Body size is perhaps the most fundamental property of an organism and is related to many biological traits, including abundance. The relationship between abundance and body size has been extensively studied in an attempt to quantify the form of the relationship and to understand the processes that generate it. However, progress has been impeded by the under appreciated fact that there are four distinct, but interrelated, relationships between size and abundance that are often confused in the literature. Here, we review and distinguish between these four patterns, and discuss the linkages between them. We argue that a synthetic understanding of size-abundance relationships will result from more detailed analyses of individual patterns and from careful consideration of how and why the patterns are related.

We describe a set of best practices for scientific software development, based on research and experience, that will improve scientists' productivity and the reliability of their software.

Power‐law frequency distributions characterize a wide array of natural phenomena. In ecology, biology, and many physical and social sciences, the exponents of these power laws are estimated to draw inference about the processes underlying the phenomenon, to test theoretical models, and to scale up from local observations to global patterns. Therefore, it is essential that these exponents be estimated accurately. Unfortunately, the binning‐based methods traditionally used in ecology and other disciplines perform quite poorly. Here we discuss more sophisticated methods for fitting these exponents based on cumulative distribution functions and maximum likelihood estimation. We illustrate their superior performance at estimating known exponents and provide details on how and when ecologists should use them. Our results confirm that maximum likelihood estimation outperforms other methods in both accuracy and precision. Because of the use of biased statistical methods for estimating the exponent, the conclusions of several recently published papers should be revisited.

Remote sensing can transform the speed, scale, and cost of biodiversity and forestry surveys. Data acquisition currently outpaces the ability to identify individual organisms in high resolution imagery. We outline an approach for identifying tree-crowns in RGB imagery while using a semi-supervised deep learning detection network. Individual crown delineation has been a long-standing challenge in remote sensing and available algorithms produce mixed results. We show that deep learning models can leverage existing Light Detection and Ranging (LIDAR)-based unsupervised delineation to generate trees that are used for training an initial RGB crown detection model. Despite limitations in the original unsupervised detection approach, this noisy training data may contain information from which the neural network can learn initial tree features. We then refine the initial model using a small number of higher-quality hand-annotated RGB images. We validate our proposed approach while using an open-canopy site in the National Ecological Observation Network. Our results show that a model using 434,551 self-generated trees with the addition of 2848 hand-annotated trees yields accurate predictions in natural landscapes. Using an intersection-over-union threshold of 0.5, the full model had an average tree crown recall of 0.69, with a precision of 0.61 for the visually-annotated data. The model had an average tree detection rate of 0.82 for the field collected stems. The addition of a small number of hand-annotated trees improved the performance over the initial self-supervised model. This semi-supervised deep learning approach demonstrates that remote sensing can overcome a lack of labeled training data by generating noisy data for initial training using unsupervised methods and retraining the resulting models with high quality labeled data.

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 ha...