Mass invariance of population nitrogen flux by terrestrial mammalian herbivores: an extension of the energetic equivalence rule

According to the energetic equivalence rule, energy use by a population is independent of average adult body mass. Energy use can be equated with carbon flux, and it has been suggested that population fluxes of other materials, such as nitrogen and phosphorus, might also be independent of body mass. We compiled data on individual nitrogen deposition rates (via faeces and urine) and average population densities of 26 species of mammalian herbivores to test the hypothesis of elemental equivalence for nitrogen. We found that the mass scaling of individual nitrogen flux was opposite to that of population density for the species in our dataset. By computing the product of individual nitrogen flux and average population density for each species in our dataset, we found that population-level nitrogen flux was independent of species mass, averaging c. 3.22 g N ha⁻¹ day⁻¹. Results from this analysis can be used to understand the influence of mammalian herbivore communities on nitrogen cycling in terrestrial ecosystems.     

Body size and abundance of benthic animals in Mirror Lake, New Hampshire

1. There is a strong negative correlation between body mass and population density for 192 species from the zoobenthos of Mirror Lake, a small, oligotrophic lake. This correlation spans seven—nine orders of magnitude in body mass. 2. The slopes of both the regression and the upper bound on the distribution of data points are significantly shallower than -0.75, the slope that has been suggested to imply that metabolic constraints limit animal abundance. 3. The regressions for individual taxonomic groups (i.e. classes, phyla) do not conform closely to the overall regression line. 4. It is suggested that metabolic constraints on community structure need not be expressed by a slope of -0.75 for regressions (or upper bounds) on body mass—abundance functions.     

Body mass, population density, and offspring number in mammals

The negative relationship between population density and body mass with the body mass exponent of -0.75 implies that the energy flow through populations of small- and large-bodied species is the same, for individual metabolism scales to body mass raised to the power of +0.75. This relationship called the energetic equivalence rule, has often been observed for mammal species assemblages studied at regional scales. Here we suggest a demography-based mechanism that may generate it. Having analyzed about 130 literature sources, mostly in Russian, we collected demography and body-mass data for 88 mammalian species from the territory and coastal waters of the former Soviet Union. The data were used to construct a number of interspecific relationships. It is shown that (1) the number of offspring per lifetime is approximately inversely proportional to the relative mass at birth (the exponent is not significantly different from -1), (2) the average lifespan is proportional to body mass to the 0.25 power, (3) body mass at birth is proportional to the adult body mass. We develop a simple theory to demonstrate that relations (1) to (3) entail the energetic equivalence rule. The theory also allows us to explain violation of this rule (in non-flying birds, for example), namely, to predict the exponent of relation (1) for any given exponent of the relation between population density and body mass. This is possible because relations (2) and (3) are likely to more universally hold than relation (1). Finally, since natural selection acts on individual traits rather than on population-level ones such as population density, the theory opens up the way to an evolutionary explanation for the energetic equivalence rule.     

Home range, home range overlap, and species energy use among herbivorous mammals

Harestad & Bunnell (1979) showed that, at least for North American species, home ranges of large herbivorous mammals are relatively larger than we would expect on metabolic grounds, and suggested that the productivity of the environment for mammal species decreases with increasing body size. This interpretation assumes that the number of conspecifics that share an individual's home range is independent of body size. Data presented here show that this is not true for the species in their sample; the home range is shared with an increasing number of conspecifics in larger herbivore species. The productivity of the environment for a species is independent of body size and the area available to an individual for its own use scales approximately as do individual metabolic requirements. These results agree with conclusions based upon the scaling of population density with body mass and illustrate the interrelationship between home range and dietary and social organization trends among mammalian herbivores. Individual home range area is a function of the way in which the local population of a species, not merely an individual, exploits the environment.     

Bioenergetic Constraints on Primate Abundance

Explaining variation in primate population densities is central to understanding primate ecology, evolution, and conservation. Yet no researchers to date have successfully explained variation in primate population density across dietary class and phylogeny. Most previous work has focused on measures of food availability, as access to food energy likely constrains the number of individuals supported in a given area. However, energy output may provide a measure of energy constraints on population density that does not require detailed data on food availability for a given taxon. Across mammals, many studies have shown that population densities generally scale with body mass^−0.75. Because individual energy expenditures scale with body mass^0.75, population energy use (the product of population density and individual energy use) does not change with body mass, which suggests the existence of energy constraints on population density across body sizes, i.e., taxa are limited to a given amount of energy use, constraining larger taxa to lower densities. We examined population energy use and individual energy expenditure in primates and tested this energy equivalence across body mass. We also used a residual analysis to remove the effects of body mass on primate population densities and energy expenditures using basal metabolic rates (BMR; kcal/d) as a proxy for total daily energy expenditure. After taking into account phylogeny, population energy use did not significantly correlate with body mass. Larger primates, which use more energy per day, live at lower population densities than smaller primates. In addition, we found a significant negative correlation between residuals of BMR from body mass and residuals of population density from body mass after taking phylogeny into account. Thus, energy costs constrain population density across a diverse sample of primates at a given body mass, and primate species that have relatively low BMRs exist at relatively high densities. A better understanding of the determinants of primate energy costs across geography and phylogeny will ultimately help us explain and predict primate population densities.     

On the determinants of census area: implications for mammalian macroecological patterns

The aim of this study was to examine the effects of various biological factors such as body mass, trophic level, climate and geography on census area in terrestrial mammals. We also examine the effects of census area on the population density–body mass relationship. The geographic areas covered in this study include most major terrestrial biomes including taïga, desert, savanna, grassland, tropical dry forest, temperate dry forest, tropical rain forest and temperate rain forest. An extensive literature search was conducted and we compiled data on census area and body mass from 377 mammalian populations and 59 communities. Statistical analyses include linear regression, Kruskal–Wallis analysis of variance, LOWESS, and multiple regression. Overall, the regression between log census area (A) and log body mass (M) yielded a slope of 0.710, which did not differ significantly from 0.75, but it was significantly different from 1.0. The analyses also showed that the log A–log M relationship is constrained within a well‐defined space in a similar fashion to the home range–body mass relationship. When mammals were separated into trophic groups, regression lines differed significantly in their intercepts, but not in slopes. At the community level, the census area was particularly affected by the population with the largest body mass within the community. Both the number of species and number of taxa encompassed by the community were found to be correlated positively with log A (r = 0.26, P = 0.0464 and r = 0.27, P = 0.0398, respectively). Sampling of mammalian species is not usually random. Not only is census area significantly associated with the technique used to sample a given species, but it is also influenced by biological factors that have been shown previously to influence population density. Striking similarities were found between the census area–body mass relationship and the home range–body mass relationship, suggesting that investigators may sample mammalian populations over areas that actually reflect the use of space of their focal species.     

Body Mass Estimates in Extinct Mammals from Limb Bone Dimensions: the Case of North American Hyaenodontids

The body mass estimation of several limb bone dimensions (shaft cross-sectional properties, articular sizes, and bone lengths) were examined using bivariate linear regression analyses. The sample included taxonomically and behaviourally diverse small to medium-sized Recent carnivorans and carnivorous marsupials. All examined limb bone dimensions indicated low errors (percentage standard error of estimate, 8–13) for the body mass estimations. Among them, humeral and femoral shaft properties correlated best with body weight, while limb bone lengths gave larger errors. Both humeral and femoral head dimensions have relatively large individual variations, and distal humeral articular dimensions seem to be influenced more by phylogenetic differences. The regressions based on each locomotor group gave slightly lower errors than those based on the total pooled sample. The results were then applied to hyaenodontid creodonts from the Eocene–Oligocene of North America. The estimated body masses (kg) are: Arfia , 5.4–9.5; Prototomus , <6.0; Pyrocyon , 2.6; Sinopa , 1.3–1.4; Tritemnodon , 7.6–13; Prolimnocyon , 1.6; Thinocyon , 0.7–2.5; Machaeroides , 12; Limnocyon , 7.8– 16; Hyaenodon , 9.1–43. The various limb bone dimensions give different body mass values, but the variation in estimates is smaller compared to those derived from dental or cranial measurements.     

Population energy use scales positively with body size in natural aquatic microcosms

Aim  We test the 'energetic equivalence rule' (EER) – the idea that the amount of energy used by a population per unit area per unit time is independent of body mass – in meio-invertebrate communities from a series of natural, multitrophic aquatic 'rock pool' microcosms. Our study represents the first rigorous test of the EER at local scales of observation in a community of naturally coexisting species.
Location  Discovery Bay, Jamaica.
Method  We estimated population energy use (PEU) for every occurrence of every species of meio-invertebrate fauna found in each of 29 microcosms (233 observations of 31 species) using estimates of population density obtained in January 2005 in combination with published metabolism–mass relations for closely related taxa.
Results  In the rock pool system as a whole, population density decreased ( ancova : b  = –0.38 (–0.55 to –0.19), r ² = 0.19, P  < 0.001) and PEU increased with body mass ( ancova : b  = 0.55 (0.36–0.73), r ² = 0.28, P  < 0.001).
Main conclusions  The positive PEU–body mass relation found here suggests that larger organisms are energetically dominant and points to the importance of size-structured competition in these systems. Our results contrast those obtained in the few other previously published tests of the EER and challenge the idea that all species use similar amounts of energy regardless of their size.     

Individual and population energetics of a lizard on a Mediterranean islet

Summary Population density in the lacertid lizardPodarcis lilfordi on the Mediterranean islet of Nitge, Menorca, Balearic Islands, was found to be 12 190 ind · ha^-1 (SE, ±2135), exceeding densities reported for other island or mainland lizard populations. Field metabolic rates inP. lilfordi were measured by the doubly labeled water method, allowing estimation of a population metabolizable energy demand of 13.86 MJ · ha^-1 · day^-1-only 9.8% of that for a theoretical mammal population of the same body mass and density. Energy demand was considerably higher than that estimated for other lizard populations, primarily due to high population density but also because of high individual daily energy expenditure (1255 KJ · day^-1; body mass=5.13 g). Field metabolic rates were partitioned into maintenance and activity components by respirometry of captive animals at field body temperatures. Activity metabolism formed the main component (77.4%) of total respiratory metabolism resulting from a combination of long daily activity periods (ca. 12 h), and greatly elevated metabolism during activity (5.7 times greater than resting levels). It is hypothesized that low food availability per individual constrains the time-energy budget of this species, obligating long periods of intense foraging.     

A refined model of body mass and population density in flightless birds reconciles extreme bimodal population estimates for extinct moa

Flightless birds were once the largest and heaviest terrestrial fauna on many archipelagos around the world. Robust approaches for estimating their population parameters are essential for understanding prehistoric insular ecosystems and extinction processes. Body mass and population density are negatively related for extant flightless bird species, providing a method for quantifying densities and population sizes of extinct flightless species. Here we assemble an updated global data set of body mass and population densities for extant flightless birds and estimate the relationship between these variables. We use generalised least squares models that account for phylogenetic relatedness and incorporate the effects of limiting factors (e.g. habitat suitability) on population density. We demonstrate the applicability of this allometric relationship to extinct species by estimating densities for each of the nine species of moa (Dinornithiformes) and generating a combined spatially explicit map of total moa density across New Zealand. To compare our density estimates with those previously published, we summed individual species' abundances to generate a mean national density of 2.02–9.66 birds km⁻² for low- and high-density scenarios, respectively. Our results reconcile the extreme bimodality of previous estimates (< 2 birds km⁻² and > 10 birds km⁻²) and are comparable to contemporary densities of large herbivorous wild mammals introduced into New Zealand about 150 yr ago. The revised moa density has little effect on the harvest rates required to bring about extinction within 150–200 yr, indicating that rapid extinction was an inevitable response to human hunting, irrespective of the initial population of moa.     

Natural enemy ravine revisited: the importance of sample size for determining population growth

Abstract. 1. The population growth of three aphid species, Metopolophium dirhodum (Walker), Rhopalosiphum padi (L.), and Sitobion avenae (F.), on winter wheat, was analysed by regression. The calculations were based on censuses of aphids made in 268 plots at 3- or 7-day intervals for 10 years on leaves and 6 years on ears. The calculations were made separately for each plot each year, then repeated on the pooled data from all plots monitored in a year.
2. At the level of individual plots, no population growth was detected at very low densities. At high densities, the populations grew exponentially and the growth rates did not decrease with increasing aphid density.
3. Significant growth was always detected in the pooled data. These growth rates decreased significantly at the highest densities. Field estimates of the intrinsic rate of increase derived from these data ranged from 0.010 to 0.026 for M. dirhodum , 0.0071–0.011 for R. padi , and 0.00078–0.0061 and 0.0015–0.13 for S. avenae , on leaves and ears respectively .
4. The apparent lack of growth in the individual plots at low densities is attributable to small sample size. It is concluded that the natural enemy ravine in the population dynamics of cereal aphids, identified by Southwood and Comins (1976), is a consequence of low population densities at which population increase is undetectable unless very large samples are taken.     

A macroevolutionary explanation for energy equivalence in the scaling of body size and population density

Across a wide array of animal species, mean population densities decline with species body mass such that the rate of energy use of local populations is approximately independent of body size. This "energetic equivalence" is particularly evident when ecological population densities are plotted across several or more orders of magnitude in body mass and is supported by a considerable body of evidence. Nevertheless, interpretation of the data has remained controversial, largely because of the difficulty of explaining the origin and maintenance of such a size-abundance relationship in terms of purely ecological processes. Here I describe results of a simulation model suggesting that an extremely simple mechanism operating over evolutionary time can explain the major features of the empirical data. The model specifies only the size scaling of metabolism and a process where randomly chosen species evolve to take resource energy from other species. This process of energy exchange among particular species is distinct from a random walk of species abundances and creates a situation in which species populations using relatively low amounts of energy at any body size have an elevated extinction risk. Selective extinction of such species rapidly drives size-abundance allometry in faunas toward approximate energetic equivalence and maintains it there.     

Energy In-Equivalence in Australian Marsupials: Evidence for Disruption of the Continent’s Mammal Assemblage,or Are Rules Meant to Be Broken?

The energy equivalence rule (EER) is a macroecological hypothesis that posits that total population energy use (PEU) should be independent of species body mass, because population densities and energy metabolisms scale with body mass in a directly inverse manner. However, evidence supporting the EER is equivocal, and the use of basal metabolic rate (BMR) in such studies has been questioned; ecologically-relevant indices like field metabolic rate (FMR) are probably more appropriate. In this regard, Australian marsupials present a novel test for the EER because, unlike eutherians, marsupial BMRs and FMRs scale differently with body mass. Based on either FMR or BMR, Australian marsupial PEU did not obey an EER, and scaled positively with body mass based on ordinary least squares (OLS) regressions. Importantly, the scaling of marsupial population density with body mass had a slope of −0.37, significantly shallower than the expected slope of −0.75, and not directly inverse of body-mass scaling exponents for BMR (0.72) or FMR (0.62). The findings suggest that the EER may not be a causal, universal rule, or that for reasons not yet clear, it is not operating for Australia’s unique native fauna.     

Scaling of offspring number and mass to plant and animal size: model and meta-analysis

The scaling of reproductive parameters to body size is important for understanding ecological and evolutionary patterns. Here, we derived allometric relationships for the number and mass of seeds, eggs and neonates from an existing model on population production. In a separate meta-analysis, we collected 79 empirical regressions on offspring mass and number covering different taxa and various habitats. The literature review served as a validation of the model, whereas, vice versa, consistency of isolated regressions with each other and related ecological quantities was checked with the model. The total offspring mass delivered in a reproductive event scaled to adult size with slopes in the range of about 3/4 to 1. Exponents for individual seed, egg and neonate mass varied around 1/2 for most heterotherms and between 3/4 and 1 for most homeotherms. The scaling of the progeny number released in a sowing, clutch or litter was opposite to that of their size. The linear regressions fitted into a triangular envelope where maximum offspring mass is limited by the size of the adult. Minimum seed and egg size scaled with weight exponents of approximately 0 up to 1/4. These patterns can be explained by the influence of parents on the fate of their offspring, covering the continuum of r-strategists (pelagic–aquatic, arial, most invertebrates, heterotherms) and K-strategists (littoral–terrestrial, some invertebrates, homeotherms).     

Host population density and body mass as determinants of species richness in parasite communities: comparative analyses of directly transmitted nematodes of mammals

Epidemiological theory predicts positive correlations between host population density or body mass and species richness among parasite communities. Here I test these predictions by a comparative study of communities of directly transmitted mammalian parasites, gastrointestinal strongylid nematodes. I use data from 45 species of mammals, representing examination of 17 200 individual hosts. The variable studied was the average number of gastrointestinal strongylid nematode species per host population, and three different methods were used to obtain estimates of parasite species richness that are unbiased by number of host individuals examined. Analyses were done using the phylogenetically independent contrast method. Host population density and parasite species richness were strongly positively correlated when the effects of host body weight had been controlled for. Controlling for other variables did not change this, and the relationship was found regardless of method used to correct for uneven sampling effort among host species. A positive relationship between parasite species richness and host body weight was also found, but the effect of host densities had to be controlled for to see this. These relationships between host traits and species richness of directly transmitted parasites are stronger than patterns found using data on indirectly transmitted mammalian parasites, and suggests that links between host traits and parasite species richness are stronger than previously suggested. The results are consistent with parasite species richness being positively linked to pathogen transmission rates and reductions in transmission rates possibly increasing extinction probabilities in parasite populations. The results also suggest that parasites may exert a cost of increases in rate of population energy usage, and thus show that pathogens may be important in generating independence between body mass and rate of population energy usage among host species.     

Spatial organization and recruitment of lynx (Lynx lynx) in a re-introduced population in the Swiss Jura Mountains

We monitored seven resident (three males and four females) and six dispersing subadult Eurasian lynx from to in a population that was re-introduced to the Swiss Jura Mountains in the early 1970s. Home-range areas of the neighbouring adults were 71–281 km², and significant core areas 34–252 km². Males occupied significantly larger areas than females. Home-range overlap was 9% for neighbouring males and 3%) for females. Core areas of males did touch, but those of females were clearly separated. Each male's home range covered those of one or two females. Population density was 0.94 lynx/100 km² for resident animals. Pre-dispersal mortality was estimated to be 50%. Juveniles dispersed from their mothers' home area at the age of 10 months. Of six monitored subadults. only one survived the first year of independence. Human-caused mortality (traffic accidents. illegal killing) was high. This was also the case among resident adults. This might be a threat to the long-term survival of the reintroduced population.     

Towards a coherent allometric framework for individual home ranges,key population patches and geographic ranges

Spatial requirements of species have often been related to body size, usually focusing on one area variable and one taxonomic group at a time. Here, we carried out a quantitative meta‐analysis and developed a minimal model, covering different types of spatial characteristics and several species groups. In a global literature review, 46 empirical regressions on home ranges and geographic ranges were collected, covering thousands of species monitored in various countries. In addition, regional data on minimum key population patches of 167 species occurring in the Netherlands were retrieved from reports. To check consistency, a theoretical model was derived from rate and density variables based on energy equivalency. The minimum number of individuals needed to sustain a viable population was considered invariant to size. According to the equations, areas were expected to scale to mass with an exponent of 1 for the individual home range and of about ¾ for the minimum population ranges. The meta‐analysis of the empirical regressions showed that average slopes for individual home ranges were between 0.74 for cold‐blooded species and 1.05 for birds and mammals. Minimum and average species geographic range scaled to mass with exponents of 1.16–1.29 and 0.28–0.46 respectively. Allometric correlations for the minimum key patch area were weak. The intercepts indicated that carnivores require more space than equally sized herbivores, while homeotherms occupy larger areas than heterotherms. Observed slopes and intercepts were often near model estimations, but important deviations from the average level were noted as well, especially for birds. Although variability was substantial in some cases, allometric approaches can contribute considerably to understanding and protecting area requirements of species.     

Global patterns and predictors of avian population density

Aim

How population density varies across animal species in the context of environmental gradients, and associated migratory strategies, remains poorly understood. The recent influx of avian trait data and population density estimates allows these patterns to be described and explored in unprecedented detail. This study aims to identify the main macroecological drivers of population density in birds.

Location

Global.

Time period

1970–2021.

Major taxa studied

Birds (Aves).

Methods

We collated a dataset of 5072 local population density estimates for 1853 species and modelled population density as a function of trait and environmental predictors in a Bayesian framework accounting for phylogenetic and spatial autocorrelation. We explored the influence of body mass, diet, primary lifestyle, mating system, nesting behaviour, territoriality, and migratory behaviour on population density, accounting for a range of environmental variables, including preferred habitat type, primary productivity, precipitation and temperature. Based on this empirical baseline, we then predicted the mean population density for 9089 species of birds and estimated global geographic patterns of bird population density.

Results

Population density was lower in species with larger body mass and higher trophic levels, and also declined in territorial species, migratory species, brood parasites and species inhabiting resource-poor habitat types (e.g., deserts). Conversely, population density increased in cooperative breeders. Environmental drivers were most influential for migratory birds, with precipitation and temperature both associated with higher population density. Overall, bird population densities were higher at lower latitudes.

Main conclusions

Our results support previous findings on the role of body mass, diet and environmental gradients, but also reveal novel species-specific drivers of avian densities related to reproduction, migration and resource-holding behaviour. Substantial fine-scale variation remains unexplained. We provide a global dataset of population density predictions for use in macroecological analyses and conservation assessments.     

Body condition and nutritional ecology of Oreochromis mossambicus (Pisces, Cichlidae) populations of man-made lakes in Sri Lanka

The nutritive quality of ingested material of adult Oreochromis mossambicus wild populations from 12 perennial, man-made lakes were evaluated for four climatic seasons. The seasonal variation in condition of each population, and the overall condition of each population, considered as the theoretical weight of a 20cm individual, was computed from the length-weight regressions, which were curvilinear. The mean overall condition of the O. mossambicus reservoir population was 152.6 g ( s.d. ± 9.5) and ranged between 139.8 and 167.8 g. Distinct patterns in the seasonal changes in condition of an individual population were not apparent. The mean percentage of protein and total organic matter (TOM) and calorific content (kJg⁻¹) of the ingested material were 20.7% ( s.d. ± 3.7; range 9.6–35.2%), 46.0% ( s.d. ± 9.8; range 20.9–73.7%) and 11.6 ( s.d. ± 3.4; range 4.6–20.9) respectively. The amount of each of the above components for any one population varied seasonally in relation to the changes in feeding habit. The protein content of the ingested material of those populations devouring predominantly detritus also showed seasonal variability. The amount of protein (mg) in the digestible total organic matter (DTOM) and the calorific content (Cal) in the ingested material were related to the TOM content as follows: The overall body condition (BC) of O. mossambicus populations was linearly rebated to the digestible protein: energy ratio (PER) thus: The study indicates that a mixed diet was superior in nutritional quality to a single-component diet. especially with respect to detrital material.