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

Predicted short-term mesoscavenger release gives way to apex-scavenger dominance

Vultures play a crucial role in scavenging communities as apex scavengers. Scavenging communities in turn are a key component of terrestrial ecosystems, ensuring that dead biomass is removed quickly and efficiently. Anthropogenic disturbances, particularly mass poisonings, have caused crashes in vulture populations in Africa and Asia. We ask if vultures can re-establish themselves in a scavenging community from a point of near extirpation. To allow for maximum knowledge transfer across ecosystems, we focus on an ecosystem that is otherwise considered pristine. We chose Kruger National Park (KNP), a well-documented African scavenging community, as our focal ecosystem and parameterised a mathematical model of scavenging-community dynamics using field data from the park. We predicted the upper limit of vulture population size in an ecosystem like KNP. We then analysed vultures' path to recovery, using this empirically parameterised scavenging-community model. We used perturbation methods to determine how parameter values that may be specific to KNP influence our predictions. Comparisons of predicted vulture carrying capacity with recent population estimates suggest that the cumulative effect of human activities on vulture abundance is larger than previously believed. Our analysis shows that vulture populations can reach their carrying capacity approximately five decades after a poisoning event that would almost extirpate the population. Over shorter time scales, we predict a decade of enhanced mammal abundance (i.e. mesoscavenger release) before the mammals are excluded from the scavenging community. In our study system, jackals and hyenas are the mammalian groups predicted to benefit from the absence of vultures. However, neither group removes biomass as efficiently as vultures and animal carcasses are predicted to accumulate in the ecosystem while the vulture population recovers. In our framework, the carrying capacity for vulture populations is determined by carcass availability. As evidence for an alternative regulating factor is lacking, we conclude that present-day vulture population densities are orders of magnitude below their upper limits. Our results therefore suggest that with a recovery plan in place, the long-term prospects for vulture species and the associated ecosystems are positive.

Annual Mortality Limit for Four Gull Species in the Atlantic Flyway

We estimated the allowable annual take of great black-backed gulls Larus marinus, herring gulls L. argentatus, ring-billed gulls L. delawarensis, and laughing gulls Leucophaeus atricilla in the U.S. portion of the Atlantic Flyway to help meet human safety and resource management goals. Gulls can pose a serious threat to aviation, negatively impact other colonial-nesting migratory bird species, and conflict with other human activities. We estimated an annual take limit using a model that incorporated intrinsic population growth rate, minimum population size, and a recovery factor for each species. We estimated intrinsic population growth by combining allometric with life table approaches. We used the recovery factor to restrict the take level of the great black-backed gull beyond that of the other species because of poor data quality and concern about its population status. The herring gull was the only species with comprehensive demographic data. Population sizes used in estimating potential take limit varied greatly among the four species, but estimates of intrinsic population growth rate were similar (range 0.118 to 0.197). The annual potential take limits for the four gull species were 7,963 for herring gulls, 2,081 for great black-backed gulls, 15,039 for laughing gulls, and 14,826 for ring-billed gulls. Comparing average annual take from 2012–2019 to our modeled potential take limit, overharvest has not occurred for great black-backed and laughing gulls, occurred once every 8 y for ring-billed gulls, and occurred over half the time for herring gulls.

Climate-driven ecological stability as a globally shared cause of Late Quaternary megafaunal extinctions: the Plaids and Stripes Hypothesis

Controversy persists about why so many large-bodied mammal species went extinct around the end of the last ice age. Resolving this is important for understanding extinction processes in general, for assessing the ecological roles of humans, and for conserving remaining megafaunal species, many of which are endangered today. Here we explore an integrative hypothesis that asserts that an underlying cause of Late Quaternary megafaunal extinctions was a fundamental shift in the spatio-temporal fabric of ecosystems worldwide. This shift was triggered by the loss of the millennial-scale climate fluctuations that were characteristic of the ice age but ceased approximately 11700 years ago on most continents. Under ice-age conditions, which prevailed for much of the preceding 2.6 Ma, these radical and rapid climate changes prevented many ecosystems from fully equilibrating with their contemporary climates. Instead of today's 'striped' world in which species' ranges have equilibrated with gradients of temperature, moisture, and seasonality, the ice-age world was a disequilibrial 'plaid' in which species' ranges shifted rapidly and repeatedly over time and space, rarely catching up with contemporary climate. In the transient ecosystems that resulted, certain physiological, anatomical, and ecological attributes shared by megafaunal species pre-adapted them for success. These traits included greater metabolic and locomotory efficiency, increased resistance to starvation, longer life spans, greater sensory ranges, and the ability to be nomadic or migratory. When the plaid world of the ice age ended, many of the advantages of being large were either lost or became disadvantages. For instance in a striped world, the low population densities and slow reproductive rates associated with large body size reduced the resiliency of megafaunal species to population bottlenecks. As the ice age ended, the downsides of being large in striped environments lowered the extinction thresholds of megafauna worldwide, which then increased the vulnerability of individual species to a variety of proximate threats they had previously tolerated, such as human predation, competition with other species, and habitat loss. For many megafaunal species, the plaid-to-stripes transition may have been near the base of a hierarchy of extinction causes whose relative importances varied geographically, temporally, and taxonomically.

Improved estimation of intrinsic growth r(max) for long-lived species: integrating matrix models and allometry

Intrinsic population growth rate (r(max)) is an important parameter for many ecological applications, such as population risk assessment and harvest management. However, r(max) can be a difficult parameter to estimate, particularly for long-lived species, for which appropriate life table data or abundance time series are typically not obtainable. We describe a method for improving estimates of r(max) for long-lived species by integrating life-history theory (allometric models) and population-specific demographic data (life table models). Broad allometric relationships, such as those between life history traits and body size, have long been recognized by ecologists. These relationships are useful for deriving theoretical expectations for r(max), but r(max) for real populations may vary from simple allometric estimators for "archetypical" species of a given taxa or body mass. Meanwhile, life table approaches can provide population-specific estimates of r(max) from empirical data, but these may have poor precision from imprecise and missing vital rate parameter estimates. Our method borrows strength from both approaches to provide estimates that are consistent with both life-history theory and population-specific empirical data, and are likely to be more robust than estimates provided by either method alone. Our method uses an' allometric constant: the product of r(max) and the associated generation time for a stable-age population growing at this rate. We conducted a meta-analysis to estimate the mean and variance of this allometric constant across well-studied populations from three vertebrate taxa (birds, mammals, and elasmobranchs) and found that the mean was approximately 1.0 for each taxon. We used these as informative Bayesian priors that determine how much to "shrink" imprecise vital rate estimates for a data-limited population toward the allometric expectation. The approach ultimately provides estimates of r(max) (and other vital rates) that reflect a balance of information from the individual studied population, theoretical expectation, and meta-analysis of other populations. We applied the method specifically to an archetypical petrel (representing the genus Procellaria) and to white sharks (Carcharodon carcharias) in the context of estimating sustainable-fishery bycatch limits.

The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes

Ecosystems exhibit surprising regularities in structure and function across terrestrial and aquatic biomes worldwide. We assembled a global data set for 2260 communities of large mammals, invertebrates, plants, and plankton. We find that predator and prey biomass follow a general scaling law with exponents consistently near ¾. This pervasive pattern implies that the structure of the biomass pyramid becomes increasingly bottom-heavy at higher biomass. Similar exponents are obtained for community production-biomass relations, suggesting conserved links between ecosystem structure and function. These exponents are similar to many body mass allometries, and yet ecosystem scaling emerges independently from individual-level scaling, which is not fully understood. These patterns suggest a greater degree of ecosystem-level organization than previously recognized and a more predictive approach to ecological theory.

Limits to captive breeding of mammals in zoos

Captive breeding of mammals in zoos is the last hope for many of the best-known endangered species and has succeeded in saving some from certain extinction. However, the number of managed species selected is relatively small and focused on large-bodied, charismatic mammals that are not necessarily under strong threat and not always good candidates for reintroduction into the wild. Two interrelated and more fundamental questions go unanswered: have the major breeding programs succeeded at the basic level of maintaining and expanding populations, and is there room to expand them? I used published counts of births and deaths from 1970 to 2011 to quantify rates of growth of 118 captive-bred mammalian populations. These rates did not vary with body mass, contrary to strong predictions made in the ecological literature. Most of the larger managed mammalian populations expanded consistently and very few programs failed. However, growth rates have declined dramatically. The decline was predicted by changes in the ratio of the number of individuals within programs to the number of mammal populations held in major zoos. Rates decreased as the ratio of individuals in programs to populations increased. In other words, most of the programs that could exist already do exist. It therefore appears that debates over the general need for captive-breeding programs and the best selection of species are moot. Only a concerted effort could create room to manage a substantially larger number of endangered mammals.

Phylogenetic prediction of the maximum per capita rate of population growth

The maximum per capita rate of population growth, r, is a central measure of population biology. However, researchers can only directly calculate r when adequate time series, life tables and similar datasets are available. We instead view r as an evolvable, synthetic life-history trait and use comparative phylogenetic approaches to predict r for poorly known species. Combining molecular phylogenies, life-history trait data and stochastic macroevolutionary models, we predicted r for mammals of the Caniformia and Cervidae. Cross-validation analyses demonstrated that, even with sparse life-history data, comparative methods estimated r well and outperformed models based on body mass. Values of r predicted via comparative methods were in strong rank agreement with observed values and reduced mean prediction errors by approximately 68 per cent compared with two null models. We demonstrate the utility of our method by estimating r for 102 extant species in these mammal groups with unknown life-history traits.

Impact of stochasticity in immigration and reintroduction on colonizing and extirpating populations

A thorough quantitative understanding of populations at the edge of extinction is needed to manage both invasive and extirpating populations. Immigration can govern the population dynamics when the population levels are low. It increases the probability of a population establishing (or reestablishing) before going extinct (EBE). However, the rate of immigration can be highly fluctuating. Here, we investigate how the stochasticity in immigration impacts the EBE probability for small populations in variable environments. We use a population model with an Allee effect described by a stochastic differential equation (SDE) and employ the Fokker-Planck diffusion approximation to quantify the EBE probability. We find that, the effect of the stochasticity in immigration on the EBE probability depends on both the intrinsic growth rate (r) and the mean rate of immigration (p). In general, if r is large and positive (e.g. invasive species introduced to favorable habitats), or if p is greater than the rate of population decline due to the demographic Allee effect (e.g., effective stocking of declining populations), then the stochasticity in immigration decreases the EBE probability. If r is large and negative (e.g. endangered populations in unfavorable habitats), or if the rate of decline due to the demographic Allee effect is much greater than p (e.g., weak stocking of declining populations), then the stochasticity in immigration increases the EBE probability. However, the mean time for EBE decreases with the increasing stochasticity in immigration with both positive and negative large r. Thus, results suggest that ecological management of populations involves a tradeoff as to whether to increase or decrease the stochasticity in immigration in order to optimize the desired outcome. Moreover, the control of invasive species spread through stochastic means, for example, by stochastic monitoring and treatment of vectors such as ship-ballast water, may be suitable strategies given the environmental and demographic uncertainties at introductions. Similarly, the recovery of declining and extirpated populations through stochastic stocking, translocation, and reintroduction, may also be suitable strategies.

Survivorship patterns in captive mammalian populations: implications for estimating population growth rates

For species of conservation concern, ecologists often need to estimate potential population growth rates with minimal life history data. We use a survivorship database for captive mammals to show that, although survivorship scale (i.e., longevity) varies widely across mammals, survivorship shape (i.e., the age-specific pattern of mortality once survivorship has been scaled to maximum longevity) varies little. Consequently, reasonable estimates of population growth rate can be achieved for diverse taxa using a model of survivorship shape along with an estimate of longevity. In addition, we find that the parameters of survivorship shape are related to taxonomic group, a fact that may be used to further improve estimates of survivorship when full life history data are unavailable. Finally, we compare survivorship shape in captive and wild populations of the same species and find higher adult survivorship in captive populations but no corresponding increase in juvenile survivorship. These differences likely reflect a convolution of true differences in captive vs. wild survivorship and the difficulty of observing juvenile mortality in field studies.