Intestine length in the fishes of a tropical stream: 2. Relationships to diet — the long and short of a convoluted issue

Synopsis We examined the relationship between the intestine length and the amount of plant material in the diet of 21 species of fish from forest streams in Panama. Alimentary tract analyses supplemented by literature reports showed that four loricariid catfish species and one poeciliid were specialized herbivores consuming almost exclusively periphyton and detritus. Four species, including one erythrinid, one characid, one trichomyctycterid and one eleotrid, were carnivores consuming almost entirely food of animal origin. Twelve species, including five characids, one lebiasinid, two pimelodelids, three cichlids and one poeciliid, were omnivores consuming food of both plant and animal origin, but the average proportion of food of plant origin (detritus and algae plus higher plant parts) varied from 4–60%. Most omnivores increased plant food consumption with increasing size. Because intestine length increases allometrically with body size and the pattern of increase differs considerably among species and is influenced by length:mass relationships, we compared species at the same size and took both length and mass into account. At a given size, intestine lengths of herbivores were longer than those of omnivores, and these were longer than those of carnivores. Differences in intestine length among the dietary categories were greater at larger body sizes and when the common size was defined by body mass than when it was defined by body length. There was no trend for the average proportion of plant material consumed to be related to intestine length among the omnivores, when confounding effects of body mass were taken into account. The slopes of the allometric equations relating log₁₀ intestine length to log₁₀ body size for herbivores tended to be higher than for omnivores and higher for omnivores than for carnivores, but both herbivores and omnivores showed extensive variation and overlap with the other dietary categories. Among the omnivores, there was no trend for slopes to be steeper for species consuming more plant material on average or for species showing larger ontogenetic increases in plant consumption. These results permit increased precision in describing diet-intestine length relationships, but indicate that the widely held belief that intestine length reflects diet in fishes should only be applied to broad dietary categories and not to finer divisions among omnivores.     

Organ growth of selected lines of chickens and their F1 crosses to a common body weight or age

Summary Organ growth of male chickens selected for high and low 56-day body weight and their reciprocal F₁ crosses was compared at a common age (56 days) or at a common body weight (180 g). Organs that differed at a common body weight included weights of proventriculus, small intestine, lungs, feathers and abdominal fat and length of esophagus. Organ weights that differed at a common age included esophagus, gizzard, heart, liver, lungs, breast, legs, feathers and abdominal fat, and lengths of shank, esophagus and small intestine. Heterosis for most organs was less than 15%. Those exhibiting heterosis greater than 30% included weights of fat depots and feathers, plus lengths of the esophagus, small intestine and shank. Heterosis for these traits, however, varied depending on whether comparisons were made at common body weight or age. These results imply that biological functions of organs at specific ages may not reflect the situations at common body weights and suggest differences in resource allocations among populations.     

Spatial scaling of allometry for terrestrial,mammalian carnivores

A regression slope of –0.75 between log₁₀ density and log₁₀ body mass is thought to express equivalence of energy conversion among species' populations of similar taxonomic and trophic status. Using larger sample sizes than the usual 1–3 density estimates per species, we estimated a regression slope of –0.71 for terrestrial mammalian carnivores. We investigated the sampling variation in this estimate, and those derived from smaller intra-specific subsets, using 1000-iteration bootstrap analyses to obtain 90% confidence intervals. As expected, these widened as random subsets were reduced in size, but always contained the postulated –0.75. However, log₁₀ density also declined as 3/4 of the log₁₀ spatial extent of study area, and study area accounted for virtually all of the variation in density that was previously thought due to body mass. We removed the effect of study area by using the species-specific regression models between density and study area to predict density at a common scale of 400 km². These common-scale densities regressed against body mass with a slope of –0.16, but separated into body mass classes less than and greater than 11 kg, they produced slopes that were not significantly different from zero. We show that the allometry of density could be a case of circular logic, whereby body mass has influenced the investigator's choice of study area, and the resulting scale-dependent densities are related back to body mass. To test the allometry hypothesis, the effect of study area on density estimates needs to be removed. This requires conducting larger-scale studies of the smaller-bodied species so that all species compared are represented by an average study area that is near the common scale. Furthermore, study sites need to be selected and designed to represent more than the local detail in species' density.     

Body Weight and Relative Brain Size (Encephalization) in Eocene Archaeoceti (Cetacea)

Calibration of the Brownian diffusion model of Felsenstein indicates that phylogeny may have an influence on body length and other phenotypic measures in Cetacea for as many as 10,000 generations or about 180,000 years, which is negligible in the 35 million year history of extant Cetacea. Observations of phenotypic traits in cetacean species living today are independent of phylogeny and independent statistically. Four methods for estimating body weight in fossil cetaceans are compared: (1) median serial regression involving a set of multiple regressions of log body weight on log centrum length, width, and height for core vertebrae; (2) regression of log whole body weight on log body length for individuals; (3) regression of log whole body weight on log body length for species means; and (4) regression of log lean body weight on log body length for individuals. These yield body weight estimates for the Eocene archaeocete Dorudon atrox of 1126, 1118, 1132, and 847 kg, respectively, with consistency and applicability to partial skeletons favoring the first approach. The whole-body weight expected, P_e (in kg), for a given body length, L_i (in cm), is given by log₁₀ P_e?=?2.784 ? log₁₀ L_i???4.429. Negative allometry of body weight and body length (slope 2.784?<?3.000) means that small cetaceans are shorter and more maneuverable than expected for their weight, while large cetaceans are longer and more efficient energetically than expected for their weight. Encephalization is necessarily quantified relative to a reference sample, most mammals are terrestrial, and terrestrial mammals provide a logical baseline. The encephalization residual for living terrestrial mammals as a class (ER_TC), is the difference between observed log₂ brain weight (E_i in g) and expected log₂ brain weight (E_e in g), where the latter is estimated from body weight (P_i in g), as log₂ E_e?=?0.740 ? log₂ P_i???4.004. ER_TC is positive for brains that are larger than expected for a given body size, and negative for brains that are smaller than expected. Base-2 logarithms make the ER_TC scale intuitive, in uniform units of halving or doubling. Encephalization quotients (EQ) are unsuitable for comparison because they are proportions on a non-uniform scale. Middle Eocene archaeocetes have ER_TC values close to ?2 (two halvings compared to expectation), while late Eocene archaeocetes have ER_TC values close to ?1 (one halving compared to expectation). ER_TC is not known for fossil mysticetes, but living mysticetes have ER_TC values averaging about ?2. Oligocene-Recent odontocetes appear to have ER_TC values averaging about +1 (one doubling compared to expectation) through their temporal range. Definitive interpretation of the evolution of encephalization in Cetacea will require better documentation for Oligocene–Recent mysticetes and odontocetes.     

Scaling population density and spatial pattern for terrestrial,mammalian carnivores

A large part of ecological theory has been developed with the assumption that intra- and inter-specific patterns of density and spatial distribution can be consistently and reliably compared, and that these patterns have represented populations across nonstudied landscapes. These assumptions are erroneous. We found that log₁₀ population density estimates consistently decreased linearly with log₁₀ spatial extent of study areas for species of terrestrial Carnivora. The size of the study area accounted for most of the variation in population estimates, and study areas increased with the female body mass of the study species. But study sites consistently had higher densities than can be expected for nonstudy sites, regardless of the size of the study area, because study sites are typically chosen based on a priori knowledge of high density. Inter-specific comparisons of density and distribution might provide more insight into community organization after intra-specific density estimates have been scaled by the study areas, and related to the nonstudied landscapes within each species' geographic range.     

The effects of posterolateral spine length and body length on feeding rate in the rotifer,Brachionus calyciflorus

The length of the posterolateral spines in the rotifer, Brachionus calyciflorus, is variable. The effect of the length of these spines on the clearance rates of B. calyciflorus was examined under laboratory conditions using radioactively-labelled yeast (Rhodotorula) and bacteria (Aerobacter). The hypothesis that individuals with longer spines have higher clearance rates than those of similarly-sized individuals with shorter spines was rejected. The effect of body length (L) on the clearance rates (C) of short-spined and long-spined animals was also examined. Statistically significant linear regressions of the form log₁₀ C = aL + b, were derived for both types. The slopes of both regressions were similar and suggest that clearance rate in B. calyciflorus increases as a cube function of body length.     

Relationships between otolith size and fish length in some mesopelagic teleosts (Myctophidae,Paralepididae, Phosichthyidae and Stomiidae)

Length–mass relationships and linear regressions are given for otolith size (length and height) and standard length (L_S) of certain mesopelagic fishes (Myctophidae, Paralepididae, Phosichthyidae and Stomiidae) living in the central Mediterranean Sea. The length–mass relationship showed isometric growth in six species, whereas linear regressions of L_S and otolith size fit the data well for all species. These equations represent a useful tool for dietary studies on Mediterranean marine predators.     

Converting forests to agriculture decreases body size of Carabid assemblages in Zambia

Body size affects both intraspecific and interspecific competition. Land‐use affects such interactions within assemblages of species and should, therefore, also change the size structure of these assemblages. In particular one expects a decrease of mean body size with disturbances. We compared interspecific size structure of carabid assemblages between agricultural fields (frequent disturbances) and forests in Zambia using pitfall traps operated across 1 year. Mean body length across species co‐occurring within sites in agricultural fields was significantly smaller than in natural forests. Furthermore, in both habitats, we found evidence for ecological clustering in respect to body size, although in forests, body size differences between adjacent‐sized species tended to be overdispersed. We also found a positive relationship between log₁₀‐transformed body length and log₁₀‐transformed activity abundance in forests, suggesting competitive asymmetries between large and small species. Overall, these observations suggest that the size structure of carabid assemblages depends on disturbances as well as competitive interactions. Such interactions seem to be, however, of lower importance within agricultural fields.     

The annual reproductive cycle of pike, Esox lucius L., in two Scottish lakes

Histological changes in the ovaries of pike from two shallow, adjacent, Scottish lakes are described and related to a macroscopic scale of maturity stages and to changes in gonad weight. There was no evidence of pre-ovulatory degeneration although occasional residual oocytes were present in spent ovaries. The gonadosomatic index (GSI) was high in males from October to March, and in females it increased through the winter months to a maximum immediately prior to spawning. Maximum ovarian weight was 8.3–9.0% of total body weight compared with only 0.9–1.1% for testes. These GSIs were low compared with other reports for the British Isles, suggesting lower reproductive output. Spawning occurred in the first two weeks of April at a water temperature of 6.0–7.5° C. Fecundity was described from a regression of egg number (F) on fork length (f.l.): log₁₀F= -1.51 + 3.33 log₁₀ f.l. (cm). Mean egg diameter after preservation varied from 1.1 to 2.4 mm over the size range examined. Males were mature at age 2 at a length of ≥ 27 cm, while females first spawned at age 3 at a length of ≤ 28 cm, although a minority were mature at age 2. The sex ratio was 1.2 males: 1 female at Kinord and 1.4 : 1 at Davan. Greater egg production at Davan, 50 678 ha^?1, compared with Kinord, 33 557 ha^?1, was due to higher individual fecundity-at-age resulting from better growth. Fecundity (19.29 × 10³ calculated for a pike of 55 cm F.L.), relative fecundity of only 10–24 eggs per gram wet weight of adult, and GSI values were low compared with pike in North America and Eurasia. Food supply may restrict reproductive output of pike in Lochs Kinord and Davan. The abundance ratio of predator: prey is high with the main prey species, perch, present in low numbers, and the only alternative species is eel in these simple fish communities.     

Length–weight and length–length relationships for cavedano chub Squalius squalus (Bonaparte, 1837) in Italy

Data of 31496 specimens of cavedano chub Squalius squalus were collected in 89 different waterbodies distributed geographically throughout Italy and used to provide length–weight and length–length relationship for this species. The linear relationship between total length (TL) and standard length (SL) was described by the equation TL (cm) = 4.007 + 0.874 SL (cm). The resulting total length–weight equation for cavedano chub in Italy was: log₁₀ W = ?2.121 + 3.083 log₁₀ TL (cm).     

Determinants of alpha and beta vascular plant diversity in Mediterranean island systems: the Ionian islands,Greece

The Ionian archipelago is the second largest Greek archipelago after the Aegean, but the factors driving plant species diversity in the Ionian islands are still barely known. We used stepwise multiple regressions to investigate the factors affecting plant species diversity in 17 Ionian islands. Generalized dissimilarity modelling was applied to examine variation in the magnitude and rate of species turnover along environmental gradients, as well as to assess the relative importance of geographical and climatic factors in explaining species turnover. The values of the residuals from the ISAR log₁₀‐transfomed models of native and endemic taxa were used as a measure of island floristic diversity. Area was confirmed to be the most powerful single explanatory predictor of all diversity metrics. Mean annual precipitation and temperature, as well as shortest distance to the nearest island are also significant predictors of vascular plant diversity. The island of Kalamos constitutes an important plant diversity hotspot in the Ionian archipelago. The recent formation of the islands, the close proximity to the mainland source and the relatively low dispersal filtering of the Ionian archipelago has resulted in islands with a flora principally comprising common species and a low proportion of endemics. Small islands keep a key role in conservation of plant priority sites.     

Range size in North American Enallagma damselflies correlates with wing size

1. Cross-species macroecological comparisons in freshwater invertebrates have been restricted by a lack of large-scale distributional data, and robust phylogenies. Here, we use data from the OdonataCentral database to explore body length–range size and wing length–range size relationships in damselflies from the genus Enallagma ; the recent publication of a phylogeny for this group meant that, as well as a cross-species analysis, we were able to assess relationships in a phylogenetically controlled manner.
2. For cross-species comparisons, only wing length showed significant (positive) regression relationships with range size and occupancy, although the inclusion of body length in multiple regressions increased the fit of the models. Damselflies with larger wings relative to their body length had larger distributions, a result confirmed by a significant positive relationship between range size and residuals from the regression of wing size on body size.
3. For the phylogenetically controlled analyses, only wing length contrast scores were significantly related to distribution patterns and entered into regression models; the significant positive relationships between wing length contrasts and both range size and occupancy contrasts suggested that evolutionary increases in wing length had occurred alongside range expansions.
4. Together these results suggest that species of Enallagma with larger wings (both absolute and relative to body length) tend to be more widely distributed in North America and that the evolution of wing size may have played a role in range expansion. No such relationships were evident for body size. We discuss the potential importance of wing morphometrics for studying the evolutionary ecology of freshwater insects.     

Intestine lengths of Southern African savanna rodents and insectivores: intra- and interspecific comparisons

Comparative intestine lengths of 15 Southern African savanna rodents and insectivores are presented. Differences in relative intestine length (ratio between hind gut length to head/body length) between seasons were significant in Aethomys chrysophilus . In various species, breeding females, with their increased energy requirement, had hind gut lengths that were well above average. These females also accounted for the differences between sexes which were significant in two species ( Aethomys chrysophilus and A. namaquensis ). Within species no correlation was found between relative intestine length and body size (length and weight) of the animals. Between species the correlation was significant and the larger species had relatively longer intestines. Three groups can be distinguished according to the different feeding types of the species. The omnivorous Praomys natalensis has by far the longest intestine. It is followed by a group of species that can be considered as granivore/herbivore. The species that are partly or predominantly insectivorous have the shortest intestine. The results of the field study are found to be in agreement with reports from laboratory experiments concerning adaptations of intestine length to different environmental situations.     

Understanding reproductive allometry in turtles: A slippery “slope”

Measures of reproductive output in turtles are generally positively correlated with female body size. However, a full understanding of reproductive allometry in turtles requires logarithmic transformation of reproductive and body size variables prior to regression analyses. This allows for slope comparisons with expected linear or cubic relationships for linear to linear and linear to volumetric variables, respectively. We compiled scaling data using this approach from published and unpublished turtle studies (46 populations of 25 species from eight families) to quantify patterns among taxa. Our results suggest that for log–log comparisons of clutch size, egg width, egg mass, clutch mass, and pelvic aperture width to shell length, all scale hypoallometrically despite theoretical predictions of isometry. Clutch size generally scaled at ~1.7 to 2.0 (compared to an isometric expectation of 3.0), egg width at ~0.5 (compared to an expectation of 1.0), egg mass at ~1.1 to 1.3 (3.0), clutch mass at ~2.5 to 2.8 (3.0), and pelvic aperture width at 0.8–0.9 (1.0). We also found preliminary evidence that scaling may differ across years and clutches even in the same population, as well as across populations of the same species. Future investigators should aspire to collect data on all these reproductive parameters and to report log–log allometric analyses to test our preliminary conclusions regarding reproductive allometry in turtles.     

A quantitative study of the morphological development and bacterial colonisation of the gut of the tammar wallaby Macropus eugenii eugenii and brushtail possum Trichosurus vulpecula during in-pouch development

We compared the rates of change of various morphological parameters of the stomach, small intestine, caecum and colon of tammar wallabies and brushtail possums with body mass during in-pouch development. These were correlated with changes in the numbers of bacterial species in the various gut segments. In the pouch-young of both species, the wet tissue masses of all gut segments increased with body mass in a positively allometric manner (i.e. with a body mass exponent > 1), suggesting that the mass of each component was disproportionately low at birth, but increased disproportionately rapidly postnatally. However, the lengths of the wallaby stomach and small intestine scaled isometrically with respect to body mass (i.e. with a body mass exponent around 0.33), which may indicate that the shape of these components changes to the adult form during early neonatal development. Conversely, the length of the caecum and colon of both wallabies and possums scaled in a positively allometric manner with respect to body mass, showing area to volume compensation. This may indicate a more general pattern of disproportionately rapid postnatal enlargement in areas that are distal to the principal sites of neonatal digestion (i.e. the stomach). The numbers of bacterial species present in the various gastrointestinal segments of both species were low in animals aged 100 days or less but there was a significant increase in microbial diversity in the caecum of brushtail possums aged over 100 days. The possum caecum also showed the greatest rate of increase in wet tissue mass relative to body mass. It is postulated that caecal development may act as a nidus for establishment of communities of commensal microflora in the developing marsupial.     

Polymorphic aspects of male anthropoid canines

Interspecific variation in the architecture of male anthropoid maxillary canines is documented. Extant taxa are polymorphic, and most can be sorted into two major groupings based on quantitative measures of shape, distal edge sharpness, and interspecific changes in their linear dimensions (projection, mesiodistal length, and buccolingual breadth) relative to each other and to body mass (scaling). One group includes the great apes and ceboids; the other includes cercopithecoids and hylobatids. Statistically significant differences between these groups were found for canine shape, for trajectories of regressions for canine projection on canine length and canine breadth, and for canine projection and canine breadth relative to body mass. The data indicate that explantations of canine variation in male anthropoids must include a mechanical interpretation of form in addition to assessments of habitus, heritage, and body mass.     

The evolution of energetics in eutherian “insectivorans”: an alternate approach

An analysis of standard energetics in 57 species of “insectivorans”, small eutherians that preferentially feed on soil invertebrates, indicated that a combination of climate, the use of torpor, substrate, food habits, and log₁₀ body mass accounted for 92.5% of the variation in log10 basal rate of metabolism in insectivorans, whereas log₁₀ body mass alone accounted for 76.7% of the variation. With the addition of subfamily affiliation, this analysis accounted for 95.5% of the variation in log₁₀ basal rate, the most distinctive subfamilies being Soricinae and the Talpinae, which have equally high basal rates.Sorex species have basal rates that average 2.5 times those of tropical crocidurines, reflecting an approach bySorex to life in cold climates that does not include the use of torpor, a stratagem widely used by crocidurines in warm-temperate and tropical climates. The absence of torpor inSorex may facilitate a high reproductive rate through a high basal rate of metabolism, a combination that may be incompatible with a small mass, insectivorous food habits, and life in the lowland tropics, but required in cold-temperate environments. Insectivorans other than shrews, moles, and cold-temperature hedgehogs have low basal rates principally in association with tropical distributions and the use of torpor. Basal rate of metabolism in insectivorans also correlated with ordinal, familial, subfamilial, and tribal affiliations. The suggestion that phylogeny is an important determinant of performance characters like rate of metabolism ignores the requirement that performance must be compatible with conditions in the environment and with a species’ other characteristics. The principal reason why performance characters are correlated with taxonomic affiliation is that many clades consist of species that share a common approach to the environment. Thus, clades not only represent evolutionary histories, they also are crude measures of physiological and behavioral performances.     

Discharge�Ccalcium concentration relationships in streams of the Amazon and Cerrado of Brazil: soil or land use controlled

Stream discharge?Cconcentration relationships are indicators of terrestrial ecosystem function. Throughout the Amazon and Cerrado regions of Brazil rapid changes in land use and land cover may be altering these hydrochemical relationships. The current analysis focuses on factors controlling the discharge?Ccalcium (Ca) concentration relationship since previous research in these regions has demonstrated both positive and negative slopes in linear log₁₀discharge?Clog₁₀Ca concentration regressions. The objective of the current study was to evaluate factors controlling stream discharge?CCa concentration relationships including year, season, stream order, vegetation cover, land use, and soil classification. It was hypothesized that land use and soil class are the most critical attributes controlling discharge?CCa concentration relationships. A multilevel, linear regression approach was utilized with data from 28 streams throughout Brazil. These streams come from three distinct regions and varied broadly in watershed size (<1 to >10⁶ ha) and discharge (10^?5.7?C10^3.2 m³ s^?1). Linear regressions of log₁₀Ca versus log₁₀discharge in 13 streams have a preponderance of negative slopes with only two streams having significant positive slopes. An ANOVA decomposition suggests the effect of discharge on Ca concentration is large but variable. Vegetation cover, which incorporates aspects of land use, explains the largest proportion of the variance in the effect of discharge on Ca followed by season and year. In contrast, stream order, land use, and soil class explain most of the variation in stream Ca concentration. In the current data set, soil class, which is related to lithology, has an important effect on Ca concentration but land use, likely through its effect on runoff concentration and hydrology, has a greater effect on discharge?Cconcentration relationships.     

Latitude, seed predation and seed mass

Aim We set out to test the hypothesis that rates of pre‐ and post‐dispersal seed predation would be higher towards the tropics, across a broad range of species from around the world. We also aimed to quantify the slope and predictive power of the relationship between seed mass and latitude both within and across species. Methods Seed mass, pre‐dispersal seed predation and post‐dispersal seed removal data were compiled from the literature. Wherever possible, these data were combined with information regarding the latitude at which the data were collected. Analyses were performed using both cross‐species and phylogenetic regressions. Results Contrary to expectations, we found no significant relationship between seed predation and latitude (log₁₀ proportion of seeds surviving predispersal seed predation vs. latitude, P = 0.63; R² = 0.02; n = 122 species: log₁₀ proportion of seeds remaining after postdispersal seed removal vs. latitude, P = 0.54; R² = 0.02; n = 205 species). These relationships remained non‐significant after variation because of seed mass was accounted for. We also found a very substantial (R² = 0.21) relationship between seed mass and latitude across 2706 species, with seed mass being significantly higher towards the tropics. Within‐species seed mass decline with latitude was significant, but only about two‐sevenths, as rapid as the cross‐species decline with latitude. Results of phylogenetic analyses were very similar to cross‐species analyses. We also demonstrated a positive relationship between seed mass and development time across ten species from dry sclerophyll woodland in Sydney (P < 0.001; R² = 0.77; Standardized Major Axis slope = 0.14). These data lend support to the hypothesis that growing period might affect the maximum attainable seed mass in a given environment. Main conclusions There was no evidence that seed predation is higher towards the tropics. The strong relationship between seed mass and latitude shown here had been observed in previous studies, but had not previously been quantified at a global scale. There was a tenfold reduction in mean seed mass for every c. 23° moved towards the poles, despite a wide range of seed mass within each latitude.     

Mammalian intestinal allometry,phylogeny, trophic level and climate

An often-stated ecomorphological assumption that has the status of ‘textbook knowledge’ is that the dimensions of the digestive tract correlate with diet, where herbivores—consuming diets of lower digestibility—have longer intestinal tracts than faunivores—consuming diets of higher digestibility. However, statistical approaches have so far failed to demonstrate this link. Here, we collated data on the length of intestinal sections and body mass of 519 mammal species, and test for various relationships with trophic, climatic and other biological characteristics. All models showed a strong phylogenetic signal. Scaling relationships with body mass showed positive allometry at exponents greater than 0.33, except for the caecum, which is particularly large in smaller species. Body mass was more tightly linked to small intestine than to large intestine length. Adding a diet proxy to the relationships increased model fit for all intestinal sections, except for the small intestine when accounting for phylogeny. Thus, the diet has a main effect on the components of the large intestine, with longer measures in herbivores. Additionally, measures of habitat aridity had a positive relationship with large intestine length. The small intestine was longer in species from colder habitats at higher latitudes, possibly facilitating the processing of peak intake rates during the growing season. This study corroborates intuitive expectations on digestive tract anatomy, while the dependence of significant results on large sample sizes and inclusion of specific taxonomic groups indicates that the relationships cannot be considered fixed biological laws.