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1. Mudskippers Modulate their Locomotor Kinematics when Moving on Deformable and Inclined Substrates

   https://doi.org/10.1093/icb/icac084  

   Naylor, Emily R. ; Kawano, Sandy M. ( June 2022 , Integrative and Comparative Biology)

   Many ecological factors influence animal movement, including properties of the media that they move on or through. Animals moving in terrestrial environments encounter conditions that can be challenging for generating propulsion and maintaining stability, such as inclines and deformable substrates that can cause slipping and sinking. In response, tetrapods tend to adopt a more crouched posture and lower their center of mass on inclines and increase the surface area of contact on deformable substrates, such as sand. Many amphibious fishes encounter the same challenges when moving on land, but how these finned animals modulate their locomotion with respect to different environmental conditions and how these modifications compare with those seen within tetrapods is relatively understudied. Mudskippers (Gobiidae: Oxudercinae) are a particularly noteworthy group of amphibious fishes in this context given that they navigate a wide range of environmental conditions, from flat mud to inclined mangrove trees. They use a unique form of terrestrial locomotion called “crutching,” where their pectoral fins synchronously lift and vault the front half of the body forward before landing on their pelvic fins, while the lower half of the body and tail are kept straight. However, recent work has shown that mudskippers modify some aspectsmore »of their locomotion when crutching on deformable surfaces, particularly those at an incline. For example, on inclined dry sand, mudskippers bent their bodies laterally and curled and extended their tails to potentially act as a secondary propulsor and/or anti-slip device. In order to gain a more comprehensive understanding of the functional diversity and context-dependency of mudskipper crutching, we compared their kinematics on different combinations of substrate types (solid, mud, and dry sand) and inclines (0°, 10°, and 20°). In addition to increasing lateral bending on deformable and inclined substrates, we found that mudskippers increased the relative contact time and contact area of their paired fins, while becoming more crouched, which are responses comparable to those seen in tetrapods and other amphibious fish. Mudskippers on these substrates also exhibited previously undocumented behaviors, such as extending and adpressing the distal portions of their pectoral fins more anteriorly, dorsoventrally bending their trunk, “belly-flopping” on sand, and “gripping” the mud substrate with their pectoral fin rays. Our study highlights potential compensatory mechanisms shared among vertebrates in terrestrial environments while also illustrating that locomotor flexibility and even novelty can emerge when animals are challenged with environmental variation.

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2. Phosphorus availability and leaching losses in annual and perennial cropping systems in an upper US Midwest landscape

   https://doi.org/10.5061/dryad.8sf7m0cpx  

   Hussain, Mir Zaman ; Hamilton, Stephen ; Robertson, G. Philip ; Basso, Bruno ( January 2021 )

   Abstract

   Excessive phosphorus (P) applications to croplands can contribute to eutrophication of surface waters through surface runoff and subsurface (leaching) losses. We analyzed leaching losses of total dissolved P (TDP) from no-till corn, hybrid poplar (Populus nigra X P. maximowiczii), switchgrass (Panicum virgatum), miscanthus (Miscanthus giganteus), native grasses, and restored prairie, all planted in 2008 on former cropland in Michigan, USA. All crops except corn (13 kg P ha−1 year−1) were grown without P fertilization. Biomass was harvested at the end of each growing season except for poplar. Soil water at 1.2 m depth was sampled weekly to biweekly for TDP determination during March–November 2009–2016 using tension lysimeters. Soil test P (0–25 cm depth) was measured every autumn. Soil water TDP concentrations were usually below levels where eutrophication of surface waters is frequently observed (> 0.02 mg L−1) but often higher than in deep groundwater or nearby streams and lakes. Rates of P leaching, estimated from measured concentrations and modeled drainage, did not differ statistically among cropping systems across years; 7-year cropping system means ranged from 0.035 to 0.072 kg P ha−1 year−1 with large interannual variation. Leached P was positively related to STP, which decreased over the 7 years in all systems. These results indicate that both P-fertilized and unfertilized cropping systems may leach legacy P from past cropland management.
   

   Methods

   Experimental details The Biofuel Cropping System Experiment (BCSE) is located at the W.K. Kellogg Biological Station (KBS) (42.3956° N, 85.3749° W; elevation 288 m asl) in southwestern Michigan, USA. This site is a part of the Great Lakes Bioenergy Research Center (www.glbrc.org) and is a Long-term Ecological Research site (www.lter.kbs.msu.edu). Soils are mesic Typic Hapludalfs developed on glacial outwash54 with high sand content (76% in the upper 150 cm) intermixed with silt-rich loess in the upper 50 cm55. The water table lies approximately 12–14 m below the surface. The climate is humid temperate with a mean annual air temperature of 9.1 °C and annual precipitation of 1005 mm, 511 mm of which falls between May and September (1981–2010)56,57. The BCSE was established as a randomized complete block design in 2008 on preexisting farmland. Prior to BCSE establishment, the field was used for grain crop and alfalfa (Medicago sativa L.) production for several decades. Between 2003 and 2007, the field received a total of ~ 300 kg P ha−1 as manure, and the southern half, which contains one of four replicate plots, received an additional 206 kg P ha−1 as inorganic fertilizer. The experimental design consists of five randomized blocks each containing one replicate plot (28 by 40 m) of 10 cropping systems (treatments) (Supplementary Fig. S1; also see Sanford et al.58). Block 5 is not included in the present study. Details on experimental design and site history are provided in Robertson and Hamilton57 and Gelfand et al.59. Leaching of P is analyzed in six of the cropping systems: (i) continuous no-till corn, (ii) switchgrass, (iii) miscanthus, (iv) a mixture of five species of native grasses, (v) a restored native prairie containing 18 plant species (Supplementary Table S1), and (vi) hybrid poplar. Agronomic management Phenological cameras and field observations indicated that the perennial herbaceous crops emerged each year between mid-April and mid-May. Corn was planted each year in early May. Herbaceous crops were harvested at the end of each growing season with the timing depending on weather: between October and November for corn and between November and December for herbaceous perennial crops. Corn stover was harvested shortly after corn grain, leaving approximately 10 cm height of stubble above the ground. The poplar was harvested only once, as the culmination of a 6-year rotation, in the winter of 2013–2014. Leaf emergence and senescence based on daily phenological images indicated the beginning and end of the poplar growing season, respectively, in each year. Application of inorganic fertilizers to the different crops followed a management approach typical for the region (Table 1). Corn was fertilized with 13 kg P ha−1 year−1 as starter fertilizer (N-P-K of 19-17-0) at the time of planting and an additional 33 kg P ha−1 year−1 was added as superphosphate in spring 2015. Corn also received N fertilizer around the time of planting and in mid-June at typical rates for the region (Table 1). No P fertilizer was applied to the perennial grassland or poplar systems (Table 1). All perennial grasses (except restored prairie) were provided 56 kg N ha−1 year−1 of N fertilizer in early summer between 2010 and 2016; an additional 77 kg N ha−1 was applied to miscanthus in 2009. Poplar was fertilized once with 157 kg N ha−1 in 2010 after the canopy had closed. Sampling of subsurface soil water and soil for P determination Subsurface soil water samples were collected beneath the root zone (1.2 m depth) using samplers installed at approximately 20 cm into the unconsolidated sand of 2Bt2 and 2E/Bt horizons (soils at the site are described in Crum and Collins54). Soil water was collected from two kinds of samplers: Prenart samplers constructed of Teflon and silica (http://www.prenart.dk/soil-water-samplers/) in replicate blocks 1 and 2 and Eijkelkamp ceramic samplers (http://www.eijkelkamp.com) in blocks 3 and 4 (Supplementary Fig. S1). The samplers were installed in 2008 at an angle using a hydraulic corer, with the sampling tubes buried underground within the plots and the sampler located about 9 m from the plot edge. There were no consistent differences in TDP concentrations between the two sampler types. Beginning in the 2009 growing season, subsurface soil water was sampled at weekly to biweekly intervals during non-frozen periods (April–November) by applying 50 kPa of vacuum to each sampler for 24 h, during which the extracted water was collected in glass bottles. Samples were filtered using different filter types (all 0.45 µm pore size) depending on the volume of leachate collected: 33-mm dia. cellulose acetate membrane filters when volumes were less than 50 mL; and 47-mm dia. Supor 450 polyethersulfone membrane filters for larger volumes. Total dissolved phosphorus (TDP) in water samples was analyzed by persulfate digestion of filtered samples to convert all phosphorus forms to soluble reactive phosphorus, followed by colorimetric analysis by long-pathlength spectrophotometry (UV-1800 Shimadzu, Japan) using the molybdate blue method60, for which the method detection limit was ~ 0.005 mg P L−1. Between 2009 and 2016, soil samples (0–25 cm depth) were collected each autumn from all plots for determination of soil test P (STP) by the Bray-1 method61, using as an extractant a dilute hydrochloric acid and ammonium fluoride solution, as is recommended for neutral to slightly acidic soils. The measured STP concentration in mg P kg−1 was converted to kg P ha−1 based on soil sampling depth and soil bulk density (mean, 1.5 g cm−3). Sampling of water samples from lakes, streams and wells for P determination In addition to chemistry of soil and subsurface soil water in the BCSE, waters from lakes, streams, and residential water supply wells were also sampled during 2009–2016 for TDP analysis using Supor 450 membrane filters and the same analytical method as for soil water. These water bodies are within 15 km of the study site, within a landscape mosaic of row crops, grasslands, deciduous forest, and wetlands, with some residential development (Supplementary Fig. S2, Supplementary Table S2). Details of land use and cover change in the vicinity of KBS are given in Hamilton et al.48, and patterns in nutrient concentrations in local surface waters are further discussed in Hamilton62. Leaching estimates, modeled drainage, and data analysis Leaching was estimated at daily time steps and summarized as total leaching on a crop-year basis, defined from the date of planting or leaf emergence in a given year to the day prior to planting or emergence in the following year. TDP concentrations (mg L−1) of subsurface soil water were linearly interpolated between sampling dates during non-freezing periods (April–November) and over non-sampling periods (December–March) based on the preceding November and subsequent April samples. Daily rates of TDP leaching (kg ha−1) were calculated by multiplying concentration (mg L−1) by drainage rates (m3 ha−1 day−1) modeled by the Systems Approach for Land Use Sustainability (SALUS) model, a crop growth model that is well calibrated for KBS soil and environmental conditions. SALUS simulates yield and environmental outcomes in response to weather, soil, management (planting dates, plant population, irrigation, N fertilizer application, and tillage), and genetics63. The SALUS water balance sub-model simulates surface runoff, saturated and unsaturated water flow, drainage, root water uptake, and evapotranspiration during growing and non-growing seasons63. The SALUS model has been used in studies of evapotranspiration48,51,64 and nutrient leaching20,65,66,67 from KBS soils, and its predictions of growing-season evapotranspiration are consistent with independent measurements based on growing-season soil water drawdown53 and evapotranspiration measured by eddy covariance68. Phosphorus leaching was assumed insignificant on days when SALUS predicted no drainage. Volume-weighted mean TDP concentrations in leachate for each crop-year and for the entire 7-year study period were calculated as the total dissolved P leaching flux (kg ha−1) divided by the total drainage (m3 ha−1). One-way ANOVA with time (crop-year) as the fixed factor was conducted to compare total annual drainage rates, P leaching rates, volume-weighted mean TDP concentrations, and maximum aboveground biomass among the cropping systems over all seven crop-years as well as with TDP concentrations from local lakes, streams, and groundwater wells. When a significant (α = 0.05) difference was detected among the groups, we used the Tukey honest significant difference (HSD) post-hoc test to make pairwise comparisons among the groups. In the case of maximum aboveground biomass, we used the Tukey–Kramer method to make pairwise comparisons among the groups because the absence of poplar data after the 2013 harvest resulted in unequal sample sizes. We also used the Tukey–Kramer method to compare the frequency distributions of TDP concentrations in all of the soil leachate samples with concentrations in lakes, streams, and groundwater wells, since each sample category had very different numbers of measurements.
   

   Other

   Individual spreadsheets in “data table_leaching_dissolved organic carbon and nitrogen.xls” 1.    annual precip_drainage 2.    biomass_corn, perennial grasses 3.    biomass_poplar 4.    annual N leaching _vol-wtd conc 5.    Summary_N leached 6.    annual DOC leachin_vol-wtd conc 7.    growing season length 8.    correlation_nh4 VS no3 9.    correlations_don VS no3_doc VS don Each spreadsheet is described below along with an explanation of variates. Note that ‘nan’ indicate data are missing or not available. First row indicates header; second row indicates units 1. Spreadsheet: annual precip_drainage Description: Precipitation measured from nearby Kellogg Biological Station (KBS) Long Term Ecological Research (LTER) Weather station, over 2009-2016 study period. Data shown in Figure 1; original data source for precipitation (https://lter.kbs.msu.edu/datatables/7). Drainage estimated from SALUS crop model. Note that drainage is percolation out of the root zone (0-125 cm). Annual precipitation and drainage values shown here are calculated for growing and non-growing crop periods. Variate    Description year    year of the observation crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” precip_G    precipitation during growing period (milliMeter) precip_NG    precipitation during non-growing period (milliMeter) drainage_G    drainage during growing period (milliMeter) drainage_NG    drainage during non-growing period (milliMeter)      2. Spreadsheet: biomass_corn, perennial grasses Description: Maximum aboveground biomass measurements from corn, switchgrass, miscanthus, native grass and restored prairie plots in Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2009-2015. Data shown in Figure 2.   Variate    Description year    year of the observation date    day of the observation (mm/dd/yyyy) crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” replicate    each crop has four replicated plots, R1, R2, R3 and R4 station    stations (S1, S2 and S3) of samplings within the plot. For more details, refer to link (https://data.sustainability.glbrc.org/protocols/156) species    plant species that are rooted within the quadrat during the time of maximum biomass harvest. See protocol for more information, refer to link (http://lter.kbs.msu.edu/datatables/36) For maize biomass, grain and whole biomass reported in the paper (weed biomass or surface litter are excluded). Surface litter biomass not included in any crops; weed biomass not included in switchgrass and miscanthus, but included in grass mixture and prairie. fraction    Fraction of biomass biomass_plot    biomass per plot on dry-weight basis (Grams_Per_SquareMeter) biomass_ha    biomass (megaGrams_Per_Hectare) by multiplying column biomass per plot with 0.01 3. Spreadsheet: biomass_poplar Description: Maximum aboveground biomass measurements from poplar plots in Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2009-2015. Data shown in Figure 2. Note that poplar biomass was estimated from crop growth curves until the poplar was harvested in the winter of 2013-14. Variate    Description year    year of the observation method    methods of poplar biomass sampling date    day of the observation (mm/dd/yyyy) replicate    each crop has four replicated plots, R1, R2, R3 and R4 diameter_at_ground    poplar diameter (milliMeter) at the ground diameter_at_15cm    poplar diameter (milliMeter) at 15 cm height biomass_tree    biomass per plot (Grams_Per_Tree) biomass_ha    biomass (megaGrams_Per_Hectare) by multiplying biomass per tree with 0.01 4. Spreadsheet: annual N leaching_vol-wtd conc Description: Annual leaching rate (kiloGrams_N_Per_Hectare) and volume-weighted mean N concentrations (milliGrams_N_Per_Liter) of nitrate (no3) and dissolved organic nitrogen (don) in the leachate samples collected from corn, switchgrass, miscanthus, native grass, restored prairie and poplar plots in Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2009-2016. Data for nitrogen leached and volume-wtd mean N concentration shown in Figure 3a and Figure 3b, respectively. Note that ammonium (nh4) concentration were much lower and often undetectable (<0.07 milliGrams_N_Per_Liter). Also note that in 2009 and 2010 crop-years, data from some replicates are missing.    Variate    Description crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” crop-year    year of the observation replicate    each crop has four replicated plots, R1, R2, R3 and R4 no3 leached    annual leaching rates of nitrate (kiloGrams_N_Per_Hectare) don leached    annual leaching rates of don (kiloGrams_N_Per_Hectare) vol-wtd no3 conc.    Volume-weighted mean no3 concentration (milliGrams_N_Per_Liter) vol-wtd don conc.    Volume-weighted mean don concentration (milliGrams_N_Per_Liter) 5. Spreadsheet: summary_N leached Description: Summary of total amount and forms of N leached (kiloGrams_N_Per_Hectare) and the percent of applied N lost to leaching over the seven years for corn, switchgrass, miscanthus, native grass, restored prairie and poplar plots in Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2009-2016. Data for nitrogen amount leached shown in Figure 4a and percent of applied N lost shown in Figure 4b. Note the fraction of unleached N includes in harvest, accumulation in root biomass, soil organic matter or gaseous N emissions were not measured in the study. Variate    Description crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” no3 leached    annual leaching rates of nitrate (kiloGrams_N_Per_Hectare) don leached    annual leaching rates of don (kiloGrams_N_Per_Hectare) N unleached    N unleached (kiloGrams_N_Per_Hectare) in other sources are not studied % of N applied N lost to leaching    % of N applied N lost to leaching 6. Spreadsheet: annual DOC leachin_vol-wtd conc Description: Annual leaching rate (kiloGrams_Per_Hectare) and volume-weighted mean N concentrations (milliGrams_Per_Liter) of dissolved organic carbon (DOC) in the leachate samples collected from corn, switchgrass, miscanthus, native grass, restored prairie and poplar plots in Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2009-2016. Data for DOC leached and volume-wtd mean DOC concentration shown in Figure 5a and Figure 5b, respectively. Note that in 2009 and 2010 crop-years, water samples were not available for DOC measurements.     Variate    Description crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” crop-year    year of the observation replicate    each crop has four replicated plots, R1, R2, R3 and R4 doc leached    annual leaching rates of nitrate (kiloGrams_Per_Hectare) vol-wtd doc conc.    volume-weighted mean doc concentration (milliGrams_Per_Liter) 7. Spreadsheet: growing season length Description: Growing season length (days) of corn, switchgrass, miscanthus, native grass, restored prairie and poplar plots in the Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2009-2015. Date shown in Figure S2. Note that growing season is from the date of planting or emergence to the date of harvest (or leaf senescence in case of poplar).   Variate    Description crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” year    year of the observation growing season length    growing season length (days) 8. Spreadsheet: correlation_nh4 VS no3 Description: Correlation of ammonium (nh4+) and nitrate (no3-) concentrations (milliGrams_N_Per_Liter) in the leachate samples from corn, switchgrass, miscanthus, native grass, restored prairie and poplar plots in Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2013-2015. Data shown in Figure S3. Note that nh4+ concentration in the leachates was very low compared to no3- and don concentration and often undetectable in three crop-years (2013-2015) when measurements are available. Variate    Description crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” date    date of the observation (mm/dd/yyyy) replicate    each crop has four replicated plots, R1, R2, R3 and R4 nh4 conc    nh4 concentration (milliGrams_N_Per_Liter) no3 conc    no3 concentration (milliGrams_N_Per_Liter)   9. Spreadsheet: correlations_don VS no3_doc VS don Description: Correlations of don and nitrate concentrations (milliGrams_N_Per_Liter); and doc (milliGrams_Per_Liter) and don concentrations (milliGrams_N_Per_Liter) in the leachate samples of corn, switchgrass, miscanthus, native grass, restored prairie and poplar plots in Great Lakes Bioenergy Research Center (GLBRC) Biomass Cropping System Experiment (BCSE) during 2013-2015. Data of correlation of don and nitrate concentrations shown in Figure S4 a and doc and don concentrations shown in Figure S4 b. Variate    Description crop    “corn” “switchgrass” “miscanthus” “nativegrass” “restored prairie” “poplar” year    year of the observation don    don concentration (milliGrams_N_Per_Liter) no3     no3 concentration (milliGrams_N_Per_Liter) doc    doc concentration (milliGrams_Per_Liter)
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3. Florida mangrove saltmarsh reference surface soils

   https://doi.org/10.6073/pasta/0e08cbe07c84488cb7b9dd16669946d0  

   Lewis, David Bruce ( January 2021 )

   Abstract

   Site description. This data package consists of data obtained from sampling surface soil (the 0-7.6 cm depth profile) in black mangrove (Avicennia germinans) dominated forest and black needlerush (Juncus roemerianus) saltmarsh along the Gulf of Mexico coastline in peninsular west-central Florida, USA. This location has a subtropical climate with mean daily temperatures ranging from 15.4 °C in January to 27.8 °C in August, and annual precipitation of 1336 mm. Precipitation falls as rain primarily between June and September. Tides are semi-diurnal, with 0.57 m median amplitudes during the year preceding sampling (U.S. NOAA National Ocean Service, Clearwater Beach, Florida, station 8726724). Sea-level rise is 4.0 ± 0.6 mm per year (1973-2020 trend, mean ± 95 % confidence interval, NOAA NOS Clearwater Beach station). The A. germinans mangrove zone is either adjacent to water or fringed on the seaward side by a narrow band of red mangrove (Rhizophora mangle). A near-monoculture of J. roemerianus is often adjacent to and immediately landward of the A. germinans zone. The transition from the mangrove to the J. roemerianus zone is variable in our study area. An abrupt edge between closed-canopy mangrove and J. roemerianus monoculture may extend for up to several hundred meters in some locations, while other stretches of ecotone present a gradual transition where smaller, widely spaced trees are interspersed into the herbaceous marsh. Juncus roemerianus then extends landward to a high marsh patchwork of succulent halophytes (including Salicornia bigellovi, Sesuvium sp., and Batis maritima), scattered dwarf mangrove, and salt pans, followed in turn by upland vegetation that includes Pinus sp. and Serenoa repens. Field design and sample collection. We established three study sites spaced at approximately 5 km intervals along the western coastline of the central Florida peninsula. The sites consisted of the Salt Springs (28.3298°, -82.7274°), Energy Marine Center (28.2903°, -82.7278°), and Green Key (28.2530°, -82.7496°) sites on the Gulf of Mexico coastline in Pasco County, Florida, USA. At each site, we established three plot pairs, each consisting of one saltmarsh plot and one mangrove plot. Plots were 50 m^2 in size. Plots pairs within a site were separated by 230-1070 m, and the mangrove and saltmarsh plots composing a pair were 70-170 m apart. All plot pairs consisted of directly adjacent patches of mangrove forest and J. roemerianus saltmarsh, with the mangrove forests exhibiting a closed canopy and a tree architecture (height 4-6 m, crown width 1.5-3 m). Mangrove plots were located at approximately the midpoint between the seaward edge (water-mangrove interface) and landward edge (mangrove-marsh interface) of the mangrove zone. Saltmarsh plots were located 20-25 m away from any mangrove trees and into the J. roemerianus zone (i.e., landward from the mangrove-marsh interface). Plot pairs were coarsely similar in geomorphic setting, as all were located on the Gulf of Mexico coastline, rather than within major sheltering formations like Tampa Bay, and all plot pairs fit the tide-dominated domain of the Woodroffe classification (Woodroffe, 2002, "Coasts: Form, Process and Evolution", Cambridge University Press), given their conspicuous semi-diurnal tides. There was nevertheless some geomorphic variation, as some plot pairs were directly open to the Gulf of Mexico while others sat behind keys and spits or along small tidal creeks. Our use of a plot-pair approach is intended to control for this geomorphic variation. Plot center elevations (cm above mean sea level, NAVD 88) were estimated by overlaying the plot locations determined with a global positioning system (Garmin GPS 60, Olathe, KS, USA) on a LiDAR-derived bare-earth digital elevation model (Dewberry, Inc., 2019). The digital elevation model had a vertical accuracy of ± 10 cm (95 % CI) and a horizontal accuracy of ± 116 cm (95 % CI). Soil samples were collected via coring at low tide in June 2011. From each plot, we collected a composite soil sample consisting of three discrete 5.1 cm diameter soil cores taken at equidistant points to 7.6 cm depth. Cores were taken by tapping a sleeve into the soil until its top was flush with the soil surface, sliding a hand under the core, and lifting it up. Cores were then capped and transferred on ice to our laboratory at the University of South Florida (Tampa, Florida, USA), where they were combined in plastic zipper bags, and homogenized by hand into plot-level composite samples on the day they were collected. A damp soil subsample was immediately taken from each composite sample to initiate 1 y incubations for determination of active C and N (see below). The remainder of each composite sample was then placed in a drying oven (60 °C) for 1 week with frequent mixing of the soil to prevent aggregation and liberate water. Organic wetland soils are sometimes dried at 70 °C, however high drying temperatures can volatilize non-water liquids and oxidize and decompose organic matter, so 50 °C is also a common drying temperature for organic soils (Gardner 1986, "Methods of Soil Analysis: Part 1", Soil Science Society of America); we accordingly chose 60 °C as a compromise between sufficient water removal and avoidance of non-water mass loss. Bulk density was determined as soil dry mass per core volume (adding back the dry mass equivalent of the damp subsample removed prior to drying). Dried subsamples were obtained for determination of soil organic matter (SOM), mineral texture composition, and extractable and total carbon (C) and nitrogen (N) within the following week. Sample analyses. A dried subsample was apportioned from each composite sample to determine SOM as mass loss on ignition at 550 °C for 4 h. After organic matter was removed from soil via ignition, mineral particle size composition was determined using a combination of wet sieving and density separation in 49 mM (3 %) sodium hexametaphosphate ((NaPO_3)_6) following procedures in Kettler et al. (2001, Soil Science Society of America Journal 65, 849-852). The percentage of dry soil mass composed of silt and clay particles (hereafter, fines) was calculated as the mass lost from dispersed mineral soil after sieving (0.053 mm mesh sieve). Fines could have been slightly underestimated if any clay particles were burned off during the preceding ignition of soil. An additional subsample was taken from each composite sample to determine extractable N and organic C concentrations via 0.5 M potassium sulfate (K_2SO_4) extractions. We combined soil and extractant (ratio of 1 g dry soil:5 mL extractant) in plastic bottles, reciprocally shook the slurry for 1 h at 120 rpm, and then gravity filtered it through Fisher G6 (1.6 μm pore size) glass fiber filters, followed by colorimetric detection of nitrite (NO_2^-) + nitrate (NO_3^-) and ammonium (NH_4^+) in the filtrate (Hood Nowotny et al., 2010,Soil Science Society of America Journal 74, 1018-1027) using a microplate spectrophotometer (Biotek Epoch, Winooski, VT, USA). Filtrate was also analyzed for dissolved organic C (referred to hereafter as extractable organic C) and total dissolved N via combustion and oxidation followed by detection of the evolved CO_2 and N oxide gases on a Formacs HT TOC/TN analyzer (Skalar, Breda, The Netherlands). Extractable organic N was then computed as total dissolved N in filtrate minus extractable mineral N (itself the sum of extractable NH_4-N and NO_2-N + NO_3-N). We determined soil total C and N from dried, milled subsamples subjected to elemental analysis (ECS 4010, Costech, Inc., Valencia, CA, USA) at the University of South Florida Stable Isotope Laboratory. Median concentration of inorganic C in unvegetated surface soil at our sites is 0.5 % of soil mass (Anderson, 2019, Univ. of South Florida M.S. thesis via methods in Wang et al., 2011, Environmental Monitoring and Assessment 174, 241-257). Inorganic C concentrations are likely even lower in our samples from under vegetation, where organic matter would dilute the contribution of inorganic C to soil mass. Nevertheless, the presence of a small inorganic C pool in our soils may be counted in the total C values we report. Extractable organic C is necessarily of organic C origin given the method (sparging with HCl) used in detection. Active C and N represent the fractions of organic C and N that are mineralizable by soil microorganisms under aerobic conditions in long-term soil incubations. To quantify active C and N, 60 g of field-moist soil were apportioned from each composite sample, placed in a filtration apparatus, and incubated in the dark at 25 °C and field capacity moisture for 365 d (as in Lewis et al., 2014, Ecosphere 5, art59). Moisture levels were maintained by frequently weighing incubated soil and wetting them up to target mass. Daily CO_2 flux was quantified on 29 occasions at 0.5-3 week intervals during the incubation period (with shorter intervals earlier in the incubation), and these per day flux rates were integrated over the 365 d period to compute an estimate of active C. Observations of per day flux were made by sealing samples overnight in airtight chambers fitted with septa and quantifying headspace CO_2 accumulation by injecting headspace samples (obtained through the septa via needle and syringe) into an infrared gas analyzer (PP Systems EGM 4, Amesbury, MA, USA). To estimate active N, each incubated sample was leached with a C and N free, 35 psu solution containing micronutrients (Nadelhoffer, 1990, Soil Science Society of America Journal 54, 411-415) on 19 occasions at increasing 1-6 week intervals during the 365 d incubation, and then extracted in 0.5 M K_2SO_4 at the end of the incubation in order to remove any residual mineral N. Active N was then quantified as the total mass of mineral N leached and extracted. Mineral N in leached and extracted solutions was detected as NH_4-N and NO_2-N + NO_3-N via colorimetry as above. This incubation technique precludes new C and N inputs and persistently leaches mineral N, forcing microorganisms to meet demand by mineralizing existing pools, and thereby directly assays the potential activity of soil organic C and N pools present at the time of soil sampling. Because this analysis commences with disrupting soil physical structure, it is biased toward higher estimates of active fractions. Calculations. Non-mobile C and N fractions were computed as total C and N concentrations minus the extractable and active fractions of each element. This data package reports surface-soil constituents (moisture, fines, SOM, and C and N pools and fractions) in both gravimetric units (mass constituent / mass soil) and areal units (mass constituent / soil surface area integrated through 7.6 cm soil depth, the depth of sampling). Areal concentrations were computed as X × D × 7.6, where X is the gravimetric concentration of a soil constituent, D is soil bulk density (g dry soil / cm^3), and 7.6 is the sampling depth in cm.
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4. Embedding properties of network realizations of dissipative reduced order models

   Druskin, Guddati ( July 2022 , HOUSEHOLDER SYMPOSIUM XXI)

   Embedding properties of network realizations of dissipative reduced order models Jörn Zimmerling, Mikhail Zaslavsky,Rob Remis, Shasri Moskow, Alexander Mamonov, Murthy Guddati, Vladimir Druskin, and Liliana Borcea Mathematical Sciences Department, Worcester Polytechnic Institute https://www.wpi.edu/people/vdruskin Abstract Realizations of reduced order models of passive SISO or MIMO LTI problems can be transformed to tridiagonal and block-tridiagonal forms, respectively, via dierent modications of the Lanczos algorithm. Generally, such realizations can be interpreted as ladder resistor-capacitor-inductor (RCL) networks. They gave rise to network syntheses in the rst half of the 20th century that was at the base of modern electronics design and consecutively to MOR that tremendously impacted many areas of engineering (electrical, mechanical, aerospace, etc.) by enabling ecient compression of the underlining dynamical systems. In his seminal 1950s works Krein realized that in addition to their compressing properties, network realizations can be used to embed the data back into the state space of the underlying continuum problems. In more recent works of the authors Krein's ideas gave rise to so-called nite-dierence Gaussian quadrature rules (FDGQR), allowing to approximately map the ROM state-space representation to its full order continuum counterpart on a judicially chosen grid. Thus, the state variables can be accessed directly from themore »transfer function without solving the full problem and even explicit knowledge of the PDE coecients in the interior, i.e., the FDGQR directly learns" the problem from its transfer function. This embedding property found applications in PDE solvers, inverse problems and unsupervised machine learning. Here we show a generalization of this approach to dissipative PDE problems, e.g., electromagnetic and acoustic wave propagation in lossy dispersive media. Potential applications include solution of inverse scattering problems in dispersive media, such as seismic exploration, radars and sonars. To x the idea, we consider a passive irreducible SISO ROM fn(s) = Xn j=1 yi s + σj , (62) assuming that all complex terms in (62) come in conjugate pairs. We will seek ladder realization of (62) as rjuj + vj − vj−1 = −shˆjuj , uj+1 − uj + ˆrj vj = −shj vj , (63) for j = 0, . . . , n with boundary conditions un+1 = 0, v1 = −1, and 4n real parameters hi, hˆi, ri and rˆi, i = 1, . . . , n, that can be considered, respectively, as the equivalent discrete inductances, capacitors and also primary and dual conductors. Alternatively, they can be viewed as respectively masses, spring stiness, primary and dual dampers of a mechanical string. Reordering variables would bring (63) into tridiagonal form, so from the spectral measure given by (62 ) the coecients of (63) can be obtained via a non-symmetric Lanczos algorithm written in J-symmetric form and fn(s) can be equivalently computed as fn(s) = u1. The cases considered in the original FDGQR correspond to either (i) real y, θ or (ii) real y and imaginary θ. Both cases are covered by the Stieltjes theorem, that yields in case (i) real positive h, hˆ and trivial r, rˆ, and in case (ii) real positive h,r and trivial hˆ,rˆ. This result allowed us a simple interpretation of (62) as the staggered nite-dierence approximation of the underlying PDE problem [2]. For PDEs in more than one variables (including topologically rich data-manifolds), a nite-dierence interpretation is obtained via a MIMO extensions in block form, e.g., [4, 3]. The main diculty of extending this approach to general passive problems is that the Stieltjes theory is no longer applicable. Moreover, the tridiagonal realization of a passive ROM transfer function (62) via the ladder network (63) cannot always be obtained in port-Hamiltonian form, i.e., the equivalent primary and dual conductors may change sign [1]. 100 Embedding of the Stieltjes problems, e.g., the case (i) was done by mapping h and hˆ into values of acoustic (or electromagnetic) impedance at grid cells, that required a special coordinate stretching (known as travel time coordinate transform) for continuous problems. Likewise, to circumvent possible non-positivity of conductors for the non-Stieltjes case, we introduce an additional complex s-dependent coordinate stretching, vanishing as s → ∞ [1]. This stretching applied in the discrete setting induces a diagonal factorization, removes oscillating coecients, and leads to an accurate embedding for moderate variations of the coecients of the continuum problems, i.e., it maps discrete coecients onto the values of their continuum counterparts. Not only does this embedding yields an approximate linear algebraic algorithm for the solution of the inverse problems for dissipative PDEs, it also leads to new insight into the properties of their ROM realizations. We will also discuss another approach to embedding, based on Krein-Nudelman theory [5], that results in special data-driven adaptive grids. References [1] Borcea, Liliana and Druskin, Vladimir and Zimmerling, Jörn, A reduced order model approach to inverse scattering in lossy layered media, Journal of Scientic Computing, V. 89, N1, pp. 136,2021 [2] Druskin, Vladimir and Knizhnerman, Leonid, Gaussian spectral rules for the three-point second dierences: I. A two-point positive denite problem in a semi-innite domain, SIAM Journal on Numerical Analysis, V. 37, N 2, pp.403422, 1999 [3] Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Distance preserving model order reduction of graph-Laplacians and cluster analysis, Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Journal of Scientic Computing, V. 90, N 1, pp 130, 2022 [4] Druskin, Vladimir and Moskow, Shari and Zaslavsky, Mikhail LippmannSchwingerLanczos algorithm for inverse scattering problems, Inverse Problems, V. 37, N. 7, 2021, [5] Mark Adolfovich Nudelman The Krein String and Characteristic Functions of Maximal Dissipative Operators, Journal of Mathematical Sciences, 2004, V 124, pp 49184934 Go back to Plenary Speakers Go back to Speakers Go back« less
5. Macroscopic Models for Human Circadian Rhythms

   https://doi.org/10.1177/0748730419878298  

   Hannay, Kevin M. ; Booth, Victoria ; Forger, Daniel B. ( December 2019 , Journal of Biological Rhythms)

   Mathematical models have a long and influential history in the study of human circadian rhythms. Accurate predictive models for the human circadian light response have been used to study the impact of a host of light exposures on the circadian system. However, generally, these models do not account for the physiological basis of these rhythms. We illustrate a new paradigm for deriving models of the human circadian light response. Beginning from a high-dimensional model of the circadian neural network, we systematically derive low-dimensional models using an approach motivated by experimental measurements of circadian neurons. This systematic reduction allows for the variables and parameters of the derived model to be interpreted in a physiological context. We fit and validate the resulting models to a library of experimental measurements. Finally, we compare model predictions for experimental measurements of light levels and discuss the differences between our model’s predictions and previous models. Our modeling paradigm allows for the integration of experimental measurements across the single-cell, tissue, and behavioral scales, thereby enabling the development of accurate low-dimensional models for human circadian rhythms.