Using generalized additive (mixed) models to analyze single case designs.

This article shows how to apply generalized additive models and generalized additive mixed models to single-case design data. These models excel at detecting the functional form between two variables (often called trend), that is, whether trend exists, and if it does, what its shape is (e.g., linear and nonlinear). In many respects, however, these models are also an ideal vehicle for analyzing single-case designs because they can consider level, trend, variability, overlap, immediacy of effect, and phase consistency that single-case design researchers examine when interpreting a functional relation. We show how these models can be implemented in a wide variety of ways to test whether treatment is effective, whether cases differ from each other, whether treatment effects vary over cases, and whether trend varies over cases. We illustrate diagnostic statistics and graphs, and we discuss overdispersion of data in detail, with examples of quasibinomial models for overdispersed data, including how to compute dispersion and quasi-AIC fit indices in generalized additive models. We show how generalized additive mixed models can be used to estimate autoregressive models and random effects and discuss the limitations of the mixed models compared to generalized additive models. We provide extensive annotated syntax for doing all these analyses in the free computer program R.

Resource quantity affects benthic microbial community structure and growth efficiency in a temperate intertidal mudflat.

Estuaries cover <1% of marine habitats, but the carbon dioxide (CO(2)) effluxes from these net heterotrophic systems contribute significantly to the global carbon cycle. Anthropogenic eutrophication of estuarine waterways increases the supply of labile substrates to the underlying sediments. How such changes affect the form and functioning of the resident microbial communities remains unclear. We employed a carbon-13 pulse-chase experiment to investigate how a temperate estuarine benthic microbial community at 6.5°C responded to additions of marine diatom-derived organic carbon equivalent to 4.16, 41.60 and 416.00 mmol C m(-2). The quantities of carbon mineralized and incorporated into bacterial biomass both increased significantly, albeit differentially, with resource supply. This resulted in bacterial growth efficiency increasing from 0.40 ± 0.02 to 0.55 ± 0.04 as substrates became more available. The proportions of diatom-derived carbon incorporated into individual microbial membrane fatty acids also varied with resource supply. Future increases in labile organic substrate supply have the potential to increase both the proportion of organic carbon being retained within the benthic compartment of estuaries and also the absolute quantity of CO(2) outgassing from these environments.

Resource quality affects carbon cycling in deep-sea sediments.

Deep-sea sediments cover ~70% of Earth's surface and represent the largest interface between the biological and geological cycles of carbon. Diatoms and zooplankton faecal pellets naturally transport organic material from the upper ocean down to the deep seabed, but how these qualitatively different substrates affect the fate of carbon in this permanently cold environment remains unknown. We added equal quantities of (13)C-labelled diatoms and faecal pellets to a cold water (-0.7 °C) sediment community retrieved from 1080 m in the Faroe-Shetland Channel, Northeast Atlantic, and quantified carbon mineralization and uptake by the resident bacteria and macrofauna over a 6-day period. High-quality, diatom-derived carbon was mineralized >300% faster than that from low-quality faecal pellets, demonstrating that qualitative differences in organic matter drive major changes in the residence time of carbon at the deep seabed. Benthic bacteria dominated biological carbon processing in our experiments, yet showed no evidence of resource quality-limited growth; they displayed lower growth efficiencies when respiring diatoms. These effects were consistent in contrasting months. We contend that respiration and growth in the resident sediment microbial communities were substrate and temperature limited, respectively. Our study has important implications for how future changes in the biochemical makeup of exported organic matter will affect the balance between mineralization and sequestration of organic carbon in the largest ecosystem on Earth.

Factors affecting benthic impacts at Scottish fish farms.

The factors affecting patterns of benthic [seabed] biology and chemistry around 50 Scottish fish farms were investigated using linear mixed-effects models that account for inherent correlations between observations from the same farm. The abundance of benthic macrofauna and sediment concentrations of organic carbon were both influenced by a significant, albeit weak, interaction between farm size, defined as the maximum weight of fish permitted on site at any one time, and current speed. Above a farm size threshold of between 800 and 1000 t, the magnitude of effects at farms located in areas of elevated current speeds were greater than at equivalent farms located in more quiescent waters. Sediment concentrations of total organic matter were influenced by an interaction between distance and depth, indicating that wind-driven resuspension events may help reduce the accumulation of organic waste at farms located in shallow waters. The analyses presented here demonstrate that the production and subsequent fate of organic waste at fish farms is more complex than is often assumed; in isolation, current speed, water depth, and farr size are not necessarily good predictors of benthic impact.

Stable carbon and nitrogen isotope ratio profiling of sperm whale teeth reveals ontogenetic movements and trophic ecology.

Teeth from male sperm whales (Physeter macrocephalus) stranded in the North-eastern Atlantic were used to determine whether chronological profiles of stable isotope ratios of C (delta(13)C) and N (delta(15)N) across dentine growth layers could be used to detect known ontogenetic benchmarks in movements and trophic ecology. Profiles showed a general decrease in delta(13)C (median = 1.91 per thousand) and an increase in delta(15)N (median = 2.42 per thousand) with age. A marked decline in delta(13)C occurred for all 11 teeth around 9-10 years and again for six individuals around 20 years. After the early twenties the delta(13)C continued to decline with age for all teeth. These results are consistent with males segregating from natal groups in low latitudes with the onset of puberty between 4 and 15 years and gradually dispersing pole-ward into (13)C-depleted temperate waters. Penetration into further depleted, productive high latitudes after the age of 20 might facilitate the spurt of accelerated growth rate observed around this age. Breeding migrations back to lower latitudes were not reflected in the delta(13)C profiles possibly due to being short compared to the time spent feeding in high latitudes. The timings of marked isotopic change in the delta(15)N profiles reflect those of the delta(13)C profiles, suggesting a link between dietary changes and movements. The observed increase in delta(15)N with age is likely to be caused by a trophic level increase as males grow in size, probably feeding on larger prey. An additional explanation could be that, in the higher latitudes of the North Atlantic, the main prey source is the high trophic level squid Gonatus fabricii. Also, the lower latitudes from where males disperse are depleted in basal (15)N. Profiles of delta(13)C and delta(15)N in sperm whale teeth gathered from different regions, sexes, and periods in time, could provide a unique way to understand the ecology of this species across different oceans.