Maximum Population Growth Rate Research Articles

Diagnosing the dangerous demography of manta rays using life history theory.

Background. The directed harvest and global trade in the gill plates of mantas, and devil rays, has led to increased fishing pressure and steep population declines in some locations. The slow life history, particularly of the manta rays, is cited as a key reason why such species have little capacity to withstand directed fisheries. Here, we place their life history and demography within the context of other sharks and rays.Methods. Despite the limited availability of data, we use life history theory and comparative analysis to estimate the intrinsic risk of extinction (as indexed by the maximum intrinsic rate of population increase rmax) for a typical generic manta ray using a variant of the classic Euler–Lotka demographic model. This model requires only three traits to calculate the maximum intrinsic population growth rate rmax: von Bertalanffy growth rate, annual pup production and age at maturity. To account for the uncertainty in life history parameters, we created plausible parameter ranges and propagate these uncertainties through the model to calculate a distribution of the plausible range of rmax values.Results. The maximum population growth rate rmax of manta ray is most sensitive to the length of the reproductive cycle, and the median rmax of 0.116 year−1 95th percentile [0.089–0.139] is one of the lowest known of the 106 sharks and rays for which we have comparable demographic information.Discussion. In common with other unprotected, unmanaged, high-value large-bodied sharks and rays the combination of very low population growth rates of manta rays, combined with the high value of their gill rakers and the international nature of trade, is highly likely to lead to rapid depletion and potential local extinction unless a rapid conservation management response occurs worldwide. Furthermore, we show that it is possible to derive important insights into the demography extinction risk of data-poor species using well-established life history theory.

Combined effects of four Microcystis aeruginosa strains and Scenedesmus obliquus concentrations on population dynamics and resting egg formation of two Daphnia species

We examined the hypothesis that toxic effects of Microcystis aeruginosa to population dynamics, ephippial production, and resting egg formation of Daphnia were restricted by food quality levels. Four unicellular, toxic M. aeruginosa strains with contrasting concentration of microcystin and two Daphnia species were used in this study. The number of offspring at first reproduction, population densities, and maximum population growth rate of two Daphnia species were lower at the highest toxic M. aeruginosa 7820 treatment compared with other treatments under two concentrations of Scenedesmus obliquus. The maximum number of offspring at first reproduction of two Daphnia species appeared in the higher toxic M. aeruginosa 526 strain at the high concentration of S. obliquus. The effects of M. aeruginosa strains, S. obliquus, and their combination on the number of offspring at first reproduction and the maximum population growth rate of two Daphnia species were significant (P < 0.001). Two Daphnia species could not reproduce in the highest toxic M7820 treatment under two concentrations of S. obliquus. They had lower population size and maximum population growth rate in the higher toxic M526 treatment at the low concentration of S. obliquus, but they were higher at the high concentration of S. obliquus. This result suggests that high S. obliquus concentration could relieve the toxicity of M. aeruginosa to Daphnia, and Daphnia could utilize the lower toxic Microcystis as food. The cumulative ephippia numbers of two Daphnia species were more at the high concentration of S. obliquus than those at the low concentration. The percentage of ephippia containing no resting eggs of two Daphnia species was evidently higher at the low concentration of S. obliquus but was lower at the high concentration of S. obliquus. Our results indicated that the cumulative ephippia numbers of Daphnia were population density dependent at the high-level food, and the productions of ephippia in Daphnia were significantly controlled by microcystin concentration at the low-level food.

Effects of Climate Change on Trait-Based Dynamics of a Top Predator in Freshwater Ecosystems

Predicted universal responses of ectotherms to climate warming include increased maximum population growth rate and changes in body size through the temperature-size rule. However, the mechanisms that would underlie these predicted responses are not clear. Many studies have focused on proximate mechanisms of physiological processes affecting individual growth. One can also consider ultimate mechanisms involving adaptive explanations by evaluating temperature effects on different vital rates across the life history and using the information in a population dynamical model. Here, we combine long-term data for a top predator in freshwater ecosystems (pike; Esox lucius) with a stochastic integral projection model to analyze concurrent effects of temperature on vital rates, body size, and population dynamics. As predicted, the net effect of warming on population growth rate (fitness) is positive, but the thermal sensitivity of this rate is highly size- and vital rate-dependent. These results are not sensitive to increasing variability in temperature. Somatic growth follows the temperature-size rule, and our results support an adaptive explanation for this response. The stable length structure of the population shifts with warming toward an increased proportion of medium-sized but a reduced proportion of small and large individuals. This study highlights how demographic approaches can help reveal complex underlying mechanisms for population responses to warming.

Environmental forcing and density-dependent controls of Culex pipiens abundance in a temperate climate (Northeastern Italy)

New and old mosquito-borne diseases have emerged and re-emerged in temperate regions over the recent past, but a mechanistic understanding of mosquito population dynamics, a fundamental step toward disease control, remains elusive. We propose here a Gompertz-based approach to address two obstacles to the development of vector dynamics models in temperate regions: (i) the inclusion of endogenous processes (e.g. density limitation, delayed responses, etc.) and the evaluation of their relative importance vs. exogenous environmental forcings; (ii) the inclusion of realistic descriptions of hydrologic processes and the evaluation of soil moisture as a more direct driver of mosquito population dynamics. The new model is based on a hierarchical state-space structure and is applied to the description of the abundance of Culex pipiens – a West Nile Virus vector – in the Po River Delta region (Northeastern Italy), using weekly mosquito abundance observations at more than 20 sites in the period May–September in 2010 and 2011. The hierarchical structure provides an efficient way of fully exploiting the information from a large network of observation sites. We find that Cx. pipiens abundance has significant density dependence at the one-week scale, which is coherent with its larval developmental time during the summer. This result points to the importance of endogenous population dynamics, most often neglected in mosquito population models, usually simply driven by exogenous environmental forcings. Among exogenous controls, temperature, daylight hours, and soil moisture were found to be most influential. Use of precipitation or soil moisture to force the model leads to very similar predictive skills. The negative correlation of soil moisture and mosquito population may be attributed to the abundance of water in the region (e.g. due to irrigation) and the preference for eutrophic habitats by Cx. pipiens. Variations among sites were highly correlated with land-use factors. The carrying capacity is seen to decrease with the distance to the nearest rice field, while the maximum population growth rate was positively related with the Normalized Difference Vegetation Index, a proxy of vegetation cover. The model shows a satisfactory performance in explaining the variation of mosquito abundance over a horizon of 1 week, particularly as far as peak timing and magnitude are concerned. Large rates of change of population abundance remain difficult to predict, as in other existing models, pointing to persisting gaps in our understanding of the mechanisms regulating mosquito population dynamics.

Using invasion process theory to enhance the understanding and management of introduced species: A case study reconstructing the invasion sequence of the common myna (Acridotheres tristis)

Research indicates that invasion is a multi-step process, where each stage is contingent on the stage that precedes it. Numerous hypotheses addressing the factors that influence each stage of the invasion process have been formulated, but how well does this theory match what occurs in the natural world? We created a general conceptual model for the invasion process based on invasion theory. Using a composite 41-year data set, we then reconstructed the invasion sequence of the common myna (Acridotheres tristis) to investigate the similarities between invasion theory and this observed invasion. We observed a lag period before population growth of 2.7 (±0.3) years, a maximum rate of population growth of 24.1 (±6.4) birds per km2 per year, a lag period before spreading of six years and an average spreading rate of 0.4 km per year. The length and duration of these stages correspond closely with what invasion process theory would anticipate. We suggest that a conceptual model, coupled with basic species, environment and event information, could be a useful tool to enhance the understanding and management of invasions.

Age at First Return to the Breeding Colony and Juvenile Survival of Sooty Shearwaters

Using mark-recapture, we estimated the age at first return and survival of juveniles of the Sooty Shearwater (Puffinus griseus), a medium-sized burrow-breeding procellariiform, at two New Zealand breeding colonies, Taiaroa Head and The Snares. Sooty Shearwaters were first observed at the colony between 2 and 10 years after being banded as chicks, with a mean of 5.7 years at Taiaroa Head and 5.4 years at The Snares. After accounting for imperfect detectability with a mark-recapture model, we estimate the mean age at first return as 4.8 years. Extrapolation from observed delays between arrival and breeding of the Short-tailed Shearwater (P. tenuirostris) suggests that the mean age at first breeding was 7.7 years. Annualized estimates of survival from 0 to 2 years were 0.54 at Taiaroa Head and 0.41 at The Snares. Overall estimates of the generation time and maximum rate of population growth were 13.1 years and 7.7%, respectively. Many published estimates of age at first return and age at first breeding are biased because they implicitly assume perfect detectability of individuals. Such an assumption in turn leads to bias in estimation of generation time and maximum rate of population growth. A generic population model for the Procellariiformes, in which the parameters are scaled against generation time, could prove to be a useful tool in guiding management of bycatch and sustainable harvest.

No need for disease: testing extinction hypotheses for the thylacine using multi‐species metamodels

Population viability analysis (PVA) is widely used to assess the extinction risk of threatened species and to evaluate different management strategies. However, conventional PVA neglects important biotic interactions and therefore can fail to identify important threatening processes. We designed a new PVA approach that includes species interactions explicitly by networking species models within a single 'metamodel'. We demonstrate the utility of PVA metamodels by employing them to reinterpret the extinction of the carnivorous, marsupial thylacine Thylacinus cynocephalus in Tasmania. In particular, we test the claim that well-documented impacts of European settlement cannot account for this extinction and that an unknown disease must have been an additional and necessary cause. We first constructed a classical, single-species PVA model for thylacines, which was then extended by incorporation within a dynamic predator-herbivore-vegetation metamodel that accounted for the influence of Europeans on the thylacine's prey base. Given obvious parameter uncertainties, we explored both modelling approaches with rigorous sensitivity analyses. Single-species PVA models were unable to recreate the thylacine's extinction unless a high human harvest, small starting population size or low maximum population growth rate was assumed, even if disease effects were included from 1906 to 1909. In contrast, we readily recreated the thylacine's demise using disease-free multi-species metamodels that simulated declines in native prey populations (particularly due to competition with introduced sheep). Dynamic, multi-species metamodels provide a simple, flexible framework for studying current species declines and historical extinctions caused by complex, interacting factors.

Calculating reference points for anthropogenic mortality of marine turtles

ABSTRACTHuman‐caused mortality threatens many marine turtle populations worldwide, with fisheries interactions being a primary cause for population declines. National and international management of fisheries interactions with marine turtles are rarely tied to turtle population biology. Quantitative tools tied to population‐based objectives can provide insight into the effectiveness and urgency of bycatch mitigation.A management approach is proposed based on a bycatch control rule called Reproductive Value Loss Limit (RVLL), generalized from the Potential Biological Removal management model for marine mammal populations. For RVLL, population size is scaled by reproductive value to account for strongly age‐structured population dynamics and age‐dependent fisheries mortality rates in marine turtle populations.RVLL is an estimate of maximum sustainable mortality for a population, calculated from estimates of maximum population growth rate, total reproductive value in the population, and an uncertainty factor. RVLL estimates correspond to specified management goals and risk tolerances. For demonstration, simultaneous goals of maintaining populations above the maximum net productivity level (analogous to the population size that produces maximum sustainable yield) and preventing a decrease in adults are assumed, both with 95% probability. A management‐strategy‐evaluation‐like process was used to explore parameterization of the RVLL equation for robust performance over a range of plausible life history characteristics and uncertainties in abundance and bycatch mortality estimates for marine turtle populations.The RVLL‐based management approach presented here proved robust to several important sources of uncertainty and to violation of several key underlying assumptions, and can be adapted to account for important sources of bias. The architecture presented, including tailored management strategy evaluation, provides a useful basis for further development of reference‐point‐based management of human‐added mortality in populations that experience large changes with age in reproductive value and human‐caused mortality rates, as is the case for marine turtles.Copyright © 2013 John Wiley &amp; Sons, Ltd.

Population dynamics, protein content, and lipid composition of Brachionus plicatilis fed artificial macroalgal detritus and Nannochloropsis sp. diets

Microalgae are often used in the culture of the rotifer Brachionus plicatilis, which is widely used as live feed for larval fish. However, the cultivation of large quantities of unicellular microalgae to support rotifer population growth is a heavy burden on many hatcheries. The effects of artificial detritus (detritus) from the macroalgae Ulva pertusa, Undaria pinnatifida, and Chondrus ocellatus, on the population growth and nutritional content (amino acid and fatty acid composition) of B. plicatilis were evaluated as potential substitute diets. We used the microalgae Nannochloropsis sp. as comparative food. The results show that the nutritional value of the detritus from each macroalgal species is not as good as Nannochloropsis in terms of population growth, maximum population density, and population growth rate. However, when Nannochloropsis was mixed with the detritus from the other three macroalgae, for the resulting B. plicatilis populations maintained high levels and attained higher maximum population densities and population growth rates. The nutritional value of B. plicatilis fed U. pertusa detritus, specifically, the free amino acid, polyunsaturated fatty acid, and docosahexaenoic acid (DHA), were better than those fed with other diets. The DHA/eicosapentaenoic acid (EPA) ratio in rotifers fed U. pertusa detritus was the highest at 6.9 times higher than those fed Nannochloropsis. Therefore, the detritus of macroalgae, especially U. pertusa, is an appropriate substitute diet, at least partly, for the culture and dietary enrichment of B. plicatilis.

Ecologically realistic estimates of maximum population growth using informedBayesian priors

SummaryPhenomenological density‐feedback models estimate parameters such as carrying capacity (K) and maximum population growth rate (rm) from time series of abundances. However, most series represent fluctuations aroundKwithout extending to low abundances and are thus uninformative aboutrm.We used informative prior distributions of maximum population growth rate,p(rm), to estimateBayesian posterior distributions inRicker andθ‐logistic models fitted to abundance series for 36 mammal species. We also used state‐space models to account for observation errors.We used two data sets of population growth rates from different mammal species with associated allometry (body mass) and demography (age at first reproduction) data to predictrmprior distributions.We assessed patterns of differences in posterior means () from models fitted with and without informative priors and used the deviance information criterion (DIC) to rank models for each species.Differences in posteriorfrom models with informative vs. vague priors co‐varied with the prior mean () forRicker models, but only posteriorco‐varied with priorinθ‐logistic models. Informative‐priorRicker models ranked higher than (81% of species), or equivalent to (all species), those with vague priors, which decreased to 70% ranking higher for state‐space models. Prior information also improved the precision ofby 13–45% depending on model and prior.Posteriorwere highly sensitive topriors forθ‐logistic models (halving and doubling prior mean gave −56% and 95% changes in, respectively) and less sensitive forRicker models (−25% and 35% changes in).Our results show that fitting density‐feedback models without prior information gives biologically unrealisticestimates in most cases, even from simpleRicker models. However, sensitivity analysis shows that highrm − θcorrelation inθ‐logistic models means the fit is largely determined by the prior, precluding the use of this model for most census data. Our findings are supported by applying models to simulated time series of abundance. Prior knowledge of species' life history can provide more ecologically realistic estimates (matching theoretical predictions) of regulatory dynamics even in the absence of detailed demographic data, thereby potentially improving predictions of extinction risk.

Population dynamics of invading freshwater fish: common carp (Cyprinus carpio) in the Murray-Darling Basin, Australia

There is much interest in managing invasive freshwater fish, but little is known about the dynamics of these populations following establishment. We used annual commercial catch-per-unit-effort data at multiple spatio-temporal scales to test hypotheses about the population dynamics of invading common carp (Cyprinus carpio) in the Murray-Darling Basin, Australia. We hypothesised that following establishment of the Boolara strain of this species in the Murray-Darling Basin in 1961/1962: (1) carp would undergo exponential or logistic-type population growth; and (2) carp population growth rates would be highest following over-bank flood events that provided extensive off-channel spawning and feeding habitats. The logistic (wi = 0.73) and delayed-logistic (wi = 0.27) models best explained the population dynamics of common carp in the Murray-Darling Basin during 1962/1963–2001/2002; there was negligible support for exponential growth (wi ≤ 0.01). Although we cannot exclude the possibility that floods may have been important in the early years of the invasion we found little evidence that carp population growth rates increased following flood events. Our logistic-type model-based estimates of the maximum annual population growth rate (rm; 0.378 and 0.384) indicate that >0.315 or 0.319 of the adult population would need to be removed annually to achieve eradication. We conclude that the rapid spread of the Boolara strain of common carp through the Murray-Darling Basin was facilitated by high initial population growth rates. More generally, we suggest that the lag period between an invader establishing and increasing to high abundances will be characterised by logistic-type population growth. We encourage others to investigate the long-term population dynamics of invading freshwater fish using time series and models such as those reported here.

Growth characteristics of two bloom-forming synurophytes (Mallomonas elongata and Synura petersenii) at different nitrate and phosphate concentrations

Two dominant planktonic bloom-forming algal species in a small shallow eutrophic pond were identified as Mallomonas elongata and Synura petersenii by electron microscopy. Their growth requirements were investigated as uni-algal cultures in a laboratory study. The maximum population growth and maximum growth rate of M. elongata occurred at concentrations of 24 μM nitrate (NO3) and 5 μM phosphate (PO4) at a temperature of 15°C and a pH of 6. Synura petersenii grew maximally and exhibited the highest growth rate at a NO3 concentration of 24 μM and a PO4 concentration of 2 μM. Mallomonas elongata and S. petersenii had similar nutrient requirements for optimum growth, suggesting that the biomass of these two species can be controlled by nutrient gradients.

American Chestnut Past and Future: Implications of Restoration for Resource Pulses and Consumer Populations of Eastern U.S. Forests

Forests dominated by oak, beech, hornbeam, and boreal conifers are characterized by resource pulses. Contemporary eastern U.S. oak forests may exhibit dramatic resource pulses in part because of the loss of American chestnut, which comprised 25–50% of the canopy throughout its range. Chestnut loss may have reduced mast resources for wildlife. A newly developed, blight‐resistant hybrid makes reintroduction feasible within several years. We use historical data to model the effects of American chestnut mast on consumer populations, illuminating the potential ecological effects of a successful restoration. We parameterized a stochastic population growth model with mast production data to compare consumer population dynamics both pre‐ and post‐blight. We explored the effect of maximum intrinsic population growth rate, degree of density dependence, and reliance upon mast on consumer response to chestnut loss. We parameterized the models for white‐footed mouse, eastern chipmunk, gray squirrel, and white‐tailed deer. At a northern site 14 years post‐blight, simulated annual mast production decreased 80% and the coefficient of variation (CV) increased 60%. At a southern site 35 years post‐blight, annual mast production decreased by 35% and the CV increased by 76%. Smaller, more variable mast crops translated to reduced abundance and increased variability in simulated consumer populations. White‐footed mice were the most responsive, exhibiting a 48% decrease in population size and 57% increase in interannual variation post‐blight. The reintroduction of blight‐resistant chestnut may fundamentally alter predator–prey interactions, gypsy moth outbreaks, and Lyme disease hot spots through its effect on the character of resource pulses that drive consumer dynamics.

Growth and lipid accumulation properties of a freshwater microalga, Chlorella ellipsoidea YJ1, in domestic secondary effluents

The combination of microalga-based biodiesel production and wastewater treatment is a promising approach to solve problems related to the energy crisis as well as eutrophication in bodies of water. A freshwater microalga, Chlorella ellipsoidea YJ1, with a high capacity for biomass production and lipid accumulation in secondary effluent was isolated. C. ellipsoidea YJ1 could achieve a biomass of 425 mg L −1 (dry weight) in domestic secondary effluent treated with activated sludge technology; and the lipid content per unit of algal biomass was as high as 43% (w/w) in this condition. The lipid growth rate of C. ellipsoidea YJ1 in domestic secondary effluents could attain 11.4 mg/L. Furthermore, after the cultivation of C. ellipsoidea YJ1, the removal efficiencies of nitrogen and phosphorus from the secondary effluent studied in this paper were more than 99% and 90%, respectively. Logistic and Monod models were used successfully to simulate the growth of C. ellipsoidea YJ1, and its maximum biomass and maximum population growth rate under different initial concentrations of nitrogen and phosphorus could be simulated and predicted using the models. .

Life history characters and population dynamics of the boreal larvaceanOikopleura vanhoeffeni(Tunicata) in Conception Bay, Newfoundland

We examined the population dynamics and life history characters of the boreal larvaceanOikopleura vanhoeffeniin Conception Bay over two years and determined its role in secondary production. Based on the analysis of age structure inferred from statolith diameter, the generation time was approximately one year. Recruitment of new cohorts and maximum population growth rate occurred in the spring. Somatic growth rate was 0.017 d−1from the year 2001 to 2002 and 0.043 d−1from 2002 to 2003, with an acceleration in growth rate during April in response to the spring diatom bloom despite the coldest water temperatures. The annual production rate (i.e. somatic + house production) of 8.7 g C m−2y−1in 2001/2, and 3.8 g C m−2y−1in 2002/3, represented 2.9–6.7% of primary production and 37–87% of estimated mesozooplankton production, suggesting thatO. vanhoeffeniis a major secondary producer in Conception Bay. Individuals matured at seasonally variable body size throughout the year and potential fecundity peaked as the individuals matured at their largest body size during the spring bloom, most likely resulting in maximum egg production and population growth rates at that time of year. Thus, a seasonal pulse of food is a major driving force that regulates the variation in life history characters and population dynamics of the borealO. vanhoeffeni.

Fluctuating food availability may permit coexistence in bacterivorous nematodes

The population growth of two bacterivorous nematodes, Panagrolaimus sp. and Poikilolaimus sp., isolated from Movile Cave, Romania, was studied at 20 °C at seven different densities of Escherichia coli as food source (10 7 -10 10 cells ml -1 ). By using semi-fluid media in a simple discharge system, we examined nematode and bacterial abundances over 56 days with high temporal resolution. At high nematode population densities, grazing severely reduced bacterial abundance-decreasing cell numbers by more than one order of magnitude. The two nematode species showed distinct differences in their reaction to different levels of food supply. Panagrolaimus realized its maximum population growth rate (r = 0.262 d -1 ) at the highest provided food density, i.e., 10 10 cells ml -1 . At lower food concentrations, its population growth was reduced, and at densities below 5 x 10 8 cells ml -1 reproduction could no longer compensate the experimentally induced mortality rate of 0.068 d -1 , thus resulting in extinction of the experimental populations. In contrast, Poikilolaimus thrived best at a bacterial density of 5 × 10 8 cells ml -1 (r = 0.203 d -1 ). Higher bacterial densities did not result in higher reproduction, but even somewhat hampered population growth of Poikilolaimus. Our investigation implies that, in a combined population, Poikilolaimus would be a superior competitor at low food availability whereas Panagrolaimus would benefit from high food densities. In an environment with regular fluctuations of food availability, these traits may prevent competitive exclusion and explain the observed long-term coexistence of the two species in their natural habitat.

The theta‐logistic is unreliable for modelling most census data

Summary1.The theta‐logistic is a simple and flexible model for describing how the growth rate of a population slows as abundance increases. Starting atrm(taken as the maximum population growth rate), the growth response decreases in a convex or concave way (according to the shape parameter θ) to zero when the population reaches carrying capacity.2.We demonstrate that fitting this model to census data is not robust and explain why. The parameters θ andrmare able to play‐off against each other (providing a constant product), thus allowing both to adopt extreme and ecologically implausible values.3.We use simulated data to examine: (i) a population fluctuating around a constant carrying capacity (K); (ii) recovery of a population from 10% of carrying capacity; and (iii) a population subject to variation inK. We show that estimates of extinction risk depending on this or similar models are therefore prone to imprecision. We refute the claim that concave growth responses are shown to dominate in nature.4.As the model can also be sensitive to temporal variation in carrying capacity, we argue that the assumption of a constant carrying capacity is both problematic and presents a fruitful direction for the development of phenomenological density‐feedback models.

Shifts in metabolic scaling, production, and efficiency across major evolutionary transitions of life.

The diversification of life involved enormous increases in size and complexity. The evolutionary transitions from prokaryotes to unicellular eukaryotes to metazoans were accompanied by major innovations in metabolic design. Here we show that the scalings of metabolic rate, population growth rate, and production efficiency with body size have changed across the evolutionary transitions. Metabolic rate scales with body mass superlinearly in prokaryotes, linearly in protists, and sublinearly in metazoans, so Kleiber's 3/4 power scaling law does not apply universally across organisms. The scaling of maximum population growth rate shifts from positive in prokaryotes to negative in protists and metazoans, and the efficiency of production declines across these groups. Major changes in metabolic processes during the early evolution of life overcame existing constraints, exploited new opportunities, and imposed new constraints.

Estimates of maximum annual population growth rates (rm) of mammals and their application in wildlife management

Summary 1. The maximum annual population growth rate (rm) is a critical parameter in many models of wildlife dynamics and management. An important application of rm is the estimation of the maximum proportion of a population that can be removed to stop population growth (p). 2. When rm cannot be estimated in the field, one option is to estimate it from demographic data. We evaluate the use of the relationship between rm and female age at first reproduction (α), which is independent of phylogeny, to estimate rm. We first demonstrate that the relationship between field and demographic estimates of rm is unbiased. We then show that the relationship provides an unbiased and simple method to estimate rm using data for 64 mammal species. We also show that p declines exponentially as α increases. 3. We use the fitted relationship to estimate annual rm and p for 55 mammal species in Australia and New Zealand for which there are no field estimates of rm. The estimates differ by species but have low precision (wide 95% credible intervals CIs). Our estimate of rm for the Tasmanian devil Sarcophilus harrisii is high (0·6, 95% CI: 0·05–2·39) and suggests devils would become extinct if >0·34 of the population is removed annually (e.g. by facial tumour disease). Our estimate of rm (0·77, 95% CI: 0·71–1·05) for brushtail possum Trichosurus vulpecula is much greater than published estimates and highlights the need for further field estimates of rm for the species in New Zealand. 4. Synthesis and applications. Since rm has not been estimated in the field for the majority of mammal species, our approach enables estimates with credible intervals for this important parameter to be obtained for any species for which female age at first reproduction is known. However, the estimates have wide 95% CIs. The estimated rm, and associated uncertainty can then be used in population and management models, perhaps most importantly to estimate the proportion that if removed annually would drive the population to extinction. Our approach can be used for taxa other than mammals.

Pitfalls and challenges of estimating population growth rate from empirical data: consequences for allometric scaling relations

The intrinsic rate of increase is a fundamental concept in population ecology, and a variety of problems require that estimates of population growth rate be obtained from empirical data. However, depending on the extent and type of data available (e.g. time series, life tables, life history traits), several alternative empirical estimators of population growth rate are possible. Because these estimators make different assumptions about the nature of age-dependent mortality and density-dependence of population dynamics, among other factors, these quantities capture fundamentally different aspects of population growth and are not interchangeable. Nevertheless, they have been routinely commingled in recent ecoinformatic analyses relating to allometry and conservation biology. Here we clarify some of the confusion regarding the empirical estimation of population growth rate and present separate analyses of the frequency distributions and allometric scaling of three alternative, non-interchangeable measures of population growth. Studies of allometric scaling of population growth rate with body size are additionally sensitive to the statistical line fitting approach used, and we find that different approaches yield different allometric scaling slopes. Across the mix of population growth estimators and line fitting techniques, we find scattered and limited support for the key allometric prediction from the metabolic theory of ecology, namely that log 10 (population growth rate) should scale as -0.25 power of log 10 (body mass). More importantly, we conclude that the question of allometric scaling of population growth rate with body size is highly sensitive to previously unexamined assumptions regarding both the appropriate population growth parameter to be compared and the line fitting approach used to examine the data. Finally, we suggest that the ultimate test of allometric scaling of maximum population growth rates with body size has not been done and, moreover, may require data that are not currently available.