Enumerating (2+2)-free posets by indistinguishable elements

A poset is said to be (2+2)-free if it does not contain an induced subposet that is isomorphic to 2+2, the union of two disjoint 2-element chains. Two elements in a poset are indistinguishable if they have the same strict up-set and the same strict down-set. Being indistinguishable defines an equivalence relation on the elements of the poset. We introduce the statistic maxindist, the maximum size of a set of indistinguishable elements. We show that, under a bijection of Bousquet-Melou et al., indistinguishable elements correspond to letters that belong to the same run in the so-called ascent sequence corresponding to the poset. We derive the generating function for the number of (2+2)-free posets with respect to both maxindist and the number of different strict down-sets of elements in the poset. Moreover, we show that (2+2)-free posets P with maxindist(P) at most k are in bijection with upper triangular matrices of nonnegative integers not exceeding k, where each row and each column contains a nonzero entry. (Here we consider isomorphic posets to be equal.) In particular, (2+2)-free posets P on n elements with maxindist(P)=1 correspond to upper triangular binary matrices where each row and column contains a nonzero entry, and whose entries sum to n. We derive a generating function counting such matrices, which confirms a conjecture of Jovovic, and we refine the generating function to count upper triangular matrices consisting of nonnegative integers not exceeding k and having a nonzero entry in each row and column. That refined generating function also enumerates (2+2)-free posets according to maxindist. Finally, we link our enumerative results to certain restricted permutations and matrices.Comment: 16 page

The Responses of Soil and Rhizosphere Respiration to Simulated Climatic Changes Vary by Season.

Responses of soil respiration (Rs) to anthropogenic climate change will affect terrestrial carbon storage and, thus, feed back to warming. To provide insight into how warming and changes in precipitation regimes affect the rate and temperature sensitivity of Rs and rhizosphere respiration (Rr) across the year, we subjected a New England old-field ecosystem to four levels of warming and three levels of precipitation (ambient, drought, and wet treatments). We measured Rs and heterotrophic respiration (Rh) monthly (in areas of the plots with and without plants, respectively) and estimated Rr by calculating the difference in respiration between Rs and Rh. Even in this mesic ecosystem, Rs and Rr responded strongly to the precipitation treatments. Drought reduced Rs and Rr, both annually and during the growing season. Annual cumulative Rs responded nonlinearly to precipitation treatments; both drought and supplemental precipitation suppressed Rs compared to the ambient treatment. Warming increased Rs and Rr in spring and winter when soil moisture was optimal but decreased these rates in summer when moisture was limiting. Cumulative winter Rr increased by about 200% in the high warming (approximately 3.5 degrees C) treatment. The effect of climate treatments on the temperature sensitivity of Rs depended on the season. In the fall, the drought treatment decreased apparent Q10 relative to the other precipitation treatments. The responses of Rs to warming and altered precipitation were largely driven by changes in Rr. We emphasize the importance of incorporating realistic soil moisture responses into simulations of soil carbon fluxes; the long-term effects of warming on carbon--climate feedback will depend on future precipitation regimes. Our results highlight the nonlinear responses of soil respiration to soil moisture and, to our knowledge, quantify for the first time the loss of carbon through winter rhizosphere respiration due to warming. While this additional loss is small relative to the cumulative annual flux in this system, such increases in rhizosphere respiration during the non-growing season could have greater consequences in ecosystems where they offset or reduce subsequent warming-induced gains in plant growth

Precipitation Variability and Nitrogen Deposition Alter Root Distribution in a Tallgrass Prairie

Climate change and increases in nitrogen deposition impact ecosystems globally. Projected atmospheric warming allows rain to fall in larger events with longer dry periods in between, increasing rainfall variability in many regions. Concurrently, the combustion of fossil fuels and the heavy use of nitrogen fertilizers continue to increase the availability of nitrogen globally. However, not much is known about how these global change factors, increased rainfall variability and nitrogen deposition, interact with each other to affect ecosystem functions, particularly belowground where root production contributes to soil carbon pools- an important component in regulating climate. In order to study these factors, we used partial rainout shelters and a nitrogen fertilizer in a tallgrass prairie dominated by Schizachyrium scoparium, a C4 grass, and Solidago canadensis, a rhizomatous C3 forb. We simulated increased rainfall variability by equalizing cumulative rainfall across sheltered and unsheltered plots every 30 days. Slow-release urea was applied after the first watering event to experimentally increase nitrogen availability. Root density was determined by taking two 70cm soil cores from each plot. We found increased precipitation variability shifted belowground biomass to shallower depths, while increasing nitrogen availability shifted belowground biomass deeper. To get more conclusive results, we are continuing to run this experiment with another set of soil cores in order to confirm the effects of increased rainfall variability and nitrogen levels on belowground biomass

Enumerating (2+2)-free posets by the number of minimal elements and other statistics

An unlabeled poset is said to be (2+2)-free if it does not contain an induced subposet that is isomorphic to 2+2, the union of two disjoint 2-element chains. Let $p_n$ denote the number of (2+2)-free posets of size $n$. In a recent paper, Bousquet-M\'elou et al.\cite{BCDK} found, using so called ascent sequences, the generating function for the number of (2+2)-free posets of size $n$: $P(t)=\sum_{n \geq 0} p_n t^n = \sum_{n\geq 0} \prod_{i=1}^{n} (1-(1-t)^i)$. We extend this result in two ways. First, we find the generating function for (2+2)-free posets when four statistics are taken into account, one of which is the number of minimal elements in a poset. Second, we show that if $p_{n,k}$ equals the number of (2+2)-free posets of size $n$ with $k$ minimal elements, then $P(t,z)=\sum_{n,k \geq 0} p_{n,k} t^n z^k = 1+ \sum_{n \geq 0} \frac{zt}{(1-zt)^{n+1}} \prod_{i=1}^n (1-(1-t)^i)$. The second result cannot be derived from the first one by a substitution. On the other hand, $P(t)$ can easily be obtained from $P(t,z)$ thus providing an alternative proof for the enumeration result in \cite{BCDK}. Moreover, we conjecture a simpler form of writing $P(t,z)$. Our enumeration results are extended to certain restricted permutations and to regular linearized chord diagrams through bijections in \cite{BCDK,cdk}. Finally, we define a subset of ascent sequences counted by the Catalan numbers and we discuss its relations with (2+2)- and (3+1)-free posets

Climate Influences the Content and Chemical Composition of Foliar Tannins in Green and Senesced Tissues of \u3ci\u3eQuercus rubra\u3c/i\u3e

Environmental stresses not only influence production of plant metabolites but could also modify their resorption during leaf senescence. The production-resorption dynamics of polyphenolic tannins, a class of defense compound whose ecological role extends beyond tissue senescence, could amplify the influence of climate on ecosystem processes. We studied the quantity, chemical composition, and tissue-association of tannins in green and freshly-senesced leaves of Quercus rubra exposed to different temperature (Warming and No Warming) and precipitation treatments (Dry, Ambient, Wet) at the Boston-Area Climate Experiment (BACE) in Massachusetts, USA. Climate influenced not only the quantity of tannins, but also their molecular composition and cell-wall associations. Irrespective of climatic treatments, tannin composition in Q. rubra was dominated by condensed tannins (CTs, proanthocyanidins). When exposed to Dry and Ambient*Warm conditions, Q. rubra produced higher quantities of tannins that were less polymerized. In contrast, under favorable conditions (Wet), tannins were produced in lower quantities, but the CTs were more polymerized. Further, even as the overall tissue tannin content declined, the content of hydrolysable tannins (HTs) increased under Wet treatments. The molecular composition of tannins influenced their content in senesced litter. Compared to the green leaves, the content of HTs decreased in senesced leaves across treatments, whereas the CT content was similar between green and senesced leaves in Wet treatments that produced more polymerized tannins. The content of total tannins in senesced leaves was higher in Warming treatments under both dry and ambient precipitation treatments. Our results suggest that, though climate directly influenced the production of tannins in green tissues (and similar patterns were observed in the senesced tissue), the influence of climate on tannin content of senesced tissue was partly mediated by the effect on the chemical composition of tannins. These different climatic impacts on leaves over the course of a growing season may alter forest dynamics, not only in decomposition and nutrient cycling dynamics, but also in herbivory dynamics

Effects of Warming and Altered Precipitation on Plant and Nutrient Dynamics of a New England Salt Marsh.

Salt marsh structure and function, and consequently ability to support a range of species and to provide ecosystem services, may be affected by climate change. To better understand how salt marshes will respond to warming and associated shifts in precipitation, we conducted a manipulative experiment in a tidal salt marsh in Massachusetts, USA. We exposed two plant communities (one dominated by Spartina patens–Distichlis spicata and one dominated by short form Spartina alterniflora) to five climate manipulations: warming via passive open-topped chambers, doubled precipitation, warming and doubled precipitation, extreme drought via rainout shelter, and ambient conditions. Modest daytime warming increased total aboveground biomass of the S. alterniflora community (24%), but not the S. patens–D. spicata community. Warming also increased maximum stem heights of S. alterniflora (8%), S. patens (8%), and D. spicata (15%). Decomposition was marginally accelerated by warming in the S. alterniflora community. Drought markedly increased total biomass of the S. alterniflora community (53%) and live S. patens (69%), perhaps by alleviating waterlogging of sediments. Decomposition was accelerated by increased precipitation and slowed by drought, particularly in the S. patens–D. spicata community. Flowering phenology responded minimally to the treatments, and pore water salinity, sulfide, ammonium, and phosphate concentrations showed no treatment effects in either plant community. Our results suggest that these salt marsh communities may be resilient to modest amounts of warming and large changes in precipitation. If production increases under climate change, marshes will have a greater ability to keep pace with sea-level rise, although an increase in decomposition could offset this. As long as marshes are not inundated by flooding due to sea-level rise, increases in aboveground biomass and stem heights suggest that marshes may continue to export carbon and nutrients to coastal waters and may be able to increase their carbon storage capability by increasing plant growth under future climate conditions

Strong Response of an Invasive Plant Species (Centaurea solstitialis L.) to Global Environmental Changes.

Global environmental changes are altering interactions among plant species, sometimes favoring invasive species. Here, we examine how a suite of five environmental factors, singly and in combination, can affect the success of a highly invasive plant. We introduced Centaurea solstitialis L. (yellow starthistle), which is considered by many to be California’s most troublesome wildland weed, to grassland plots in the San Francisco Bay Area. These plots experienced ambient or elevated levels of warming, atmospheric CO2, precipitation, and nitrate deposition, and an accidental fire in the previous year created an additional treatment. Centaurea grew more than six times larger in response to elevated CO2, and, outside of the burned area, grew more than three times larger in response to nitrate deposition. In contrast, resident plants in the community responded less strongly (or did not respond) to these treatments. Interactive effects among treatments were rarely significant. Results from a parallel mesocosm experiment, while less dramatic, supported the pattern of results observed in the field. Taken together, our results suggest that ongoing environmental changes may dramatically increase Centaurea’s prevalence in western North America

Leaf-Level Gas Exchange and Foliar Chemistry of Common Old-Field Species Responding to Warming and Precipitation Treatments.

We investigated the shifts in plant carbon (C) and water dynamics by measuring rates of photosynthesis, transpiration, and instantaneous water use efficiency (WUE) in three common species of “old-field” plants—two C3 forb species (Plantago lanceolata and Taraxacum officinale) and one C3 grass species (Elymus repens)—under 12 experimentally altered temperature and precipitation regimes at the Boston Area Climate Experiment (BACE) in Waltham, Massachusetts. We also measured shifts in foliar C and nitrogen (N) content to determine possible changes in plant C/nutrient balance. We hypothesized that the warming treatment would cause an increase in photosynthesis rates, unless water was limiting; therefore, we expected an interactive effect of warming and precipitation treatments. We found that warming and drought reduced leaf-level photosynthesis most dramatically when environmental or seasonal conditions produced soils that were already dry. In general, the plants transpired fastest when soils were wet and slowest when soils were dry. Drought treatments increased WUE relative to plants in the ambient and wet treatments but only during the driest and warmest background conditions. Leaf N concentration increased with warming, thereby indicating that future warming may cause some plants to take up more soil N and/or allocate more N to their leaves, possibly as consequences of increased nutrient availability. There were no significant interactive effects of the warming and precipitation treatments together across all seasons, indicating that responses were not synergistic or ameliorative

No Accession-Specific Effect of Rhizosphere Soil Communities on the Growth and Competition of Arabidopsis thaliana Accessions

Soil communities associated with specific plant species affect individual plants' growth and competitive ability. Limited evidence suggests that unique soil communities can also differentially influence growth and competition at the ecotype level. Previous work with Arabidopsis thaliana has shown that accessions produce distinct and reproducible rhizosphere bacterial communities, with significant differences in both species composition and relative abundance. We tested the hypothesis that soil communities uniquely affect the growth and reproduction of the plant accessions with which they are associated. Specifically, we examined the growth of four accessions when exposed to their own soil communities and the communities generated by each of the other three accessions. To do this we planted focal accessions inside a ring of six plants that created a “background” soil community. We grew focal plants in this design in three separate soil treatments: non-sterile soil, sterilized soil, and “preconditioned” soil. We preconditioned soil by growing accessions in non-sterile soil for six weeks before the start of the experiment. The main experiment was harvested after seven weeks of growth and we recorded height, silique number, and dry weight of each focal plant. Plants grown in the preconditioned soil treatment showed less growth relative to the non-sterile and sterile soil treatments. In addition, plants in the sterile soil grew larger than those in non-sterile soil. However, we saw no interaction between soil treatment and background accession. We conclude that the soil communities have a negative net impact on Arabidopsis thaliana growth, and that the unique soil communities associated with each accession do not differentially affect growth and competition of study species