Stephan Pelikan

Effects of lead time, length bias, and false-negative assurance on screening for breast cancer

This article presents a model of breast cancer screening programs. The model shows the effects of the screening threshold, screen sensitivity, and false‐negative assurance on the cumulative mortality rate in the screened population. It shows that factors of screen design and a penalty associated with false‐negative assurance can result in excess mortality rates in screened populations‐especially in those age classes in which the incidence of rapidly growing tumors is high. Factors related to the magnitude of this effect are described.

Deviations of trajectory averages and the defect in Pesin’s formula for Anosov diffeomorphisms

A large deviation theorem at the Donsker Varadhan level three is obtained for the convergence of trajectory averages of Anosov diffeomorphisms. It is possible to provide an explicit description of the rate function.

A dynamical meaning of fractal dimension

When two atlractors of a dynamical system have a common basin boundary B, small changes in initial conditions which lie near B can result in radically different long-term behavior of the trajectory. A quantitative description of this phenomenon is obtained in terms of the fractal dimension of the basin boundary B.

NEWGARDEN: a computer program to model the population dynamics and genetics of establishing and fragmented plant populations

Conservation of plants often involves isolated in situ or ex situ protective restoration or supplemental plantings. Plant preservation also frequently involves maintenance of recently fragmented populations. The effects of the spatial patterning of the initial target species individuals in such situations on future population growth and genetic diversity maintenance are commonly difficult to predict, especially given that plants have varying life history characteristics. NEWGARDEN allows users to create a virtual preserve or fragment of specified size, place initial individuals at designated locations (the program is spatially explicit using a grid system), and follow population development stemming from bouts of mating influenced by user-specified life history characteristics (e.g., genetic diversity of the initial individuals; age-specific mortality; age-specific reproduction; gene dispersal distances; etc.). Output, which can be reported for the entire population data set and/or specified regions of the preserve or fragments after each bout of mating, includes total population and individual newest cohort data on the number of individuals, total number of founding alleles retained, observed heterozygosity, expected heterozygosity, and FIT. Use of the program is illustrated with a NEWGARDEN analysis of the effects of varying founder pattern and gene dispersal distance on population growth and genetic diversity for an annual plant.

Genetic diversity among populations and size classes of buckeyes (Aesculus: Hippocastanaceae) examined with multilocus VNTR probes

Abstract. Little is known about genetic variation in members of the genus Aesculus (Hippocastanaceae), in particular A. flava (yellow buckeye) and A. glabra (Ohio buckeye). Here, three synthetic DNA probes (composed of tandemly repeated, core sequences) that reveal alleles at multiple variable-number tandem-repeat (VNTR) loci in these two species were used to investigate: 1) levels of genetic variation in one stand of A. flava and three isolated stands of A. glabra; 2) whether the stands of A. glabra are genetically differentiated from one another; 3) whether there has been selection for more heterozygous individuals through time in one stand each of A. flava and A. glabra; and 4) whether a possible genetic bottleneck had occurred during the formation of either species of Aesculus.First, variation of VNTR genetic markers within and among three populations of A. glabra separated by 60–180 km was examined. In each one hectare (ha) population, 22 individuals were randomly sampled. Among the three populations, the mean number of bands scored per individual was 80.35 and the average number of estimated loci surveyed was 54.17. Mean similarity and estimated heterozygosity within populations ranged from 0.634 to 0.743 and from 0.342 to 0.486, respectively. The mean similarity across populations was 0.657, while the mean estimated heterozygosity across populations was 0.484 for A. glabra. The most isolated site was the most genetically differentiated as indicated by differences in levels of similarity, heterozygosity, and Fst value comparisons.In a separate experiment, genetic variation in 22 large (reproductively mature; dbh > 8 cm) individuals was compared with that in 22 small (not yet reproductive; dbh < 1 cm) individuals collected within one ha stands for both A. flava and A. glabra. Mean similarity values among large versus small individuals of A. flava were 0.665 versus 0.662, while for A. glabra the corresponding values were 0.686 versus 0.691, respectively. Permutation tests of these similarity data detected no evidence for size class genetic differentiation in either species (both p-values > 0.050). Further, permutation tests for the number of bands per individual (average band number should be higher in more heterozygous individuals) detected no significant differences between size classes for either species. Thus, evidence of pronounced inbreeding and/or selection altering population genetics within small relative to large individuals was not detected.In addition, comparable similarity and heterozygosity values between these two closely related species (which still maintain an active zone of hybridization) suggests that either: 1) no extreme genetic bottleneck has accompanied the formation of these species from a common ancestor; or 2) signs of such a bottleneck have largely been eliminated. These studies demonstrate the utility of multilocus VNTR DNA probes for investigating genetic variation within and among plant populations, between size classes within a population, and between closely related species.

Effective seed harvesting strategies for the ex situ genetic diversity conservation of rare tropical tree populations

Tropical rain forests harbor a high diversity of tree species, a large portion of which are considered rare and threatened by anthropogenic factors such as land-use change. Addressing the global need for ex situ rescue populations of such species, we investigated whether certain methods of wild-source seed collection harvest greater amounts of genetic variation from the source population while minimizing the costs expended. We used an individual-based computer program (NEWGARDEN) to conduct simulation trials examining which aspects of seed procurement provided the most cost-effective methods for maximal rare allele capture for single isolated populations of rare tropical tree species. Aspects examined included the geometric pattern of harvesting, location of seed collections within the spatial distribution of the population (central vs. peripheral), geometric partitioning of sampling regions (contiguous vs. subdivided), gene dispersal distance, linear travelling costs, and ratio of seeds collected to plants sampled. Results demonstrated that ratio of seeds collected to plants sampled had the highest effect on genetic diversity harvested relative to sampling location or geometric pattern of collection, explaining 82 and 79% of the variance in alleles harvested, respectively. Collecting from subdivided peripheral sampling regions and populations having long distance gene dispersal led to increases of up to 39 and 51% in the amount of genetic variation conserved respectively. These results suggest that ex situ conservation efforts for rare tropical trees can benefit by collecting fewer seeds from each of a larger number of trees, sampling from peripheral subdivided regions of the population rather than in a contiguous centrally located one under the transect or nearest neighbor strategies, and adjusting harvesting based on the dispersal biology of the source population. This study underscores the need for more information regarding the dispersal characteristics of the target species and demonstrates the value of predictive modeling for planning seed collection projects.

Weed Suppression Success Can Depend on Removal Pattern and Gene Dispersal Distance: Modeling Callery Pear

Abstract Substantial resources are spent each year on weed control, but in many cases eradication projects are incomplete. Here we used the computer program NEWGARDEN to model whether alternate geometric patterns of incomplete removal (99% removed) of the increasingly invasive Callery pear from an isolated fragment differentially affect the rate of population recovery and genetic diversity retention. Geometric patterns of remaining founders within the fragment (1% of the fragment area) included: (A) a long rectangular strip centered on one edge; (B) a square at one corner; (C) a central square; or (D) scattered randomly throughout the entire fragment. Population re-growth and genetic diversity retention measures for each geometric removal pattern were modeled under two contrasting gene dispersal patterns (via both offspring and pollen): short versus long dispersal (both leptokurtic relative to the pistillate plant). After 14 bouts of mating, the greatest difference in census size among comparative recovery populations amounted to 393% (centered founders, long gene dispersal > scattered founders, short gene dispersal). The best pattern of removal for suppressing population regrowth was to leave founders scattered throughout the fragment when gene dispersal was short, or at one corner if gene dispersal was long. The only removal pattern that differed substantially in population genetics characteristics was when remnant individuals were left scattered throughout the fragment and dispersal was short (alleles continued to be lost; observed heterozygosity dropped 13.3% and was still rapidly declining; and inbreeding and/or subdivision were moderate (Fit  =  0.12) and still rapidly increasing). Such comparative modeling can be used to suggest removal patterns that might greatly outperform other removal modalities in terms of suppressing the return of weed populations. The effectiveness of such modeling will be improved by acquisition of accurate life history information of targeted species. Nomenclature: Callery pear, Pyrus calleryana Decne.

Variable gene dispersal conditions and spatial deforestation patterns can interact to affect tropical tree conservation outcomes.

Tropical lowland rain forest (TLRF) biodiversity is under threat from anthropogenic factors including deforestation which creates forest fragments of different sizes that can further undergo various internal patterns of logging. Such interventions can modify previous equilibrium abundance and spatial distribution patterns of offspring recruitment and/or pollen dispersal. Little is known about how these aspects of deforestation and fragmentation might synergistically affect TLRF tree recovery demographics and population genetics in newly formed forest fragments. To investigate these TLRF anthropogenic disturbance processes we used the computer program NEWGARDEN (NG), which models spatially-explicit, individual-based plant populations, to simulate 10% deforestation in six different spatial logging patterns for the plant functional type of a long-lived TLRF canopy tree species. Further, each logging pattern was analyzed under nine varying patterns of offspring versus pollen dispersal distances that could have arisen post-fragmentation. Results indicated that gene dispersal condition (especially via offspring) had a greater effect on population growth and genetic diversity retention (explaining 98.5% and 88.8% of the variance respectively) than spatial logging pattern (0.2% and 4.7% respectively), with ‘Near’ distance dispersal maximizing population growth and genetic diversity relative to distant dispersal. Within logged regions of the fragment, deforestation patterns closer to fragment borders more often exhibited lower population recovery rates and founding genetic diversity retention relative to more centrally located logging. These results suggest newly isolated fragments have populations that are more sensitive to the way in which their offspring and pollen dispersers are affected than the spatial pattern in which subsequent logging occurs, and that large variation in the recovery rates of different TLRF tree species attributable to altered gene dispersal regimens will be a likely outcome of fragmentation. Conservation implications include possible manual interventions (manual manipulations of offspring dispersers and/or pollinators) in forest fragments to increase population recovery and genetic diversity retention.

Earlier Flowering in a Restored Wetland–Prairie Correlated with Warmer Temperatures (Ohio)

project that is enabling us to expand the landfill,” said Steve Smith, Area Environmental Manager for Allied Waste, “We’re very happy with the results so far.” Smith noted the site will require monitoring to document the survival of the restored vegetation and the absence of harmful invasive species. “The goal of this project is to achieve a sustainable, biodiverse ecosystem using species that are native to the area,” said Moritz, “By regenerating the native species and controlling the harmful effects of invasive species, we can help improve water retention and quality, control erosion, attract wildlife, and create an aesthetically pleasing environment.”

Hopf bifurcations via zero sets

Abstract This paper gives conditions under which certain two-dimensional systems of differential equations have a Hopf bifurcation. The systems studied are used as models in cell biophysics. The conditions required can be verified easily by numerical computation.