AIC and the challenge of complexity: A case study from ecology

Generalized nonlinearity in animal ecology: Research, review, and recommendations

Generalized linear models (GLMs) are an integral tool in ecology. Like general linear models, GLMs assume linearity, which entails a linear relationship between independent and dependent variables. However, because this assumption acts on the link rather than the natural scale in GLMs, it is more easily overlooked. We reviewed recent ecological literature to quantify the use of linearity. We then used two case studies to confront the linearity assumption via two GLMs fit to empirical data. In the first case study we compared GLMs to generalized additive models (GAMs) fit to mammal relative abundance data. In the second case study we tested for linearity in occupancy models using passerine point-count data. We reviewed 162 studies published in the last 5 years in five leading ecology journals and found less than 15% reported testing for linearity. These studies used transformations and GAMs more often than they reported a linearity test. In the first case study, GAMs strongly out-performed GLMs as measured by AIC in modeling relative abundance, and GAMs helped uncover nonlinear responses of carnivore species to landscape development. In the second case study, 14% of species-specific models failed a formal statistical test for linearity. We also found that differences between linear and nonlinear (i.e., those with a transformed independent variable) model predictions were similar for some species but not for others, with implications for inference and conservation decision-making. Our review suggests that reporting tests for linearity are rare in recent studies employing GLMs. Our case studies show how formally comparing models that allow for nonlinear relationships between the dependent and independent variables has the potential to impact inference, generate new hypotheses, and alter conservation implications. We conclude by suggesting that ecological studies report tests for linearity and use formal methods to address linearity assumption violations in GLMs.

Including tree spatial extension in the evaluation of neighborhood competition effects in Bornean rain forest

Classical tree neighborhood models use size variables acting at point distances. In a new approach here, trees were spatially extended as a function of their crown sizes, represented impressionistically as points within crown areas. Extension was accompanied by plasticity in the form of crown removal or relocation under the overlap of taller trees. Root systems were supposedly extended in a similar manner. For the 38 most abundant species in the focal size class (10-<100 cm stem girth) in two 4-ha plots at Danum (Sabah), for periods P1 (1986-1996) and P2 (1996-2007), stem growth rate and tree survival were individually regressed against stem size, and neighborhood conspecific (CON) and heterospecific (HET) basal areas within incremented steps in radius. Model parameters were critically assessed, and statistical robustness in the modeling was set by randomization testing. Classical and extended models differed importantly in their outcomes. Crown extension weakened the relationship of CON effect on growth versus plot species' abundance, showing that models without plasticity overestimated negative density dependence. A significant negative trend of difference in CON effects on growth (P2-P1) versus CON or HET effect on survival in P1 was strongest with crown extension. Model outcomes did not then support an explanation of CON and HET effects being due to (asymmetric) competition for light alone. An alternative hypothesis is that changes in CON effects on small trees, largely incurred by a drought phase (relaxing light limitation) in P2, and following the more shaded (suppressing) conditions in P1, were likely due to species-specific (symmetric) root competition and mycorrhizal processes. The very high variation in neighborhood composition and abundances led to a strong "neighborhood stochasticity" and hence to largely idiosyncratic species' responses. A need to much better understand the roles of rooting structure and processes at the individual tree level was highlighted.

Allocation of forest biomass across broad precipitation gradients in China's forests

Forests act as major sinks for atmospheric CO2. An understanding of the relationship between forest biomass allocation and precipitation gradients is needed to estimate the impacts of changes in precipitation on carbon stores. Biomass patterns depend on tree size or age, making it unclear whether biomass allocation is limited by tree age at regional scales. Using a dataset of ten typical forest types spanning a large age scale, we evaluated forest biomass allocation-precipitation correlations with the aim of testing whether biomass allocation patterns vary systematically in response to altered precipitation. With increasing mean annual precipitation, a significant quadratic increase occurred in ≤30 yr and >60 yr groups in stem biomass, >60 yr group in branch biomass, and >60 yr groups in leaf biomass; and a significant cubic increase occurred in 30-60 yr and all age forest groups in stem biomass, ≤30 yr, 30-60 yr and all age forest groups in branch biomass, ≤30 yr and all age forest groups in leaf biomass, and in each group in root biomass, indicating that organ biomass is strongly limited by precipitation. Thus, forest biomass responds predictably to changes in mean annual precipitation. The results suggest that forest organ biomass-precipitation relationships hold across independent datasets that encompass a broad climatic range and forest age.

The many faces of fear: a synthesis of the methodological variation in characterizing predation risk

Predators affect prey by killing them directly (lethal effects) and by inducing costly antipredator behaviours in living prey (risk effects). Risk effects can strongly influence prey populations and cascade through trophic systems. A prerequisite for assessing risk effects is characterizing the spatiotemporal variation in predation risk. Risk effects research has experienced rapid growth in the last several decades. However, preliminary assessments of the resultant literature suggest that researchers characterize predation risk using a variety of techniques. The implications of this methodological variation for inference and comparability among studies have not been well recognized or formally synthesized. We couple a literature survey with a hierarchical framework, developed from established theory, to quantify the methodological variation in characterizing risk using carnivore-ungulate systems as a case study. Via this process, we documented 244 metrics of risk from 141 studies falling into at least 13 distinct subcategories within three broader categories. Both empirical and theoretical work suggest risk and its effects on prey constitute a complex, multi-dimensional process with expressions varying by spatiotemporal scale. Our survey suggests this multi-scale complexity is reflected in the literature as a whole but often underappreciated in any given study, which complicates comparability among studies and leads to an overemphasis on documenting the presence of risk effects rather than their mechanisms or scale of influence. We suggest risk metrics be placed in a more concrete conceptual framework to clarify inference surrounding risk effects and their cascading effects throughout ecosystems. We recommend studies (i) take a multi-scale approach to characterizing risk; (ii) explicitly consider 'true' predation risk (probability of predation per unit time); and (iii) use risk metrics that facilitate comparison among studies and the evaluation of multiple competing hypotheses. Addressing the pressing questions in risk effects research, including how, to what extent and on what scale they occur, requires leveraging the advantages of the many methods available to characterize risk while minimizing the confusion caused by variability in their application.