On Variograms in Point Process Statistics

Variograms, which are frequently used in geostatistics, are of value also in the statistics of marked point processes. When the marks come from a random field which is independent of the point process, ideas of geostatistics suffice for the interpretation of point process variograms. When this model is not appropriate, interactions between the points lead to point process variograms having forms which are unusual in geostcistics. This is shown by three theoretical examples and one from forestry.     

The ownership signature in mouse scent marks is involatile

Male house mice advertise their territory ownership through urinary scent marks and use individual-specific patterns of major urinary proteins (MUPs) to discriminate between their own scent and that of other males. It is not clear whether recognition occurs through discrimination of the non-volatile proteins or protein-ligand complexes (direct model), or by the detection of volatile ligands that are released from MUPs (indirect model). To examine the mechanism underlying individual scent mark signatures, we compared investigatory and countermarking responses of male laboratory mice presented with male scent marks from a strain with a different MUP pattern, when they could contact the scent or when contact was prevented by a porous nitrocellulose sheet to which proteins bind. Mice investigated scent marks from other males whether these were covered or not, and biochemical analysis confirmed that the porous cover did not prevent the release of volatiles from scent marks. Having gained information through investigation, mice increased their own scent marking only if they had direct contact with another male's urine, failing to do this when contact was prevented. Individual signatures in scent marks thus appear to be carried by non-volatile proteins or by non-volatile protein-ligand complexes, rather than by volatiles emanating from the scent.     

On statistical inference for the random set generated Cox process with set-marking

Cox point process is a process class for hierarchical modelling of systems of non-interacting points in Rd under environmental heterogeneity which is modelled through a random intensity function. In this work a class of Cox processes is suggested where the random intensity is generated by a random closed set. Such heterogeneity appears for example in forestry where silvicultural treatments like harvesting and site-preparation create geometrical patterns for tree density variation in two different phases. In this paper the second order property, important both in data analysis and in the context of spatial sampling, is derived. The usefulness of the random set generated Cox process is highly increased, if for each point it is observed whether it is included in the random set or not. This additional information is easy and economical to obtain in many cases and is hence of practical value; it leads to marks for the points. The resulting random set marked Cox process is a marked point process where the marks are intensity-dependent. The problem with set-marking is that the marks are not a representative sample from the random set. This paper derives the second order property of the random set marked Cox process and suggests a practical estimation method for area fraction and covariance of the random set and for the point densities within and outside the random set. A simulated example and a forestry example are given.     

A note on testing separability in spatial-temporal marked point processes

Summary .   In environmental risk analysis, it is common to assume the stochastic independence (or separability) between the marks associated with the random events of a spatial-temporal point process. Schoenberg (2004, Biometrics 60, 471–481) proposed several test statistics for this hypothesis and used simulated data to evaluate their performance. He found that a Cramér-von Mises-type test is powerful to detect gradual departures from separability although it is not uniformly powerful over a large class of alternative models. We present a semiparametric approach to model alternative hypotheses to separability and derive a score test statistic. We show that there is a relationship between this score test and some of the test statistics proposed by Schoenberg. Specifically, all are different versions of weighted Cramér-von Mises-type statistics. This gives some insight into the reasons for the similarities and differences between the test statistics' performance. We also point out some difficulties in controlling the type I error probability in Schoenberg's residual test.     

Tests for independence between marks and points of a marked point process

A convenient assumption while modeling a marked point process is that the observations (i.e., marks) and the locations (i.e., points) are independent. We propose new graphical and formal testing approaches to test for this assumption. The proposed graphical procedures are easy to obtain and can be used to diagnose the nature and range of dependence between marks and points. The formal testing procedures require only minimal conditions on marks and thus can be applied to a variety of settings. We illustrate these procedures through a simulation study and an application to some real data.     

Enigmatic traces in infaunal bivalves from the late Quaternary of Argentina,Southwestern Atlantic. Bioerosion,bioclaustration or nothing?

Ichnological investigations were carried out on late Quaternary shells of the intertidal deep infaunal bivalve Tagelus plebeius (Lightfoot, 1786) found along the southwestern Atlantic, between Uruguay and the southernmost Buenos Aires Province in Argentina. Analyses reveal distinctive marks that are spread on the outer shell surface only. The marks are regular-unbranched-elongate, perpendicular to the outer shell growth lines, with deflections on the margins, never interconnected, without bifurcations, conforming bottom-up constructions. They occur in hundreds of specimens from many samples taken from sediments ranging in age from the late Pleistocene to the Recent. These marks have never been reported or described for this species and their origin and formation remain elusive. We describe these traces thoroughly and we propose an explanation for their preservation on about half the shells examined. Potential destructive boring structures (excavated from outside-in) or bioerosion activities by other macro- or micro-organisms are dismissed. These antimarginal asymmetric traces point instead to a process of constructive bioclaustrations (grown from the bottom-up) produced in situ during the life of the bivalve by unknown symbiont organisms. Additionally, the regular pattern observed for the marks exclude host growth as a consequence of abiotic/extrinsic causes. From a palaeoecological perspective, these structures suggest a biotic interaction that was hitherto undescribed neither for bivalves nor for the late Quaternary of the southwestern Atlantic.     

A Random Field Approach to Transect Counts of Wildlife Populations

Line transect counting of a wildlife population is considered a sampling from a planar marked point process, where the marks describe the detectability of the animals. Sampling properties of transect counts and a new density estimator are derived from a counting process, which is a shot-noise field induced by the marked point process. A general formula for the sampling variance of a transect is derived and applied to compare five common types of transects. Some stereological connections of transect sampling and density estimators are shown.     

Problems of orientation associated with cocoon-spinning by Nemeritis

Abstract. 1. Larvae of Nemeritis that have reached full growth in a caterpillar of Ephestia invariably push the host remains towards the closed end of the host cocoon and pupate with their heads towards the open end. Larvae reaching full growth in a pupal host are usually orientated in the same direction, but occasionally in reverse.
2. The parasitoid does not orientate itself by direct reference to the host cocoon but in relation to the final position of the host. The host remains are probably used as a point of reference.
3. As the parasitoid spins its own cocoon, it isolates itself from some external stimuli and has need of a new point of reference. It provides this by incorporating guide marks, in the form of areas of specially woven threads, in successive layers of its cocoon.
4. The final mark, on the innermost layer, not only indicates the anterior end of the cocoon, but also may help the adult to bite its way out.
5. The presence of similar marks has been observed in the cocoons of five other species of Ichneumonidae, representing the two subfamilies Ophioninae and Cryptinae.
6. The significance of these provisions for correct orientation of ichneumon wasps is briefly discussed.     

Modelling Tree Roots in Mixed Forest Stands by Inhomogeneous Marked Gibbs Point Processes

The aim of the paper is to apply point processes to root data modelling. We propose a new approach to parametric inference when the data are inhomogeneous replicated marked point patterns. We generalize Geyer's saturation point process to a model, which combines inhomogeneity, marks and interaction between the marked points. Furthermore, the inhomogeneity influences the definition of the neighbourhood of points. Using the maximum pseudolikelihood method, this model is then fitted to root data from mixed stands of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) to quantify the degree of root aggregation in such mixed stands. According to the analysis there is no evidence that the two root systems are not independent.     

Accumulations osseuses en périphérie de terriers de petits carnivores : les stigmates de prédation et de fréquentation

Faunal remains from spoil heaps of two burrows inhabited by small carnivores (fox and badger) are analysed from a taphonomical point of view. This analysis provides characteristics for bone accumulation produced by small carnivores and will be a powerful tool for deciphering site formation about the occupational alternation of small carnivores and humans. Identified species were grouped by size classes. Faunal spectrum is composed by varied species of microfauna (70%), mesofauna (30%). Macromammal remains are under represented (less than 1%) and come from scavenged carcasses. Predators and consumed species are compared on the basis of the skeletal part representation, age classes and recording of predation marks (gnawed and digested bones). Skeletal part representation shows that all taxons exhibit a low-representation of axial skeleton and autopodial bones. Predators show a high representation of hind limb bones and a low representation of the fore limb bones whereas consumed species exhibit a reverse pattern. Mortality curve analysis provides an attritional profile for carnivores and helps for the establishment of the season of occupation of the burrow. Adults largely dominate consumed species. Moreover, predation marks are found in 1% of the carnivores’ bones and from 15% to more than 40% on prey bones. The large-sized prey bones only wear gnawed marks (20%) and anthropic marks (10–20%) whereas microfaunal remains exhibits more digested marks (40%) than gnawing stigmata (5%). Medium-sized animals bones wear both marks and with the same proportions (10–15%).     

Who was the first? An experimental application of carnivore and hominid overlapping marks at the Pleistocene archaeological sites

There are many types of evidence that provide information about methods for obtaining animal nutrients. Several researchers suggest that the main element to be considered is the skeletal representation of the different species identified in the faunal assemblage. This element must be associated to the animals’ age at death and the localisation of processing marks of the carcasses (both those of anthropic origin and those produced by carnivores). Occasionally, these marks coincide on the same point of the bone, giving cause for overlapping marks. These marks can be considered an aid more to identify the anthropic manner for obtaining animal recourses. However, these cases are very unusual at archaeological sites, and it is not always easy to identify which of the two predators has obtained the prey first. Through the experimental process presented in this article, we have observed diagnostic elements on overlapping marks that show the action sequence of the predators (hominids and carnivores) on carcasses. These experimental criteria were applied to different archaeological sites of the Lower and Middle Pleistocene in the Iberian Peninsula: Bolomor Cave (Valencia, Spain) and level TD10-1 and TD6-2 of Gran Dolina (Atapuerca, Burgos). In these assemblages, we were able to distinguish hunting and scavenging events through overlapping marks, providing a new element to the general interpretation of these sites.     

Bistability in a Metabolic Network Underpins the De Novo Evolution of Colony Switching in Pseudomonas fluorescens

Phenotype switching is commonly observed in nature. This prevalence has allowed the elucidation of a number of underlying molecular mechanisms. However, little is known about how phenotypic switches arise and function in their early evolutionary stages. The first opportunity to provide empirical insight was delivered by an experiment in which populations of the bacterium Pseudomonas fluorescens SBW25 evolved, de novo, the ability to switch between two colony phenotypes. Here we unravel the molecular mechanism behind colony switching, revealing how a single nucleotide change in a gene enmeshed in central metabolism (carB) generates such a striking phenotype. We show that colony switching is underpinned by ON/OFF expression of capsules consisting of a colanic acid-like polymer. We use molecular genetics, biochemical analyses, and experimental evolution to establish that capsule switching results from perturbation of the pyrimidine biosynthetic pathway. Of central importance is a bifurcation point at which uracil triphosphate is partitioned towards either nucleotide metabolism or polymer production. This bifurcation marks a cell-fate decision point whereby cells with relatively high pyrimidine levels favour nucleotide metabolism (capsule OFF), while cells with lower pyrimidine levels divert resources towards polymer biosynthesis (capsule ON). This decision point is present and functional in the wild-type strain. Finally, we present a simple mathematical model demonstrating that the molecular components of the decision point are capable of producing switching. Despite its simple mutational cause, the connection between genotype and phenotype is complex and multidimensional, offering a rare glimpse of how noise in regulatory networks can provide opportunity for evolution.     

Olfactory eavesdropping by a competitively foraging stingless bee, Trigona spinipes

Signals that are perceived over long distances or leave extended spatial traces are subject to eavesdropping. Eavesdropping has therefore acted as a selective pressure in the evolution of diverse animal communication systems, perhaps even in the evolution of functionally referential communication. Early work suggested that some species of stingless bees (Hymenoptera, Apidae, Meliponini) may use interceptive olfactory eavesdropping to discover food sources being exploited by competitors, but it is not clear if any stingless bee can be attracted to the odour marks deposited by an interspecific competitor. We show that foragers of the aggressive meliponine bee, Trigona spinipes, can detect and orient towards odour marks deposited by a competitor, Melipona rufiventris, and then rapidly take over the food source, driving away or killing their competitors. When searching for food sources at new locations that they are not already exploiting, T. spinipes foragers strongly prefer M. rufiventris odour marks to odour marks deposited by their own nest-mates, whereas they prefer nest-mate odour marks over M. rufiventris odour marks at a location already occupied by T. spinipes nest-mates. Melipona rufiventris foragers flee from T. spinipes odour marks. This olfactory eavesdropping may have played a role in the evolution of potentially cryptic communication mechanisms such as shortened odour trails, point-source only odour marking and functionally referential communication concealed at the nest.     

The competing countermarks hypothesis: reliable assessment of competitive ability by potential mates

Scent marking on top of (overmarking), or in the vicinity of, a scent mark already present is commonly termed countermarking. Scent marks and countermarks provide a continuous record of competitive challenges between conspecifics, thus providing a reliable advertisement of an individual's ability to dominate or defend an area to other competitors and potential mates. To test the hypothesis that females should prefer males that countermark competing scent marks in their territory over those whose own marks are partially countermarked by a competing male, we manipulated scent marks in the territories of neighbouring male house mice (captive-bred Mus domesticus). As predicted, oestrous females were more strongly attracted to approach territory owners that countermarked the scent mark challenges of competitors than those that had been countermarked, and females themselves deposited more scent marks near the scents of these males. To investigate whether female mice use scent age, overlap or intrinsic qualitative or quantitative differences between scent marks and countermarks to make this discrimination, we redeposited male scent marks artificially as marks and partially overlapping countermarks, with or without a 24-h age difference between them. While the intrinsic quality or quantity of countermarks did not affect discrimination, an age difference between the original mark and subsequent countermark was important for consistent discrimination. The ultimate function of such competitive scent signalling thus may be to provide potential mates with a reliable indicator of the competitive ability of individuals advertising their high status. Since scent marks remain in the environment and are continuously available to challenge and investigation, they may provide a particularly effective and reliable means of dominance advertisement. Copyright 1999 The Association for the Study of Animal Behaviour.     

Male and Female Meadow Voles,Microtus pennsylvanicus,Differ in Their Responses to Heterospecific/Conspecific Over‐Marks

Voles use runways, paths, and trails that may also be used by rabbits and mink. These shared areas could contain the scent marks of conspecifics and heterospecifics. Thus, it is likely that the scent marks of heterospecifics may overlap or be overlapped by those of voles, forming over‐marks. Much is known about how voles respond to over‐marks of two different conspecifics. However, we do not know how they would respond to an opposite‐sex conspecific whose scent marks are in an over‐mark with the scent marks of predator or the scent marks of a non‐predator heterospecifics. We tested the hypothesis that meadow voles, Microtus pennsylvanicus, differ in their response to the scent mark of the opposite‐sex conspecific if the scent mark was overlapped by that of a mink, a vole predator, or rabbit, a vole non‐predator. We found that female but not male voles showed a preference for the scent marks of the opposite‐sex conspecifics that were part of the mink‐vole over‐mark when compared to those of opposite‐sex conspecifics that were not part of the over‐mark. This preference by female voles was independent of whether the male vole was the top‐scent donor or bottom‐scent donor of the over‐mark. Male and female voles showed no preference between the scent marks of the opposite‐sex conspecifics whose marks were part of or not part of the rabbit‐vole over‐mark. Sex differences in the manner that meadow voles respond to rabbit‐vole and mink‐vole over‐marks are discussed.     

Female meadow voles,Microtus pennsylvanicus,do not alter their over-marking in response to female conspecifics that were food deprived

Many terrestrial mammals will deposit scent marks and over-marks, the latter being the overlapping scent marks of two conspecifics. Studies have shown that male rodents that are exposed to the overlapping scent marks of two female conspecifics later spend more time investigating the mark of the top-scent female than that of the bottom-scent female. This suggests that over-marking is a form of competition and that the top-scent female is more likely than the bottom-scent female to be chosen as a potential mate. Thus, females should over-mark the scents of neighboring females at a rate that will maximize their chances of attracting males. However, meadow voles live in areas that may contain patchy food availability and residents may differ in their nutritional status. Females in a better nutritional state may be more likely than those in poorer nutritional states to indicate their presence in an area, signal possession of a territory, and to attract mates. Thus, we tested the prediction that female meadow voles, Microtus pennsylvanicus, that were not food deprived would deposit more over-marks than female voles that were food deprived for 6 h. Food-deprived female voles and female voles that had continuous access to food deposited a similar number of scent marks and used a similar proportion of those marks as over-marks when they encountered the scent marks of female conspecifics. These findings suggest that the nutritional status of female voles does not affect their ability to signal their presence in an area marked by a female conspecific.     

Nicks and notches of the dorsal ridge: Promising mark types for the photo-identification of narwhals

The narwhal is a hunted species for which we have many knowledge gaps. Photo-identification, which uses photographs of natural markings to identify individuals, is widely used in cetacean studies and can address a broad range of biological questions. However, it has not been developed for narwhals. The marks used for other cetaceans are inappropriate for this species either because narwhals lack the body part on which these marks are found or because the marks are known to change with time. We investigated the marks apparent in photographs of narwhals. Nicks and notches on the dorsal ridge are the mark types most promising for photo-identification. They are found on 91%–98% of the individuals, thus allowing the identification of a large part of the population. They can be used to differentiate between individuals, in part because they are variable in their location, numbers, shape, and size. Although our results suggest that nicks and notches are relatively stable over time, rates of change should be formally measured to assess the probability of photographic matches over multiple years. However, we are confident that these marks can be used in studies spanning at least a field season.     

The kinetic origins of the restriction point in the mammalian cell cycle

A detailed model mechanism for the G1/S transition in the mammalian cell cycle is presented and analysed by computer simulation to investigate whether the kinetic origins of the restriction point (R-point) can be identified. The R-point occurs in mid-to-late G1 phase and marks the transition between mitogen-dependent to mitogen-independent progression of the cell cycle. For purposes of computer simulations, the R-point is defined as the first point in time after mitosis where cutting off mitogen stimulation does not prevent the cell reaching the threshold activity of cyclin-E/cdk2 required for entry into S phase. The key components of the network that generate a dynamic switching behaviour associated with the R-point include a positive feedback loop between cyclin-E/cdk2 and Cdc25A, along with the mutually negative interaction between the cdk inhibitor p27Kip1 and cyclin-E/cdk2. Simulations of the passage through the R-point were carried out and the factors affecting the position of the R-point in G1 are determined. The detailed model also shows various points in the network where the activation of cyclin-E/cdk2 can be initiated with or without the involvement of the retinoblastoma protein.     

The time of timing: how Polycomb proteins regulate neurogenesis

The study of mammalian corticogenesis has revealed a critical role for Polycomb group (PcG) factors in timing the execution of developmental choices. Meanwhile, the study of post-translational modifications of PcG factors marks a symmetrical point, namely that the activity of PcG proteins is itself timed in a manner that links progression through the cell cycle to targeting of downstream genes. Finally, in a third symmetrical twist, the studies that dissect the timing of neural fate by Polycomb are also uncovering the importance of timing in the experimental mutation, since ablation of the same PcG member at different developmental stages yields dramatically different results. Here, I weave together these three lines of evidence and develop a unifying model that clarifies the dynamics of Polycomb function in neural development and defines the salient challenges ahead.     

Mark-mark scatterplots improve pattern analysis in spatial plant ecology

Point process statistics provides valuable tools for many ecological studies, where ‘points’ are commonly determined to represent the locations of plants or animals and ‘marks’ are additional items such as species or size. In the statistical analysis of marked point patterns, various correlation functions are used such as the mark variogram or the mark correlation function. Often the interpretation of these functions is not easy and the non-spatial ecologist is in need of support. In order to make the analysis of spatial point patterns more accessible to ecologists, we introduced and tested a new graphical method, the mark-mark scatterplot. This plot visualises the marks of point pairs of inter-point distances r smaller than some small distance r_max. We tested the application of the mark-mark scatterplot by reconsidering three quite different tree patterns: a pattern of longleaf pine trees from the southern US which was strongly influenced by fires, a tropical tree pattern of the species Shorea congestiflora from Sri Lanka and a Scots pine pattern from Siberia (Russia). The new method yielded previously undetected cause-effect information on mark behaviour at short inter-point distances and thus improved the analysis with mark correlation functions as well as complemented the information they provided. We discovered important new correlations in clusters of trees at close proximity. The application of the mark-mark scatterplot will facilitate the interpretation of point process summary statistics and will make point process analysis more accessible to ecologists not specialized in point process statistics.