Small Sample Behaviors of the Delete-<i>d</i>Cross Validation Statistic

Built upon an iterative process of resampling without replacement and out-of-sample prediction, the delete-d cross validation statistic CV(d) provides a robust estimate of forecast error variance. To compute CV(d), a dataset consisting of n observations of predictor and response values is systematically and repeatedly partitioned (split) into subsets of size n – d (used for model training) and d (used for model testing). Two aspects of CV(d) are explored in this paper. First, estimates for the unknown expected value E[CV(d)] are simulated in an OLS linear regression setting. Results suggest general formulas for E[CV(d)] dependent on σ2 (“true” model error variance), n – d (training set size), and p (number of predictors in the model). The conjectured E[CV(d)] formulas are connected back to theory and generalized. The formulas break down at the two largest allowable d values (d = n – p – 1 and d = n – p, the 1 and 0 degrees of freedom cases), and numerical instabilities are observed at these points. An explanation for this distinct behavior remains an open question. For the second analysis, simulation is used to demonstrate how the previously established asymptotic conditions {d/n → 1 and n – d → ∞ as n → ∞} required for optimal linear model selection using CV(d) for model ranking are manifested in the smallest sample setting, using either independent or correlated candidate predictors.

Effects of monoculture-conditioned soils on common tallgrass prairie species productivity

Aims Within biodiversity-ecosystem function experiments,it is widely understood that yields of some species rapidly decline when planted in monoculture.This effect may arise due to decreased access to soil nutrients or an increase in detrimental soil patho-gens within monoculture plantings.To determine whether or not soil conditioning affects tall grass prairie species biomass produc-tion,we conducted a field experiment to assess species growth in conspecifically and heterospecifically conditioned soils and a greenhouse experiment to elucidate how conspecific soil biota affected species growth.Methods To test for species-specific soil effects,seedlings of the legume Astragulus canadensis,the cool-season grass Elymus canaden-sis,the forb Helianthus maximiliani and the warm-season grass Panicum virgatum were grown in field plots that had either been conspecifically or heterospecifically conditioned over 2 years.Plant growth was recorded over a single growing season,and soils were assessed for differences in their nematode(mesofauna)communities.Seedlings of these species were additionally grown over a 6-week period in conspecifically conditioned soil that was either untreated,heated to 60°C,sterilized(autoclaved at 120°C)or heated to 60°C and reinoculated with conspecific soil biota.The two heating treatments were used to compare growth responses between a low-and high-temperature soil treatment.The reinoculation treatment was used to assess the effect of soil biota in light of any nutrient changes that may have occurred with soil heating.Important Findings Elymus canadensis,H.maximiliani and P.virgatum growth was improved in field plots conditioned by the legume A.canadensis com-pared with their growth in conspecifically conditioned(home)soils.Despite variation(grass versus nongrass)in their soil nematode com-munities,there was no evidence to suggest that these three species were inhibited by conspecific or functionally conspecific soil condi-tioning in the field.Astragulus canadensis was the only species whose growth was reduced in conspecifically conditioned field soil.In the greenhouse,E.canadensis growth increased in all of the heat-treated soils,likely a response to a fertilization effect associated with soil heat-ing.Panicum virgatum growth also increased among the heated soils.However,its growth decreased in heated soils where conspecific soil mesofauna were reintroduced,indicating that this grass may be inhib-ited by soil mesofauna.Finally,A.canadensis growth decreased in soils treated to fully remove soil biota and was not affected by rein-troduction of soil mesofauna,suggesting that this species negatively responds to soil changes that occur with extreme heating.At least for the suite of tallgrass prairie species evaluated within this experiment,it appears that changes in soil chemistry and generalist soil biota,as opposed to increasing species-specific soil pathogens,more strongly contribute to temporal disparities in their performance.

Inoculation with native grassland soils improves native plant species germination in highly disturbed soil

Background:Grasslands are globally imperiled,facing continued threats from anthropogenic disturbances.Seeding remains a common grassland restoration method,and yet,is typically met with limited success,partially because soils of degraded systems inhibit the germination of native species.Methods:We assessed the germination success of 16 native grassland species sown in soils collected from a degraded grassland converted into a nonnative warm‐season perennial grass,Bothriochloa ischaemum,and areas previously subjected to the eradication of this nonnative species.Our objectives were as follows:(1)determine native seed germination in soils collected from B.ischaemum or eradication control sites,compared to germination in native grassland soil,and(2)assess if native soil inoculation improves germination,compared to germination in degraded soils without inoculation.Results:Germination of native species was exceedingly low when seeded into soil dominated by B.ischaemum,or in soil previously treated with combinations of herbicide and prescribed fire,relative to native grassland control.However,amendments with native grassland soil resulted in germination equivalent to native grasslands,alleviating the negative influences of degraded soils.Conclusions:Our results highlight the role of native soil in improving the germination of desirable plant species following intensive management and soil degradation.Our research may improve restoration outcomes for managers focused on the conservation and restoration of grasslands.