstract: Distribution models are used increasingly for species conservation assessments over extensive areas, but the spatial resolution of the modeled data and, consequently, of the predictions generated directly from these models are usually too coarse for local conservation applications. Comprehensive distribution data at finer spatial resolution, however, require a level of sampling that is impractical for most species and regions. Models can be downscaled to predict distribution at finer resolutions, but this increases uncertainty because the predictive ability of models is not necessarily consistent beyond their original scale. We analyzed the performance of downscaled, previously published models of environmental favorability (a generalized linear modeling technique) for a restricted endemic insectivore, the Iberian desman (Galemys pyrenaicus), and a more widespread carnivore, the Eurasian otter (Lutra lutra), in the Iberian Peninsula. The models, built from presence–absence data at 10 × 10 km resolution, were extrapolated to a resolution 100 times finer (1 × 1 km). We compared downscaled predictions of environmental quality for the two species with published data on local observations and on important conservation sites proposed by experts. Predictions were significantly related to observed presence or absence of species and to expert selection of sampling sites and important conservation sites. Our results suggest the potential usefulness of downscaled projections of environmental quality as a proxy for expensive and time‐consuming field studies when the field studies are not feasible. This method may be valid for other similar species if coarse‐resolution distribution data are available to define high‐quality areas at a scale that is practical for the application of concrete conservation measures.     

Dynamic growth model for Scots pine (Pinus sylvestris L.) plantations in Galicia (north-western Spain)

In this study we developed a dynamic growth model for Scots pine (Pinus sylvestris L.) plantations in Galicia (north-western Spain). The data used to develop the model were obtained from a network of permanent plots, of between 10 and 55-year-old, which the Unidade de Xestión Forestal Sostible (Sustainable Forest Management Unit) of the University of Santiago de Compostela has set up in pure plantations of this species of pine in its area of distribution in Galicia. In this model, the initial stand conditions at any point in time are defined by three state variables (number of trees per hectare, stand basal area and dominant height), and are used to estimate stand volume, classified by commercial classes, for a given projection age. The model uses three transition functions expressed as algebraic difference equations of the three corresponding state variables used to project the stand state at any point in time. In addition, the model incorporates a function for predicting initial stand basal area, which can be used to establish the starting point for the simulation. This alternative should only be used when the stand is not yet established or when no inventory data are available. Once the state variables are known for a specific moment, a distribution function is used to estimate the number of trees in each diameter class, by recovering the parameters of the Weibull function, using the moments of first and second order of the distribution (arithmetic mean diameter and variance, respectively). By using a generalized height–diameter function to estimate the height of the average tree in each diameter class, combined with a taper function that uses the above predicted diameter and height, it is then possible to estimate total or merchantable stand volume.     

Simulating correlated count data

In this study we compare two techniques for simulating count-valued random n-vectors Y with specified mean and correlation structure. The first technique is to use a lognormal-Poisson hierarchy (L-P method). A vector of correlated normals Z is generated and transformed to a vector of lognormals X. Then, Y is generated as conditionally independent Poissons with means X _i . The L-P method is simple, fast, and familiar to many researchers. However, the method requires each Y _i to be overdispersed (i.e., σ² > μ), and only low correlations are possible with this method when the variables have small means. We develop a second technique to generate the elements of Y as overlapping sums (OS) of independent X _j ’s (OS method). For example, suppose X, X ₁, and X ₂ are independent. If Y ₁ = X + X ₁ and Y ₂ = X + X ₂, then Y ₁ and Y ₂ are correlated because they share the common component X. A generalized version of the OS method for simulating n-vectors of two-parameter count-valued distributions is presented. The OS method is shown to address some of the shortcomings of the L-P method. In particular, underdispersed random variables can be simulated, and high correlations are feasible even when the means are small. However, negative correlations cannot be simulated with the OS method, and when n > 3, the OS method is more complicated to implement than the L-P method.     

Problems of the gonad index and what can be done: analysis of the purple sea urchin <Emphasis Type="Italic">Strongylocentrotus purpuratus</Emphasis>

The gonad index, GI, is widely used as a measure of changes in reproductive state. There are, however, problems with its use because it is based on the implicit assumption of an isometric relationship between gonad size and some measure of total size. If, for example, gonad weight and total weight are used, the exponent for an allometric relationship usually is ignored and hence assumed to be 1.0. It is further assumed that this exponent is fixed for all states of the reproductive cycle and that gonads begin to develop at size = 0. Data for the purple sea urchin Strongylocentrotus purpuratus at Gregory Point, Oregon, USA, gathered over a period of 31 months showed that these assumptions cannot be supported. The relationship is better modeled with a function that (1) takes into account size of initial gonad production and (2) allows allometric exponents that vary with site or season. Thus, a better approach is to use a wide range of sizes to estimate size when gonads begin to develop and then, with this correction, ANCOVA to test for differences of gonad size among samples. Gonad changes at Gregory Point were estimated using fixed sizes of 5 cm diameter and 60 g total weight. Publishing means for X and Y, the standard error of the estimate, R ², and slope for each regression are shown to be sufficient to compare our results with results across studies.     

Semi-parametric Bayesian density estimation using ranked set sample in the presence of ranking error

In this paper, we propose a Bayesian method to estimate the underlying density function of a study variable Y using a ranked set sample in which an auxiliary variable X is used to rank the sampling units. The amount of association between X and Y is not known, resulting in an unknown degree of ranking error. We assume that (X, Y) follows a Morgenstern family of distributions. The study variable Y is assumed to have a parametric distribution, with the distribution of the parameters having a Dirichlet process prior. A Markov chain Monte Carlo procedure is developed to obtain a Bayesian estimator of the desired density function as well as of the ranking error. A simulation study is used to evaluate the performance of the proposed method. An example from forestry is used to illustrate a real-life application of the proposed methodology.     

Is avian humoral immunocompetence suppressed by testosterone?

A key issue in sexual selection theory is how a correlation between male secondary sexual characters and male genetic quality can be maintained. The immunocompetence-handicap hypothesis proposes that testosterone-dependent male characters remain honest signals because of the immunosuppressive effect of elevated steroid hormone levels. The hypothesis requires that physiological levels of testosterone depress immune system function. We quantified testosterone titers and humoral immunocompetence of captive male and female red-winged blackbirds (Agelaius phoeniceus) at three points in the annual cycle (autumn, prebreeding, and breeding). We also conducted an implant experiment on the males to assess the effects of prolonged, above-normal testosterone titers on humoral immune responses. Humoral immunocompetence was measured as secondary antibody production to a non-pathogenic protein antigen, keyhole limpet hemocyanin, using an enzyme-linked immunosorbent assay we developed for A. phoeniceus. Secondary antibody responses of individuals were highly repeatable between sampling periods. Neither physiological nor above-normal levels of plasma testosterone suppressed secondary antibody production. In paired tests of the same individuals between prebreeding and breeding, and between breeding and implant, plasma testosterone increased significantly but secondary antibody responses were unaffected. We are confident in these results because with 80% power, an 11–14% difference in antibody titers would have been detected. There was no relationship between plasma testosterone levels and humoral immunocompetence in free-ranging males tested at the peak of breeding. These results cast doubt on a key assumption of the immunocompetence-handicap hypothesis. Received: 13 April 1998 / Accepted after revision: 7 October 1998     

Complex courtship in a bimodal grasshopper hybrid zone

Grasshoppers of the Chorthippus albomarginatus-group, which is outstanding with respect to its complex courtship song, were studied at fifteen localities in the Ukraine and Moldova. The analysis of the courtship songs revealed two species: C. albomarginatus in north-eastern Ukraine and Chorthippus oschei in the south-western Ukraine and Moldova. In a belt about 200 km wide, not only were one or the other pure species found, but also males with intermediate song characters. C. albomarginatus and C. oschei were hybridised in the laboratory, and F1 hybrid males as well as F2 hybrid males produced intermediate song patterns, quite similar to those recorded in the field. We defined a "hybrid song score" for intermediate songs. The score showed a bimodal distribution with most songs resembling one or other parental type, but with only a few intermediates. At several localities, where hybrids with songs similar to one of the parental species dominated, some individual males sang more similarly to the other species. In one locality, two hybrid populations only 3 km apart had different parental types. Hybrid songs can contain novel elements, even more complex than the parental ones, which may offer a new starting point for sexual selection. We suggest that genetic introgression occurs between the two sibling species C. albomarginatus and C. oschei within a wide hybrid zone stretching over a distance of several hundred kilometres, but with a patchy spatial distribution. Electronic Supplementary Material Supplementary material is available for this article if you access the article at . A link in the frame on the left on that page takes you directly to the supplementary material. Communicated by D. Gwynne     

Correlational evidence of a sexually-selected handicap

Handicap models of sexual selection predict that ornaments must be costly to produce and/or to wear and maintain; only then can they evolve as reliable signals of genetic quality. We investigated in the laboratory one potential cost of possessing ornaments, using the viviparous fish Girardinichthys multiradiatus and its natural predator, the snake Thamnophis melanogaster. We found that female G. multiradiatus show preferences for males with larger fins, as measured from body correlates. Males with a morphology attractive to females, however, were more likely to be captured by snakes than were other males (Fig. 5). Greater vulnerability to snakes cannot be explained as a result of snake visual preferences, because snakes responded similarly to males and females (Fig. 6). Finally, males, particularly dominant ones, were more likely to inspect foraging snakes than were females (Fig. 7). We conclude that male Girardinichthys multiradiatus experience a sexually-selected handicap due to reduced mobility resulting from having enlarged fins.     

Tardy females,impatient males: protandry and divergent selection on arrival date in the two sexes of the barn swallow

Protandry reflects the earlier arrival of males than females to the site of reproduction. Such protandry is hypothesised to arise from sex differences in costs and benefits of early arrival. I investigated temporal patterns of arrival date of male and female barn swallows Hirundo rustica and temporal patterns of selection to test the hypothesis that sex differences in selection account for sex differences in arrival date. Mean arrival date of male barn swallows but not of females advanced during the last 33 years, giving rise to an increasing sex difference in arrival date. Early arrival was favoured by increasingly better survival in males, while females showed an opposite pattern that did not reach significance, although the effect differed between sexes. Early arrival increased fecundity in both sexes equally.The sex difference in viability selection in relation to arrival date changed from positive to negative as the degree of protandry increased in recent years, although there was no similar significant relationship for fecundity selection. Furthermore, sex differences in viability selection in a given year affected the degree of protandry in the following year through differential survival of certain phenotypes over others. Finally, temporal changes in sex difference in viability selection and protandry were related to an increase in the interval between first and second clutches, as the duration of the breeding season increased because of climatic amelioration. These findings suggest that arrival date is under divergent selection in the two sexes, providing a mechanism for the evolution of protandry.     

Modeling resource selection using polytomous logistic regression and kernel density estimates

Wildlife resource selection studies typically compare used to available resources; selection or avoidance occurs when use is disproportionately greater or less than availability. Comparing used to available resources is problematic because results are often greatly influenced by what is considered available to the animal. Moreover, placing relocation points within resource units is often difficult due to radiotelemetry and mapping errors. Given these problems, we suggest that an animal’s resource use be summarized at the scale of the home range (i.e., the spatial distribution of all point locations of an animal) rather than by individual points that are considered used or available. To account for differences in use-intensity throughout an animal’s home range, we model resource selection using kernel density estimates and polytomous logistic regression. We present a case study of elk (Cervus elaphus) resource selection in South Dakota to illustrate the procedure. There are several advantages of our proposed approach. First, resource availability goes undefined by the investigator, which is a difficult and often arbitrary decision. Instead, the technique compares the intensity of animal use throughout the home range. This technique also avoids problems with classifying locations rigidly as used or unused. Second, location coordinates do not need to be placed within mapped resource units, which is problematic given mapping and telemetry error. Finally, resource use is considered at an appropriate scale for management because most wildlife resource decisions are made at the level of the patch. Despite the advantages of this use-intensity procedure, future research should address spatial autocorrelation and develop spatial models for ordered categorical variables.     

Sperm competition or sperm selection: no evidence for female influence over paternity in yellow dung flies Scatophaga stercoraria

Recent studies of non-random paternity have suggested that sperm selection by females may influence male fertilization success. Here we argue that the problems originally encountered in partitioning variation in non-random mating between male competition and female choice are even more pertinent to interpreting patterns of non-random paternity because of intense sperm competition between males. We describe an experiment with the yellow dung fly, Scatophaga stercoraria, designed to partition variance in the proportion of offspring sired by the second male, P ₂, between males and females, and to control for sperm competition. Large males were shown to have a higher P ₂ than small males but P ₂ was independent of the size of the female’s first mate. This result might suggest an absolute female preference for large males via sperm selection. However, large males have a higher constant rate of sperm transfer and displacement. After controlling for this effect of sperm competition, large males did not achieve higher paternity than small males. We argue that a knowledge of the mechanism of sperm competition is essential so that male effects can be controlled before conclusions are made regarding the influence of sperm selection by females in generating non-random paternity. Received: 4 April 1995 / Accepted after revision: 17 October 1995     

Maintenance of variance in sperm transfer rates in a scorpionfly: food availability,genetic basis,and heritability

Variation in traits closely related to fitness is expected to be low. This is because these traits are under directional selection and the best genotype should prevail. However, there have been a number of studies demonstrating the existence of considerable variance in sexually selected traits, which is generally known as the lek paradox. Accordingly, earlier studies found substantial variation in sperm transfer rates in Panorpa vulgaris. Aiming at finding the mechanism that maintains this variation, we analyzed the condition dependence and the narrow sense heritability of sperm transfer rates. Food deprivation in the larval/adult phase caused a decrease in the males’ capability of saliva secretion resulting in shorter copulations and a reduced number of transferred sperm. There was a positive correlation between mean sperm transfer rates and mean body mass. Additionally, intermale variation in sperm transfer rates decreased with increasing food availability. Hence, we suggest that sperm transfer rates in P. vulgaris are influenced by adult feeding history. Heritability analyses of sperm transfer rates did not provide significant results, which is consistent with the general hypothesis that additive genetic variance in traits closely related to fitness is small. Since a trait’s potential to respond to selection is proportional to the amount of contained additive genetic variance, the ascertained small heritability provides a satisfying explanation for the maintenance of substantial variation in sperm transfer rates.     

Bayesian areal wombling via adjacency modeling

Recently, public health professionals and other geostatistical researchers have shown increasing interest in boundary analysis, the detection or testing of zones or boundaries that reveal sharp changes in the values of spatially oriented variables. For areal data (i.e., data which consist only of sums or averages over geopolitical regions), Lu and Carlin (Geogr Anal 37: 265–285, 2005) suggested a fully model-based framework for areal wombling using Bayesian hierarchical models with posterior summaries computed using Markov chain Monte Carlo (MCMC) methods, and showed the approach to have advantages over existing non-stochastic alternatives. In this paper, we develop Bayesian areal boundary analysis methods that estimate the spatial neighborhood structure using the value of the process in each region and other variables that indicate how similar two regions are. Boundaries may then be determined by the posterior distribution of either this estimated neighborhood structure or the regional mean response differences themselves. Our methods do require several assumptions (including an appropriate prior distribution, a normal spatial random effect distribution, and a Bernoulli distribution for a set of spatial weights), but also deliver more in terms of full posterior inference for the boundary segments (e.g., direct probability statements regarding the probability that a particular border segment is part of the boundary). We illustrate three different remedies for the computing difficulties encountered in implementing our method. We use simulation to compare among existing purely algorithmic approaches, the Lu and Carlin (2005) method, and our new adjacency modeling methods. We also illustrate more practical modeling issues (e.g., covariate selection) in the context of a breast cancer late detection data set collected at the county level in the state of Minnesota.     

Male Mutation Bias and Possible Long‐Term Effects of Human Activities

Abstract: The ability of a population to adapt to changing environments depends critically on the amount and kind of genetic variability it possesses. Mutations are an important source of new genetic variability and may lead to new adaptations, especially if the population size is large. Mutation rates are extremely variable between and within species, and males usually have higher mutation rates as a result of elevated rates of male germ cell division. This male bias affects the overall mutation rate. We examined the factors that influence male mutation bias, and focused on the effects of classical life‐history parameters, such as the average age at reproduction and elevated rates of sperm production in response to sexual selection and sperm competition. We argue that human‐induced changes in age at reproduction or in sexual selection will affect male mutation biases and hence overall mutation rates. Depending on the effective population size, these changes are likely to influence the long‐term persistence of a population.     

Crossing the frontier: vertical transit rates of deep diving cormorants reveal depth zone of neutral buoyancy

Knowing the depth zone of neutral buoyancy of divers is important because buoyancy can determine how animals manage their energy budget. In this study, we estimate the depth zone of neutral buoyancy of free-ranging cormorants for the first time, using time-depth recorders. We discovered that vertical ascent rates of 12 Crozet and 15 Kerguelen diving blue-eyed shags (respectively Phalacrocorax melanogenis and P. verrucosus) slowed down considerably at the 50–60 m depth zone. We suggest this was due to birds trying to reach the surface from that point upwards using reduced locomotor activity because the force of buoyancy becomes greater than the force of gravity at that depth. The results show a shift of this depth zone in relation to maximum targeted dive depth, suggesting cormorants may control buoyancy through respiratory air volume adjustment. Interestingly, 60 m is close to the maximum depth zone reached by these two species during dives lasting 4 min, their estimated behavioural aerobic dive limit. This suggests that the decision to swim deeper has a direct consequence on the energy budget, with time spent recovering at the surface (time thus lost to foraging) strongly increasing relative to the preceding time of submergence. Resources found in deeper waters must be of sufficient quantity or quality to justify crossing the frontier of physical neutral buoyancy.     

Characteristics that influence male reproductive success on a lek of Lethrinops c.f. parvidens (Teleostei: Cichlidae)

Sexual selection has long been proposed as a mechanism leading to the diverse cichlid (Teleostei: Cichlidae) fauna of Lake Malawi, Africa. Many of the shallow-water, sand-dwelling, bower-building cichlid species are particularly well suited for studies of sexual selection because they participate in leks. Since females in lekking systems appear to acquire only genetic material from their mates, it has been suggested that leks are ideal systems to study female mate choice. The objectives of the investigation were to examine Lethrinops c.f. parvidens male bower characteristics (i.e., bower size and location) as well as other male characteristics (i.e., length, gular color, and duration on the lek) for their influence on male mating success as measured by the number of visits, circles, and eggs laid by females. These measures are nested in that a visit by a female may or may not lead to circling, and circling by a female may or may not lead to egg-laying. We found increased bower height and higher numbers of conspecific neighbors (analogous to shallow-water, near-shore bower positions) to be positively, significantly associated with the number of visits by females. The only significant correlate with the number of circles was visits, and similarly circles was the only significant correlate with the number of eggs laid. The R ² value for the egg-laying regression was quite low (19.8%) compared with visits (54.3%) and circling (78.9%), suggesting that females may be using additional cues, that we failed to measure, when in close proximity to males or simply that a small proportion of the females were ready to spawn. Both indirect selection and direct selection pressure due to egg predation may have influenced female choice on the lek. Received: 10 April 1999 / Received in revised form: 26 July 1999 / Accepted: 18 September 1999     

Multiannual trend of microcystin production in the toxic cyanobacterium Planktothrix rubescens in Lake Garda (Italy)

Massive developments (blooms) of cyanobacteria represent a major concern in many natural and artificial waterbodies, because of the high levels of toxins that can be released into water. Microcystins, potent hepatotoxins, represent the most frequent toxins produced by cyanobacteria. The determination of the microcystins’ profile in waterbodies is important for determining the real toxic potential. We have investigated the evolution of the microcystins’ profile of Lake Garda (Italy) from both a qualitative and a quantitative point of view over a period of five years. We have also analysed possible correlations between toxin profile and selected environmental parameters. We found that a demethylated microcystin variant (RRdm) was always dominant but showing a cyclic trend, alternating periods in which it represented the only variant, and periods in which other variants were present (LRdm, HtyrRdm, RR, and LR). These changes are probably due to changes in chemotypes composition inside the resident Planktothrix rubescens population and do not seem to be exclusively linked to the considered environmental variables. Total microcystin concentrations were always low (in the ng?L^?1 scale), and showed typical peaks in the metalimnetic layer during summer–autumn time of each year.     

Diving behaviour of gentoo penguins,Pygoscelis papua; factors keeping dive profiles in shape

The foraging ecology of seven Gentoo penguins,Pygoscelis papua, breeding at Ardley Island, Antarctica was studied using animal-attached devices which recorded swimming speed, heading and dive depth. Reconstruction of the foraging routes by vectorial analysis of the data indicated that at no time did the birds forage on the sea bed. Swimming speed was relatively constant at 1.7 m s^-1, but rates of descent and ascent in the water column during dives increased with increasing maximum dive depth due to changes in descent and ascent angles. The amount of time spent discending and ascending in the water column increased with maximum dive depth as did the duration spent at the point of maximum depth. Dive profiles were essentially either U-shaped (flat-bottomed dives), or V-shaped (bounce dives). Development of a model based on simple probability theory indicated that the optimal dive profile to maximize the chances of prey acquisition depends on vertical prey distribution and on the visual capabilities of the birds with respect to descent and ascent angles.     

A test of reproductive skew models in a field population of a multiple-queen ant

Determining the evolutionary basis of variation in reproductive skew (degree of sharing of reproduction among coexisting individuals) is an important task both because skew varies widely across social taxa and because testing models of skew evolution permits tests of kin selection theory. Using parentage analyses based on microsatellite markers, we measured skew among female eggs (n=32.3 eggs per colony, range=20–68) in 17 polygynous colonies from a UK field population of the ant Leptothorax acervorum. We used skew among eggs as our principal measure of skew because of the high degree of queen turnover in the study population. Queens within colonies did not make significantly unequal contributions to queen and worker adult or pupal offspring, indicating that skew among female eggs reflected skew among daughter queens. On average, both skew among female eggs (measured by the B index) and queen–queen relatedness proved to be low (means±SE=0.06±0.02 and 0.28±0.08, respectively). However, contrary to current skew models, there was no significant association of skew with either relatedness or worker number (used as a measure of productivity). In L. acervorum, predictions of the concession model of skew may hold between but not within populations because queens are unable to assess their relatedness to other queens within colonies. Additional phenomena that may help maintain low skew in the study population include indiscriminate infanticide in the form of egg cannibalism and split sex ratios that penalize reproductive monopoly by single queens within polygynous colonies.