Importance Tempering

Simulated tempering (ST) is an established Markov chain Monte Carlo (MCMC) method for sampling from a multimodal density $\pi(\theta)$. Typically, ST involves introducing an auxiliary variable $k$ taking values in a finite subset of $[0,1]$ and indexing a set of tempered distributions, say $\pi_k(\theta) \propto \pi(\theta)^k$. In this case, small values of $k$ encourage better mixing, but samples from $\pi$ are only obtained when the joint chain for $(\theta,k)$ reaches $k=1$. However, the entire chain can be used to estimate expectations under $\pi$ of functions of interest, provided that importance sampling (IS) weights are calculated. Unfortunately this method, which we call importance tempering (IT), can disappoint. This is partly because the most immediately obvious implementation is na\"ive and can lead to high variance estimators. We derive a new optimal method for combining multiple IS estimators and prove that the resulting estimator has a highly desirable property related to the notion of effective sample size. We briefly report on the success of the optimal combination in two modelling scenarios requiring reversible-jump MCMC, where the na\"ive approach fails.Comment: 16 pages, 2 tables, significantly shortened from version 4 in response to referee comments, to appear in Statistics and Computin

INITIAL CHARACTERIZATION OF MAJOR HISTOCOMPATIBILITY COMPLEX (MHC) CLASS IIB EXON 2 IN AN ENDANGERED RATTLESNAKE, THE EASTERN MASSASAUGA (SISTRURUS CATENATUS)

Genes of the major histocompatibility complex (MHC) play an important role in the vertebrate immune system and exhibit remarkably high levels of polymorphism, maintained by strong balancing selection. While the conservation implications of MHC variation have been explored in a variety of vertebrates, non-avian reptiles (most notably snakes) have received less attention. To address this gap and take the first steps toward more extensive population-level analyses, we cloned and sequenced MHC IIB exon 2 in an endangered rattlesnake, the Eastern Massasauga (Sistrurus catenatus). Based on three individuals, we found evidence of at least four putatively functional loci. These sequences exhibited relatively high levels of variation and significantly higher rates of nonsynonymous to synonymous substitutions, especially within the antigen-binding sites, indicating strong positive selection. Phylogenetic analysis revealed a pattern of trans-species polymorphism, also suggesting positive selection. These results contribute to our understanding of MHC variation in non-avian reptiles and form a basis for more studies of MHC variation in snakes of conservation concern

The Temporal and Spatial Scale of Microevolution: Fine-scale Color Pattern Variation in the Lake Erie Watersnake

Question: What is the temporal and spatial scale of microevolution? Hypotheses: The combined effects of natural selection and gene flow result in variation in heritable traits on fine spatial and geographic scales. Organism: The Lake Erie watersnake, Nerodia sipedon insularum. Field site: US and Canadian islands in western Lake Erie. Methods: We tested for variation in colour pattern frequency within islands, among islands, and over time using data from nearly annual censuses conducted since 1980, museum specimens, and published sources. We compared FST for a presumptive major colour pattern locus to FST for allozyme loci to determine whether spatial variation exceeded that expected by chance. We computed effective population size (Ne) based on temporal frequency changes in presumptive colour pattern alleles to determine whether temporal variation exceeded that expected by chance (Ne significantly less than ∞). Conclusions: Morph frequencies did not differ significantly within islands or between islands separated by short distances. Morph frequencies did sometimes differ significantly among distant islands and among sampling periods from 1980 to the present, but no more than expected by chance. In contrast, a marked change in morph frequency occurred between historic (prior to 1961) and recent (1980–2003) samples. Possible mechanisms include changes in the strength of selection (due to changes in predator assemblages and visual environments) and rates of gene flow (due to changes in island watersnake population size)

Microevolution in Island Water Snakes

Examples presented demonstrate that evolutionary outcomes depend not only on those processes that operate within populations(e,g.,selection) but also on interactions (via gene flow) among populations. Factors affecting rates of gene flow are likely to produce evolutionary change even when within-population processes remain constant. These examples also illustrate that the combined effects of selection and gene flow are not restricted to organisms found on islands like those in western Lake Erie but may be important in any organism whose distribution spans a range of habitat types. As human activities produce changes in habitat characteristics and distribution (e.g., by fragmenting formerly continuous habitats), changes in selection regimes and rates of gene flow may produce microevolutionary changes in other organisms that mirror those seen in island water snakes

What Does the Snake Eat? Breadth, Overlap, and Non-Native Prey in the Diet of Three Sympatric Natricine Snakes

We investigated diet breadth and diet overlap in three sympatric snakes of similar body size: Dekay’s Brownsnakes (Storeria dekayi), Red-bellied Snakes (S. occipitomaculata), and sub-adult Common Gartersnakes (Thamnophis sirtalis), by examining recently consumed prey (n = 388) collected from wild-caught snakes (n = 263) in northern Illinois. Storeria occipitomaculata were dietary specialists, feeding nearly exclusively on slugs. Storeria dekayi fed predominately on slugs but also consumed snails and earthworms. Sub-adult T. sirtalis fed predominately on earthworms but also consumed frogs and small mammals. Diet overlap was extensive between Storeria species but relatively low between Storeria and Thamnophis. It is noteworthy that the two most abundant prey types, slugs and earthworms, are non-native. These non-native prey occur in high numbers, which may ameliorate competitive interactions and influence grassland snake abundance and persistence regionally

Summer and Winter Spatial Habitat Use by the Lake Erie Watersnake

In an effort to provide information to guide habitat management for the Lake Erie watersnake Nerodia sipedon insularum, a federally threatened and Ohio state endangered species, we used radiotelemetry to obtain spatial habitat data for adult snakes during the summer active season and during winter hibernation. During the summer active season, terrestrial habitat use was limited to a narrow band of shoreline. Among individuals, maximum distance inland from shore ranged from 1 to 50 m (mean = 8 m) and linear extent of shoreline ranged from 30 to 1,360 m (mean = 261 m). Winter hibernation occurred at varying distances inland with individual hibernation sites ranging from 1 to 580 m (mean = 29 m) from shore. Habitat use did not differ between males and females. Existing U.S. Fish and Wildlife Service habitat management guidelines suggest that ground-disturbing activities within potential hibernation areas (defined as terrestrial habitat within 161 m of shore) should be avoided in winter to prevent harm to hibernating snakes. They suggest further that excavation and removal of shrubs, standing or downed trees, root masses, animal burrows, piled rocks, cliffs, or bedrock within 21 m of shore should be avoided in summer to prevent harm to active snakes. Given that Lake Erie watersnakes have recovered to the point where delisting is being proposed, these habitat guidelines appear to be sufficient. However, maintaining voluntary compliance with habitat guidelines and meeting the need for continued public outreach will be vital to ensure long-term persistence

Stages of Habitat Structural Trend That are Related to Ungulate Browsing

To maintain their structural identity, communities of tall-growing trees and shrubs depend on the growth of young plants to replace mature individuals that die. Ungulate browsing influences that structure by permitting or preventing the height growth of young plants. The resulting changes in structure are indicted by the browsing-related architectures of plants that grow within the browse zone, i.e., those ? 2.5 m tall. Using examples from six National Wildlife Refuges, we describe six stages of structural trend and their management implications: 1) Structure is Stable, i.e., all plants have Uninterrupted-growthtype architecture; 2) Early Stage of Structural Decline most or all plants have Arrested- or Retrogressed-type architecture and there is no visible evidence of dieback; 3) Intermediate Stage of Structural Decline, i.e., all plants have Arrested- or Retrogressed-type architecture, dieback is apparent, and live stems extend throughout the lower half of the browse zone; 4) Advanced Stage of Decline, i.e., all plants have Arrested- or Retrogressed-type architecture and live stems are restricted to the lowest part of the browse zone; 5) Structure is Lost, i.e., no live plants; and 6) Recovery of Structural Diversity, i.e., there is evidence that the Early, Intermediate, or Advanced Stage of Decline existed, and that young Uninterrupted-growth type plants are growing into the browse zone. Three factors influence the rate-of-change from one stage to another: Susceptibility, Resistance, and Resilience. Because the stages are independent of species composition, they provide a means of comparing the effect of browsing in diverse habitats across a region

Temperature-induced multi-species cohort effects in sympatric snakes

In reptiles, reproductive maturity is often determined by size rather than age. Consequently, growth early in life may influence population dynamics through effects on generation time and survival to reproduction. Because reproductive phenology and pre- and post-natal growth are temperature dependent, environmental conditions may induce multi-species cohort effects on body size in sympatric reptiles. I present evidence of this using 10 years of neonatal size data for three sympatric viviparous snakes, Dekay's Brown snakes (Storeria dekayi), Red-bellied Snakes (S. occipitomaculata), and Common Garter snakes (Thamnophis sirtalis). End-of-season neonatal size varied in parallel across species such that snout–vent length was 36%–61% greater and mass was 65%–223% greater in years when gestating females could achieve higher April–May (vs. June–July or August–September) operative temperatures. Thus, temperature had a larger impact during follicular enlargement and ovulation than during gestation or post-natal growth. Multi-species cohort effects like these may affect population dynamics and the magnitude of these effects may increase with climate change.Open Access funding provided by Northern Illinois University Libraries and the Division of Research and Innovation Partnerships