On the use of log-transformation vs. nonlinear regression for analyzing biological power laws

Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain.     

A novel statistical method for classifying habitat generalists and specialists

We develop a novel statistical approach for classifying generalists and specialists in two distinct habitats. Using a multinomial model based on estimated species relative abundance in two habitats, our method minimizes bias due to differences in sampling intensities between two habitat types as well as bias due to insufficient sampling within each habitat. The method permits a robust statistical classification of habitat specialists and generalists, without excluding rare species a priori. Based on a user-defined specialization threshold, the model classifies species into one of four groups: (1) generalist; (2) habitat A specialist; (3) habitat B specialist; and (4) too rare to classify with confidence. We illustrate our multinomial classification method using two contrasting data sets: (1) bird abundance in woodland and heath habitats in southeastern Australia and (2) tree abundance in second-growth (SG) and old-growth (OG) rain forests in the Caribbean lowlands of northeastern Costa Rica. We evaluate the multinomial model in detail for the tree data set. Our results for birds were highly concordant with a previous nonstatistical classification, but our method classified a higher fraction (57.7%) of bird species with statistical confidence. Based on a conservative specialization threshold and adjustment for multiple comparisons, 64.4% of tree species in the full sample were too rare to classify with confidence. Among the species classified, OG specialists constituted the largest class (40.6%), followed by generalist tree species (36.7%) and SG specialists (22.7%). The multinomial model was more sensitive than indicator value analysis or abundance-based phi coefficient indices in detecting habitat specialists and also detects generalists statistically. Classification of specialists and generalists based on rarefied subsamples was highly consistent with classification based on the full sample, even for sampling percentages as low as 20%. Major advantages of the new method are (1) its ability to distinguish habitat generalists (species with no significant habitat affinity) from species that are simply too rare to classify and (2) applicability to a single representative sample or a single pooled set of representative samples from each of two habitat types. The method as currently developed can be applied to no more than two habitats at a time.     

A test of the mismatch hypothesis: How is timing of reproduction related to food abundance in an aerial insectivore?

In seasonal environments, vertebrates are generally thought to time their reproduction so offspring are raised during the peak of food abundance. The mismatch hypothesis predicts that reproductive success is maximized when animals synchronize their reproduction with the food supply. Understanding the mechanisms influencing the timing of reproduction has taken on new urgency as climate change is altering environmental conditions during reproduction, and there is concern that species will not be able to synchronize their reproduction with changing food supplies. Using data from five sites over 24 years (37 site-years), we tested the assumptions of the mismatch hypothesis in the Tree Swallow (Tachycineta bicolor), a widespread aerial insectivore, whose timing of egg-laying has shifted earlier by nine days since the 1950s. Contrary to the mismatch hypothesis, the start of egg-laying was strongly related to food abundance (flying insect biomass) during the laying period and not to timing of the seasonal peak in food supply. In fact, food abundance generally continued to increase throughout the breeding season, and there was no evidence of selection based on the mistiming of laying with the seasonal peak of food abundance. In contrast, there was selection for laying earlier, because birds that lay earlier generally have larger clutches and fledge more young. Overall, initial reproductive decisions in this insectivore appear to be based on the food supply during egg formation and not the nestling period. Thus, the mismatch hypothesis may not apply in environments with relatively constant or abundant food throughout the breeding season. Although climate change is often associated with earlier reproduction, our results caution that it is not necessarily driven by selection for synchronized reproduction.     

Morphology and distribution of the ampullary electroreceptors in wobbegong sharks: implications for feeding behaviour

The electrosensory capabilities of wobbegong sharks are of particular interest, partly because very little is known about their behavioural ecology and specifically because of their unusual ambush predatory strategy and benthic lifestyle. While several biological functions of electroreception have been proposed, less consideration has been given to the functional significance of interspecific differences in the morphology and topographic distribution of the ampullary organs. The morphology of the ampullary organs was examined in four species of wobbegong shark, and the distribution of electroreceptive pores was mapped in two species. The ampullary systems of wobbegongs are similar in morphology to other marine elasmobranchs. The number of alveoli per ampullae is not significantly different between the four species; however, differences are seen between ampullary cell size in some species. Ampullary pore distribution patterns are relatively unique, with the majority of pores occurring on the dorsal region of the head. Wobbegongs feed primarily on demersal teleost fishes, and as the benthic and well-camouflaged wobbegong remains motionless, these fish could be easily detected by the dorsal pores when swimming within range.     

The influence of suburban land use on habitat and biotic integrity of coastal Rhode Island streams

Watershed land use in suburban areas can affect stream biota through degradation of instream habitat, water quality, and riparian vegetation. By monitoring stream biotic communities in various geographic regions, we can better understand and conserve our watershed ecosystems. The objective of this study was to examine the relationship between watershed land use and the integrity of benthic invertebrate communities in eight streams that were assessed over a 3-year period (2001-2003). Sites were selected from coastal Rhode Island watersheds along a residential land-use gradient (4-59%). Using the rapid bioassessment protocol, we collected biological, physicochemical, habitat, and nutrient data from wadeable stream reaches and compared metrics of structure and integrity. Principal component analyses showed significant negative correlation of indicators for stream physicochemical, habitat, and instream biodiversity with increasing residential land use (RLU) in the watershed. The physicochemical variables that were most responsive to percent RLU were conductivity, instream habitat, nitrate, and dissolved inorganic nitrogen (DIN). The positive correlation of DIN with percent RLU indicated an anthropogenic source of pollution affecting the streams. The biotic composition of the streams shifted from sensitive to insensitive taxa as percent RLU increased; the most responsive biological variables were percent Ephemeroptera, percent Scrapers, percent Insects, and the Hilsenhoff biotic index. These data show the importance of land management and conservation at the watershed scale to sustaining the biotic integrity of coastal stream ecosystems.     

Liver lesions in demersal fishes near a large ocean outfall on the San Pedro Shelf, California

The prevalence of toxicopathic liver lesions in demersal fish on the San Pedro Shelf, California was determined for a 15-year period (1988–2003). Fish livers were sampled at fixed locations as part of the Orange County Sanitation Districts (OCSD) ocean monitoring program. Histopathological examination of selected fish liver tissues was studied to determine whether the wastewater discharge had affected fish health. The prevalence of toxicopathic lesion classes neoplasms (NEO), preneoplastic foci of cellular alteration (FCA), and hydropic vacuolation (HYDVAC) varied among species and locations. For all species sampled, severe lesions occurred in 6.2% of the fish examined (n = 7,694). HYDVAC (4.1%) was the most common toxicopathic lesion type followed by FCA (1.4%) and NEO (0.7%). HYDVAC occurred only in white croaker (Genyonemus lineatus), accounting for 84.8% of the toxicopathic lesions for this species. Prevalence of HYDVAC, NEO, and FCA in white croaker was 15.2, 2.0, and 0.7%, respectively. The prevalence of HYDVAC and NEO in white croaker increased with age and size but there was no sexual difference. A linear regression model was used for hypothesis testing to account for significant differences in fish size (and age for croakers) at the different sampling locations. This analysis showed that for HYDVAC there was no spatial or location effect for lesion rate or size/age of onset. For NEO, the model predicted that white croaker near the wastewater outfall may acquire these lesions at a smaller size/younger age, and at a higher rate, than at other sites. However, this result may be biased due to the unequal size frequency distributions and the low prevalence of NEO in white croaker at the different sampling sites. Bigmouth sole (Hippoglossina stomata) had a prevalence of FCA and NEO of 1.3 and 0.35%, respectively, but the prevalence and distribution of lesions was too few for statistical testing. There was no sexual difference for lesion prevalence in hornyhead turbot (Pleuronichthys verticalis) and the prevalence of FCA and NEO was 3.4 and 0.37%, respectively. FCA prevalence increased with size in hornyhead turbot and there were no significant spatial differences for lesion rates and fish size at lesion onset. Overall, consistent spatial differences for lesion prevalence were not demonstrated and highlight the analytical difficulties of detecting a possible point source impact when the effect is rare, correlated with the size/age structure of the population, and may be caused by exposure to unknown multiple sources. Thus, the usefulness of liver histopathology as a point-source monitoring tool is best applied to where the spatial scale of impact generally exceeds the home range of the target species.     

The role of GC-MS and LC-MS in the discovery of drinking water disinfection by-products

Gas chromatography-mass spectrometry (GC-MS) has played a pivotal role in the discovery of disinfection by-products (DBPs) in drinking water. DBPs are formed when disinfectants, such as chlorine, ozone, chlorine dioxide or chloramine, react with natural organic matter in the water. The first DBP known--chloroform--was identified by Rook in 1974 using GC-MS. Soon thereafter, chloroform and other trihalomethanes were found to be ubiquitous in chlorinated drinking water. In 1976, the National Cancer Institute published results linking chloroform to cancer in laboratory animals, and an important public health issue was born. Mass spectrometry and, specifically, GC-MS became the key tool used for measuring these DBPs in water and for discovering other DBPs that were formed. Over the last 25 years, hundreds of DBPs have been identified, mostly through the use of GC-MS, which has spawned additional health effects studies and regulations. Early on, GC with low resolution electron ionization (EI)-MS was used, together with confirmation with chemical standards, for identification work. Later, researchers utilized chemical ionization (CI)-MS to provide molecular weight information and high resolution El-MS to aid in the determination of empirical formulae for the molecular ions and fragments. More recently, liquid chromatography-mass spectrometry (LC-MS) with either electrospray ionization (ESI) or atmospheric pressure chemical ionization (APCI) has been used to try to uncover highly polar DBPs that most experts believe have been missed by earlier GC-MS studies. Despite 25 years of research in the identification of new DBPs, new ones are being discovered every year, even for chlorine which has been the most extensively studied.     

Simultaneous extraction of bromide, chloride, fluoride and sulfate from soils, waste- and building materials

The simultaneous extraction of bromide, chloride, fluoride and sulfate was studied in soils, waste- and building materials. Acid, neutral and alkaline extractants were used; 0.01 mol l(-1) H(3)PO(4), milliQ-water and 0.01 mol l(-1) NaOH, respectively. The extracts were analysed by ion chromatography and ion selective electrode. Extracted concentrations were compared with the amount obtained by an alkaline smelt, as an approximation of the total extractable content. The results indicate that there is a significant difference in extraction behaviour between waste- and building materials and soils. Bromide and chloride were in general completely extracted from the former solid materials, but less than 10% and 50%, respectively, from soils. Fluoride is strongly bound in all investigated samples; less than 10% of the total content was extracted with any of the three extractants. The fraction of extracted sulfate varied between 4 and 87% of the total content, and was in general larger in waste- and building materials than in soils. Differences in extracted concentration between the 3 extractants occurred mainly for fluoride and sulfate. Extracted bromide was similar with all three extractants and extracted chloride showed differences for the various soil samples only. Increasing the NaOH concentration up to 1 mol l(-1) resulted mainly in an increase of extracted amount of fluoride and for soils also in extracted amounts of bromide and sulfate. Although, the results show that the composition of the solid material strongly influences the final pH of the extract and the extracted amount of investigated anions, application of Milli-Q water as an extractant might be a very fruitful option within the development of the Dutch Building Materials Decree.     

Amniotic fluid calcium concentration in the prenatal diagnosis of cystic fibrosis

Calcium concentrations were measured in supernatant amniotic fluid in order to establish whether they may be used as a marker for cystic fibrosis. No difference in values were found, whether the sample was derived from a normal pregnancy or from a pregnancy which resulted in a baby affected with cystic fibrosis.