Homogenization techniques for population dynamics in strongly heterogeneous landscapes

An important problem in spatial ecology is to understand how population-scale patterns emerge from individual-level birth, death, and movement processes. These processes, which depend on local landscape characteristics, vary spatially and may exhibit sharp transitions through behavioural responses to habitat edges, leading to discontinuous population densities. Such systems can be modelled using reaction–diffusion equations with interface conditions that capture local behaviour at patch boundaries. In this work we develop a novel homogenization technique to approximate the large-scale dynamics of the system. We illustrate our approach, which also generalizes to multiple species, with an example of logistic growth within a periodic environment. We find that population persistence and the large-scale population carrying capacity is influenced by patch residence times that depend on patch preference, as well as movement rates in adjacent patches. The forms of the homogenized coefficients yield key theoretical insights into how large-scale dynamics arise from the small-scale features

Modeling the Evolution of Insect Phenology with Particular Reference to Mountain Pine Beetle

Climate change is likely to disrupt the timing of developmental events (phenology) in insect populations in which development time is largely determined by temperature. Shifting phenology puts insects at risk of being exposed to seasonal weather extremes during sensitive life stages and losing synchrony with biotic resources. Additionally, warming may result in loss of developmental synchronization within a population, making it difficult to find mates or mount mass attacks against well-defended resources at low population densities. It is unknown whether genetic evolution of development time can occur rapidly enough to moderate these effects. The work presented here is largely motivated by the need to understand how mountain pine beetle (MPB) populations will respond to climate change. MPB is an important forest pest from both an economic and ecological perspective, because MPB outbreaks often result in massive timber loss. Recent MPB range expansion and increased outbreak frequency have been linked to warming temperatures. We present a novel approach to modeling the evolution of phenology by allowing the parameters of a phenology model to evolve in response to selection on emergence time and density. We also develop a temperature-dependent phenology model for MPB that accounts for multiple types of developmental variation: variation that persists throughout a life stage, random variation, and variation due to the MPB oviposition mechanism. This model is parameterized using MPB development time data from constant temperature laboratory experiments. We use Laplace\u27s method to approximate steady distributions of the evolution model under stable temperatures. Here the mean phenotype allows for parents and offspring to be oviposited at exactly the same time of year in consecutive generations. These results are verified numerically for both MPB and a two-stage model insect. The evolution model is also applied to investigate the evolution of phenology for MPB and the two-stage model insect under warming temperatures. The model predicts that local populations can only adapt to climate change if development time can adapt so that individuals can complete exactly one generation per year and if the rate of temperature change is moderate

A Deadtime Model For The Calibration Of Impact Sensors With An Application To A Modified Miniphone Sensor

Due to deadtime effects, undercounting by aeolian impact sensors is present at all sediment flux levels. During a short time interval following an impact (the deadtime), an impact sensor is unable to detect new impacts. The degree of undercounting increases with increasing flux so that the sensor eventually becomes saturated. We develop an undercounting model for aeolian impact sensors that accounts for deadtime. This model was applied to field data obtained using a miniphone sensor modified from Ellis et al. (2009). The modified miniphone is inexpensive ($75.00 USD per pair, including datalogging) and easy to assemble. A protective layer of foil increases longevity at the probable expense of sensitivity. Modified Wilson and Cooke (MWAC) sand traps were paired with modified miniphones (MM) for intervals of up to 50 min during two winter storms along the coast of Lake Michigan. Sand from each MWAC was sieved, and the masses were fit to a continuous density function to estimate grain counts. MM deployed for cumulative periods of up to 200 showed no evidence of signal degradation. Fitting a deadtime model to the MM/MWAC data yielded a R-2 value of 0.9766. While short segments of the response curve can be approximated by a linear fit, linear models will fail if applied much beyond the experimental conditions at which they were calibrated. The deadtime curve is based on a more realistic model of how impact sensors work and should give a better approximation of aeolian sand flux over a broader range of impact rates. (C) 2013 Elsevier B.V. All rights reserved

The Role of Storm Winds in Shaping Dunes Along Southern and Southeastern Lake Michigan

It has been hypothesized that rates of coastal dune growth and migration depend largely on the frequency and intensity of storms. We are pooling observations from three separate research sites to study effects of storms along Lake Michigan. At our southern site, Indiana Dunes National Lakeshore, we use marked trees and erosion pins to monitor sand movement on two large blowout dunes with north-facing troughs. From Oct. 2010 to May 2011 over 80% of the erosion on the stoss slopes occurred during four storms with strong northwest winds. The greatest erosion occurred during a March storm after a thaw had removed ice between surface sand grains. During the winter, sand eroded from the stoss slope tends to freeze in place near the dune crest. Thus deposition on the middle and lower lee slopes does not immediately follow storms but is delayed until the spring thaw. At the Saugatuck Harbor Natural Area (southeastern shore) we use an array of 211 pins and six anemometers to monitor sand movement and wind patterns in a complex blowout with a large northwest-facing trough and smaller troughs facing west and northwest. Topographic steering of winds in the dune is accompanied by a loss of energy. Sand transportation is most effective when storm winds approach the opening of a trough at a relatively low angle. The storm with the strongest northwest winds during the 8-month measuring period (10/26/10–10/28/10) accounted for 25% of the period’s measured sand transport. Farther north, at Hoffmaster State Park, we use 135 pins and an anemometer tower to monitor an active foredune and a west-facing blowout on an established foredune ridge. The average change at pins along the foredune during the 10/26–10/28 storm was 24% of the average measured seasonal change. Wetting of the beach by waves appears to have inhibited sand transportation to the foredune during the early part of this storm. Although high-energy wind events appear to be responsible for a significant part of sand transport at all three sites, the amount of transport also depends on the angle of the wind, the wetting of sand by waves and precipitation, and the presence of ice between sand grains

Dune Complexes Along The Southeastern Shore Of Lake Michigan: Geomorphic History And Contemporary Processes

This field guide explores the geomorphology, ecology, contemporary processes, sedimentary structures, and geomorphic history of the large freshwater dune systems on the southeastern shore of Lake Michigan. Recent research studies on varying aspects of the dunes are highlighted at each stop. From north to south, these stops include P.J. Hoffmaster State Park near Muskegon, Michigan; Gilligan Lake and Green Mountain Beach southwest of Holland, Michigan; Saugatuck Dunes State Park and Saugatuck Harbor Natural Area, both near Saugatuck, Michigan; Warren Dunes State Park and Grand Mere State Park between the Indiana–Michigan border and Benton Harbor, Michigan; and Mount Baldy on the eastern edge of the Indiana Dunes National Lakeshore, Indiana. All of the complexes described are low perched transgressive dune complexes that are migrating inland over former lake plains or baymouth bars. Moving from the lake inland, the typical dune complex in this area consists of incipient foredunes, an established foredune ridge, a parabolic dune complex, and a back-dune ridge complex. All stages of ecological succession—beginning with a pioneer community dominated by beach grasses and ending with a mesic forest dominated by oak, maple, and beech—are typically present in the larger dune complexes. Like coastal dunes everywhere, surface changes in Lake Michigan dunes are driven by spatial gradients in sand flux, which, in turn, are determined by a complex interaction among wind, vegetation patterns, and preexisting topography. The patterns of surface change are modified by seasonal effects, with the majority of sand transport being associated with strong storms in the autumn, winter, and early spring. Sand can be temporarily stored in niveolian deposits during the winter, leading to oversteepened slopes, which collapse during the spring thaw. A variety of sedimentary bed forms and structures can be viewed in dunes along the southeastern shore of Lake Michigan, including wind ripples, lag deposits, raindrop impressions, adhesion ripples, adhesion warts, eolian turrets, sand pedestals, surface patches of fine-grained dark sand, pinstripes, paleosols, cross-bedding, climbing ripple lamination, niveolian deposits, and avalanche lobes. Most of these features are best seen immediately after strong storms in the autumn and winter. Remnants of older dune surfaces are exposed in a few places in back-dune ridge complexes; however, the current dune complexes are largely a product of events that occurred during and after the rise in lake levels to the Nipissing peak (ca. 4.5 ka). Broad fields of relatively low dunes developed during the drop in lake levels following the Nipissing peak. Beginning with the rise to the Algoma high lake level (ca. 3.2 ka), the lakeward edges of these fields were episodically reworked, forming the large parabolic dune complexes. A period of widespread dune stability resulted in the development of the Holland Paleosol, a particularly well-developed paleosol with Spodosol characteristics. Widespread dune growth and migration resumed prior to European settlement of the area and continue today