A simple way to calculate the volume and surface area of avian eggs.

Egg geometry can be described using Preston's equation, which has seldom been used to calculate egg volume (V) and surface area (S) to explore S versus V scaling relationships. Herein, we provide an explicit re-expression of Preston's equation (designated as EPE) to calculate V and S, assuming that an egg is a solid of revolution. The side (longitudinal) profiles of 2221 eggs of six avian species were digitized, and the EPE was used to describe each egg profile. The volumes of 486 eggs from two avian species predicted by the EPE were compared with those obtained using water displacement in graduated cylinders. There was no significant difference in V using the two methods, which verified the utility of the EPE and the hypothesis that eggs are solids of revolution. The data also indicated that V is proportional to the product of egg length (L) and maximum width (W) squared. A 2/3-power scaling relationship between S and V for each species was observed, that is, S is proportional to (LW2 )2/3 . These results can be extended to describe the shapes of the eggs of other species to study the evolution of avian (and perhaps reptilian) eggs.

The Modified Brière Equation and Its Applications.

The Brière equation (BE) is widely used to describe the effect of temperature on the development rate of insects, and it can produce both symmetrical and asymmetrical bell-shaped curves. Because of its elasticity in curve fitting, the integrated form of BE has been recommended for use as a sigmoid growth equation to describe the increase in plant biomass with time. However, the start time of growth predicted by the sigmoid growth equation based on the BE is not completely comparable to empirical crop growth data. In the present study, we modified the BE by adding an additional parameter to further increase its elasticity for data fitting. We termed this new equation the modified Brière equation (MBE). Data for the actual height and biomass of 15 species of plants (with two cultivars for one species) were fit with the sigmoid growth equations based on both the BE and MBE assuming that the growth start time was zero for both. The goodness of fit of the BE and MBE sigmoid growth equations were compared based on their root-mean-square errors and the corresponding absolute percentage error between them when fit to these data. For most species, we found that the MBE sigmoid growth equation achieved a better goodness of fit than the BE sigmoid growth equation. This work provides a useful tool for quantifying the ontogenetic or population growth of plants.

'biogeom': An R package for simulating and fitting natural shapes.

Many natural objects exhibit radial or axial symmetry in a single plane. However, a universal tool for simulating and fitting the shapes of such objects is lacking. Herein, we present an R package called 'biogeom' that simulates and fits many shapes found in nature. The package incorporates novel universal parametric equations that generate the profiles of bird eggs, flowers, linear and lanceolate leaves, seeds, starfish, and tree-rings, and three growth-rate equations that generate the profiles of ovate leaves and the ontogenetic growth curves of animals and plants. 'biogeom' includes several empirical datasets comprising the boundary coordinates of bird eggs, fruits, lanceolate and ovate leaves, tree rings, seeds, and sea stars. The package can also be applied to other kinds of natural shapes similar to those in the datasets. In addition, the package includes sigmoid curves derived from the three growth-rate equations, which can be used to model animal and plant growth trajectories and predict the times associated with maximum growth rate. 'biogeom' can quantify the intra- or interspecific similarity of natural outlines, and it provides quantitative information of shape and ontogenetic modification of shape with important ecological and evolutionary implications for the growth and form of the living world.

Performance of the SSI development function compared with 33 other functions applied to 79 arthropod species' datasets.

The development rates of arthropods are temperature-dependent. Studies aiming to predict the dynamics of arachnid, crustacean, and insect populations in nature often require the derivation of development functions representing this phenomenon. A previous study (Quinn, B.K., 2017, J. Therm. Biol. 63, 65-77) identified 33 development functions commonly used in past studies on temperature-dependent development of arthropods, and illustrated that: (1) most of 99 past studies only applied one or few (2-5) development functions to their data without considering others; and (2) most of a subset of 79 studies' data were not fit with the actual best function for them, resulting in sometimes substantial differences in model performance and predictive ability. However, that study did not test the class of development functions based on theoretical enzyme thermodynamics, including the Sharpe-Schoolfield-Ikemoto (SSI) function. Herein, the meta-analyses done in that previous study were redone, after fitting all 79 reanalyzed datasets with the SSI function. Estimates of the intrinsic optimum temperature (TΦ) for development of each tested species were also derived using the SSI function and compared among taxa. Including the SSI function in analyses did not change the conclusions of the previous study concerning development function usage, choice, and consequences. Notably, the SSI function performed as well as or relatively better than other functions of comparable or lower complexity in terms of R2, AICC-based rankings, ΔAICC values, and prediction errors, which may recommend its more widespread use in future studies. Overall differences in TΦ were found among arthropod subphyla, as well as between most species pairs. Most TΦ estimates produced herein were novel, and could be used to make inferences about or comparisons among arthropod taxa in future studies.

Occurrence and predictive utility of isochronal, equiproportional, and other types of development among arthropods.

In isochronal (ICD) and equiproportional development (EPD), the proportion of total immature (egg, larval, and/or juvenile) development spent in each stage (developmental proportion) does not vary among stages or temperatures, respectively. ICD and EPD have mainly been reported in copepods, and whether they occur in other arthropods is not known. If they did, then rearing studies could be simplified because the durations of later developmental stages could be predicted based on those of earlier ones. The goal of this study was to test whether different taxa have ICD, EPD, or an alternative development type in which stage-specific proportions depend on temperature, termed 'variable proportional' development (VPD), and also how well each development type allowed later-stage durations to be predicted from earlier ones. Data for 71 arthropods (arachnids, copepod and decapod crustaceans, and insects) were tested, and most (85.9%) species were concluded to have VPD, meaning that ICD and EPD do not occur generally. However, EPD predicted later-stage durations comparably well to VPD (within 19-23%), and thus may still be useful. Interestingly, some species showed a 'mixed' form of development, where some stages' developmental proportions varied with temperature while those of others did not, which should be further investigated.

Dramatic decline and limited recovery of a green crab (Carcinus maenas) population in the Minas Basin, Canada after the summer of 2013.

This paper reports the results of a ten-year monitoring program of an Atlantic Canadian population of green crabs, Carcinus maenas, in the Minas Basin of the Bay of Fundy. Intertidal densities, sex and reproductive ratios, juvenile recruitment, subtidal catch-per-unit-effort (CPUE), and sizes of crabs in this population were recorded from 2008 to 2017. In 2013 intertidal densities, mean crab sizes, subtidal CPUE, and proportions of crabs mature and reproducing all dramatically decreased to all-time lows, and large crabs virtually disappeared from the population. From 2014 to 2017 the population partially recovered but remained in an altered state. Potential causes of interannual changes to this population were investigated by correlating intertidal densities to 257 monthly environmental variables and performing stepwise multiple regression analyses. Crab densities in a given year were best explained by potential settlement during the summer and the maximum sea-surface temperature during March of the same year. However, potential roles of other factors (e.g., autumn winds, summer temperatures, North Atlantic Oscillation index) could not be ruled out. Changes in abundances of other species in the area, particularly predators and prey of green crabs, have also been observed and present possible alternative causative agents that should be investigated. Populations of other marine species in the Gulf of Maine-Bay of Fundy region within which the Minas Basin is situated have also been reported to have undergone dramatic changes in and after 2013, suggesting the occurrence of some oceanographic event or regime shift in the region. Declines to the monitored crab population in this study may have resulted from this same 2013 event. These observations have implications for recruitment to marine populations in this region.

A critical review of the use and performance of different function types for modeling temperature-dependent development of arthropod larvae.

Temperature-dependent development influences production rates of arthropods, including crustaceans important to fisheries and agricultural pests. Numerous candidate equation types (development functions) exist to describe the effect of temperature on development time, yet most studies use only a single type of equation and there is no consensus as to which, if any model predicts development rates better than the others, nor what the consequences of selecting a potentially incorrect model equation are on predicted development times. In this study, a literature search was performed of studies fitting development functions to development data of arthropod larvae (99 species). The published data of most (79) of these species were then fit with 33 commonly-used development functions. Overall performance of each function type and consequences of using a function other than the best one to model data were assessed. Performance was also related to taxonomy and the range of temperatures examined. The majority (91.1%) of studies were found to not use the best function out of those tested. Using the incorrect model lead to significantly less accurate (e.g., mean difference±SE 85.9±27.4%, range: -1.7 to 1725.5%) predictions of development times than the best function. Overall, more complex functions performed poorly relative to simpler ones. However, performance of some complex functions improved when wide temperature ranges were tested, which tended to be confined to studies of insects or arachnids compared with those of crustaceans. Results indicate the biological significance of choosing the best-fitting model to describe temperature-dependent development time data.

Seascape genomics provides evidence for thermal adaptation and current-mediated population structure in American lobster (Homarus americanus).

Investigating how environmental features shape the genetic structure of populations is crucial for understanding how they are potentially adapted to their habitats, as well as for sound management. In this study, we assessed the relative importance of spatial distribution, ocean currents and sea surface temperature (SST) on patterns of putatively neutral and adaptive genetic variation among American lobster from 19 locations using population differentiation (PD) approaches combined with environmental association (EA) analyses. First, PD approaches (using bayescan, arlequin and outflank) found 28 outlier SNPs putatively under divergent selection and 9770 neutral SNPs in common. Redundancy analysis revealed that spatial distribution, ocean current-mediated larval connectivity and SST explained 31.7% of the neutral genetic differentiation, with ocean currents driving the majority of this relationship (21.0%). After removing the influence of spatial distribution, no SST were significant for putatively neutral genetic variation whereas minimum annual SST still had a significant impact and explained 8.1% of the putatively adaptive genetic variation. Second, EA analyses (using Pearson correlation tests, bayescenv and lfmm) jointly identified seven SNPs as candidates for thermal adaptation. Covariation at these SNPs was assessed with a spatial multivariate analysis that highlighted a significant temperature association, after accounting for the influence of spatial distribution. Among the 505 candidate SNPs detected by at least one of the three approaches, we discovered three polymorphisms located in genes previously shown to play a role in thermal adaptation. Our results have implications for the management of the American lobster and provide a foundation on which to predict how this species will cope with climate change.