Effect of stage-specific vital rates on population growth rates and effective population sizes in an endangered iteroparous plant

Effective population size (N(e)) determines the strength of genetic drift and can influence the level of genetic diversity a population can maintain. Assessing how changes in demographic rates associated with environmental variables and management actions affect N(e) thus can be crucial to the conservation of endangered species. Calculation of N(e) through demographic models makes it possible to use elasticity analyses to study this issue. The elasticity of N(e) to a given vital rate is the proportional change in N(e) associated with a proportional increase in that vital rate. In addition, demographic models can be used to study N(e) and population growth rate (λ) simultaneously. Simultaneous examination is important because some vital rates differ diametrically in their associations with λ and N(e). For example, in some cases increasing these vital rates increases λ and decreases N(e). We used elasticity analysis to study the effect of stage-specific survival and flowering rates on N(e), annual effective population size (N(a)), and λ in seven populations of the endangered plant Austrian dragonhead (Dracocephalum austriacum). In populations with λ ≥ 1, the elasticities of N(e) and N(a) were similar to those of λ. Survival rates of adults were associated with greater elasticities than survival rates of juveniles, flowering rates, or fecundity. In populations with λ < 1, N(e) and N(a) exhibited greater elasticities to juvenile than to adult vital rates. These patterns are similar to those observed in other species with similar life histories. We did not observe contrasting effects of any vital rate on λ and N(e); thus, management actions that increase the λ of populations of Austrian dragonhead will not increase genetic drift. Our results show that elasticity analyses of N(e) and N(a) can complement elasticity analysis of λ. Moreover, such analyses do not require more data than standard matrix models of population dynamics.     

Reliability of Absolute and Relative Predictions of Population Persistence Based on Time Series

Abstract:  Conventional population viability analysis (PVA) is often impractical because data are scarce for many threatened species. For this reason, simple count-based models are being advocated. The simplest of these models requires nothing more than a time series of abundance estimates, from which variance and autocorrelation in growth rate are estimated and predictions of population persistence are generated. What remains unclear, however, is how many years of data are needed to generate reliable estimates of these parameters and hence reliable predictions of persistence. By analyzing published and simulated time series, we show that several decades of data are needed. Predictions based on short time series were very unreliable mainly because limited data yielded biased, unreliable estimates of variance in growth rate, especially when growth rate was strongly autocorrelated. More optimistically, our results suggest that count-based PVA is sometimes useful for relative risk assessment (i.e., for ranking populations by extinction risk), even when time series are only a decade long. However, some conditions consistently lead to backward rankings. We explored the limited conditions under which simple count-based PVA may be useful for relative risk assessment.     

How sensitive are elasticities of long-run stochastic growth to how environmental variability is modelled?

A variable environment leaves a signature in a population's dynamics. Deriving statistical and mathematical models of how environmental variability affects population projections has - in the wake of reports of substantial climatic fluctuations - received much recent attention. If the model changes, then so too does the population projection. This is because a different model of environmental variability changes estimates of long-run stochastic growth, which is a function of demographic rates and their temporal sequence. Decomposing elasticities of long-run stochastic growth into constituent parts can assess the relative influence of different components. Here, we investigate the consequences of changing the environmental state definition, and therefore altering the shape of demographic rate distributions and their temporal sequence, by using age-structured matrix models to project vertebrate populations into the future under a range of environmental scenarios. The identity of the most influential demographic rate was consistent among all approaches that perturbed only the mean, but was not when only the variance was perturbed. Furthermore, the influence of each demographic rate fluctuated among projections by up to factors of six and two for changes to the variance and mean, respectively. These changes in influence depend in part upon how environmental variability - in particular, the color of environmental noise - is incorporated. In the light of predictions of increasing climatic variability in the future, these results suggest caution when drawing quantitative conclusions from stochastic population projections.     

Using demography and movement behavior to predict range expansion of the southern sea otter

In addition to forecasting population growth, basic demographic data combined with movement data provide a means for predicting rates of range expansion. Quantitative models of range expansion have rarely been applied to large vertebrates, although such tools could be useful for restoration and management of many threatened but recovering populations. Using the southern sea otter (Enhydra lutris nereis) as a case study, we utilized integro-difference equations in combination with a stage-structured projection matrix that incorporated spatial variation in dispersal and demography to make forecasts of population recovery and range recolonization. In addition to these basic predictions, we emphasize how to make these modeling predictions useful in a management context through the inclusion of parameter uncertainty and sensitivity analysis. Our models resulted in hind-cast (1989-2003) predictions of net population growth and range expansion that closely matched observed patterns. We next made projections of future range expansion and population growth, incorporating uncertainty in all model parameters, and explored the sensitivity of model predictions to variation in spatially explicit survival and dispersal rates. The predicted rate of southward range expansion (median = 5.2 km/yr) was sensitive to both dispersal and survival rates; elasticity analysis indicated that changes in adult survival would have the greatest potential effect on the rate of range expansion, while perturbation analysis showed that variation in subadult dispersal contributed most to variance in model predictions. Variation in survival and dispersal of females at the south end of the range contributed most of the variance in predicted southward range expansion. Our approach provides guidance for the acquisition of further data and a means of forecasting the consequence of specific management actions. Similar methods could aid in the management of other recovering populations.     

Conserving Slow-Growing, Long-Lived Tree Species: Input from the Demography of a Rare Understory Conifer, Taxus floridana

Abstract:  Although land preservation and promotion of successful regeneration are important conservation actions, their ability to increase population growth rates of slow-growing, long-lived trees is limited. We investigated the demography of Taxus floridana Nutt., a rare understory conifer, in three populations in different ravine forests spanning its entire geographic range along the Apalachicola River Bluffs in northern Florida (U.S.A.). We examined spatial and temporal patterns in demographic parameters and projected population growth rates by using four years of data on the recruitment and survival of seedlings and established stems, and on diameter growth from cross-sections of dead stems. All populations experienced a roughly 10-fold increase in seedling recruitment in 1996 compared with other years. The fates of seedlings and stems between 8 and 16 mm differed among populations. The fates of stems in two other size classes (the 2- to 4-mm class and the 4- to 8-mm class) differed among both populations and years. Individual stems in all populations exhibited similarly slow growth rates. Stochastic matrix models projected declines in all populations. Stochastic matrix analysis revealed the high elasticity of a measure of stochastic population growth rate to perturbations in the stasis of large reproductive stems for all populations. Additional analyses also indicated that occasional episodes of high recruitment do not greatly affect population growth rates. Conservation efforts directed at long-lived, slow-growing rare plants like Taxus floridana should both protect established reproductive individuals and further enhance survival of individuals in other life-history stages, such as juveniles, that often do not appear to contribute greatly to population growth rates.     

Testing sustainability by prospective and retrospective demographic analyses: evaluation for palm leaf harvest.

Harvesting nontimber forest products (NTFPs) is a major economic activity in tropical forests. As many NTFPs are overexploited, sustainability analyses are required to set harvest guidelines. Here we introduce and apply a new approach to evaluating sustainability, which combines prospective (elasticity) and retrospective (Life Table Response Experiments [LTRE]) demographic analyses of matrix population models. We relate the elasticity of vital rates (representing their importance for population growth rate, lamda) to their contribution to harvest-induced change in lamda ("LTRE contribution"). When high-elasticity vital rates have a low LTRE contribution, exploitation is potentially sustainable as negative effects for population growth are buffered. If the reverse is found, there is little scope for sustainability because crucial vital rates are affected. Our approach is less sensitive to chance fluctuations than the commonly used sustainability criterion of lamda = 1.0, as it does not depend on the absolute value of lamda. We applied this analysis to Geonoma deversa, a clustered forest understory palm. We studied three experimentally defoliated and control populations in a Bolivian rainforest during two years. Cutting all leaves of large ramets did not change mortality but strongly affected growth and reproduction. In spite of severe changes in some vital rates, population growth rate was not significantly reduced after defoliation. A literature review revealed that six other understory palms species responded very similarly to defoliation. The combination of LTRE contributions and elasticity analyses showed that low-elasticity vital rates were mainly responsible for the defoliation-induced change in lamda for Geonoma deversa. For two other understory palms (Astrocaryum mexicanum and Chamaedorea radicalis) new demographic analyses yielded very similar results. For Geonoma, the LTRE contribution-elasticity relation strongly changed when we mimicked harvest damage. Adding 5% mortality to defoliated palms caused stronger change in lamda, mainly due to changes in a high-elasticity vital rate (survival). Therefore, harvest practices that involve stem killing are clearly unsustainable. Our results show that commercial leaf cutting in Geonoma deversa is potentially sustainable, and that this is likely the case for understory palms in general. Our approach to evaluating harvest sustainability can be applied to other NTFPs.     

Elasticity analyses of size-based red and white abalone matrix models: management and conservation.

Prospective elasticity analyses have been used to aid in the management of fished species and the conservation of endangered species. Elasticities were examined for deterministic size-based matrix models of red abalone, Haliotis rufescens, and white abalone, H. sorenseni, to evaluate which size classes influenced population growth (lambda) the most. In the red abalone matrix, growth transitions were determined from a tag recapture study and grouped into nine size classes. In the white abalone matrix, abalone growth was determined from a laboratory study and grouped into five size classes. Survivorship was estimated from tag recapture data for red abalone using a Jolly-Seber model with size as a covariate and used for both red and white abalone. Reproduction estimates for both models used averages of the number of mature eggs produced by female red and white abalone in each size class from four-year reproduction studies. Population growth rate (lambda) was set to 1.0, and the first-year survival (larval survival through to the first size class) was estimated by iteration. Survival elasticities were higher than fecundity elasticities in both the red and white matrix models. The sizes classes with the greatest survival elasticities, and therefore the most influence on population growth in the model, were the sublegal red abalone (150-178 mm) and the largest white abalone size class (140-175 mm). For red abalone, the existing minimum legal size (178 mm) protects the size class the model suggests is critical to population growth. Implementation of education programs for novice divers coupled with renewed enforcement may serve to minimize incidental mortality of the critical size class. For white abalone, conservation efforts directed at restoring adults may have more of an impact on population growth than efforts focusing on juveniles. Our work is an example of how prospective elasticity analyses of size-structured matrix models can be used to quantitatively evaluate research priorities, fishery management strategies, and conservation options.     

Conservation and Management of a Threatened Madagascar Palm Species, Neodypsis decaryi, Jumelle

The dynamics of a remnant population of the palm Neodypsis decaryi were characterized using a linear, stage-structured demographic model. This palm is a threatened keystone species restricted to a narrow ecological zone in southeastern Madagascar. The population showed high mortality rates in the early stages of the life cycle, followed by a period of lower adult mortality. Demographic results indicated that the population was either stable or increasing inside the reserve (λ _m close to 1.0). Sensitivity and elasticity analyses indicated that adult stage classes were the most sensitive to producing changes in population growth rates. Continued biological monitoring is appropriate for the long-term conservation management of this palm inside the reserve. Outside the protected area the population appears to be declining rapidly, mainly because of anthropogenic effects (especially fire and grazing). If the conservation of Neodypsis decaryi is to be successful in the long term, then conservation methods must be carried out in cooperation with local villagers, and the species should be managed as a renewable resource in situ and ex situ. In situ conservation should include cultivation of this species throughout its natural range and protection of the existing viable natural populations. Alternative conservation management practices, both ecologically and economically sustainable, may be useful to alleviate the human pressures on this renewable resource. If leaves of N. decaryi are to be harvested by local people, we recommend restricting annual harvesting to about 25% of leaves per tree per year. Based on sensitivity analysis, seed collection should be kept well below 95% of the yearly crop if harvesting is not to have a significant impact on population growth rates.     

Demographic Characteristics of Extinction in a Small, Insular Population of House Sparrows in Northern Norway

Abstract:  In conservation ecology there is an urgent need for indicators that can be used to predict the risk of extinction of populations. Identifying extinction-prone populations has been difficult because few data sets on the demographic characteristics of the final stage to extinction are available and because of problems in separating out stochastic effects from changes in the expected dynamics. We documented the demographic changes that occurred during the period prior to extinction of a small island population of House Sparrows ( Passer domesticus ) after the end of permanent human settlement. A mark-recapture analysis revealed that this decline to extinction was mainly due to increased mortality after closure of the last farm that resulted in a negative long-term-specific growth rate. No change occurred in either the structural composition (breeding sex ratio and age distribution) of the population or in female recruitment. No male, however, recruits were produced on the island after the farm closure. Based on a simple, stochastic, density-dependent model we constructed a population prediction interval (PPI) to estimate the time to extinction. The 95% PPI slightly overestimated the time to extinction with large uncertainty in predictions, especially due to the influence of demographic stochasticity and parameter drift. Our results strongly emphasize the importance of access to data on temporal variation that can be used to parameterize simple population models that allow estimation of critical parameters for credible prediction of time to extinction.     

Climate influences the demography of three dominant sagebrush steppe plants

Climate change could alter the population growth of dominant species, leading to profound effects on community structure and ecosystem dynamics. Understanding the links between historical variation in climate and population vital rates (survival, growth, recruitment) is one way to predict the impact of future climate change. Using a unique, long-term data set from eastern Idaho, USA, we parameterized integral projection models (IPMs) for Pseudoroegneria spicata, Hesperostipa comata, and Artemisia tripartita to identify the demographic rates and climate variables most important for population growth. We described survival, growth, and recruitment as a function of genet size using mixed-effect regression models that incorporated climate variables. Elasticites for the survival + growth portion of the kernel were larger than the recruitment portion for all three species, with survival + growth accounting for 87-95% of the total elasticity. The genet sizes with the highest elasticity values in each species were very close to the genet size threshold where survival approached 100%. We found strong effects of climate on the population growth rate of two of our three species. In H. comata, a 1% decrease in previous year's precipitation would lead to a 0.6% decrease in population growth. In A. tripartita, a 1% increase in summer temperature would result in a 1.3% increase in population growth. In both H. comata and A. tripartita, climate influenced population growth by affecting genet growth more than survival or recruitment. Late-winter snow was the most important climate variable for P. spicata, but its effect on population growth was smaller than the climate effects we found in H. comata or A. tripartita. For all three species, demographic responses lagged climate by at least one year. Our analysis indicates that understanding climate effects on genet growth may be crucial for anticipating future changes in the structure and function of sagebrush steppe vegetation.     

Life history and viability of a long-lived marine invertebrate: the octocoral Paramuricea clavata

The red gorgonian Paramuricea clavata is a long-lived, slow-growing sessile invertebrate of ecological and conservation importance in the northwestern Mediterranean Sea. We develop a series of size-based matrix models for two Paramuricea clavata populations. These models were used to estimate basic life history traits for this species and to evaluate the viability of the red gorgonian populations we studied. As for many other slow-growing species, sensitivity and elasticity analysis demonstrate that gorgonian population growth is far more sensitive to changes in survival rates than to growth, shrinkage, or reproductive rates. The slow growth and low mortality of red gorgonians results in low damping ratios, indicating slow convergence to stable size structures (at least 50 years). The stable distributions predicted by the model did not differ from the observed ones. However, our simulations point out the fragility of this species, showing both populations in decline and high risk of extinction over moderate time horizons. These declines appear to be related to a recent increase in anthropogenic disturbances. Relative to their life span, the values of recruitment elasticity for Paramuricea clavata are lower than those reported for other marine organisms but are similar to those reported for some long-lived plants. These values and the delayed age of sexual maturity, in combination with the longevity of the species, show a clear fecundity/mortality trade-off. Full demographic studies of sessile marine species are quite scarce but can provide insight into population dynamics and life history patterns for these difficult and under-studied species. While our work shows clear results for the red gorgonian, the variability in some of our estimates suggest that future work should include data collection over longer temporal and spatial scales to better understand the long-term effects of natural and anthropogenic disturbances on red gorgonian populations.     

Environment-specific elasticity and sensitivity analysis of the stochastic growth rate

For matrix population models, analyses of how sensitive the population growth rate is to changes in vital rates (i.e. perturbations) are important for studies of life history evolution as well as for management and conservation of threatened species. There are two types of sensitivity analyses corresponding to absolute (sensitivity) or relative (elasticity) changes in the vital rates and both types can be applied to both deterministic and stochastic matrix population models. To date, most empirical studies of elasticity and sensitivity of the stochastic growth rate have examined the response to perturbations in the vital rates in a complete set of possible environments. However, it is often of interest to examine the response to perturbations occurring in only a subset of the possible environments. This has been done for periodic time-varying models elsewhere, but here we describe a recently published method for calculating the environment-specific sensitivity and elasticity of the stochastic growth rate and apply this method to data. These environment-specific perturbation analyses provide a logical way of dividing the sensitivity and elasticity among the environments. They give important insight into the selection regime in different environments and can provide valuable information for making management decisions and management evaluations in stochastic environments.     

Use of Integrated Modeling to Enhance Estimates of Population Dynamics Obtained from Limited Data

Abstract:  Demographic data of rare and endangered species are often too sparse to estimate vital rates and population size with sufficient precision for understanding population growth and decline. Yet, the combination of different sources of demographic data into one statistical model holds promise. We applied Bayesian integrated population modeling to demographic data from a colony of the endangered greater horseshoe bats (Rhinolophus ferrumequinum) . Available data were the number of subadults and adults emerging from the colony roost at dusk, the number of newborns from 1991 to 2005, and recapture data of subadults and adults from 2004 and 2005. Survival rates did not differ between sexes, and demographic rates remained constant across time. The greater horseshoe bat is a long-lived species with high survival rates (first year: 0.49 [SD 0.06]; adults: 0.91 [SD 0.02]) and low fecundity (0.74 [SD 0.12]). The yearly average population growth was 4.4% (SD 0.1%) and there were 92 (SD 10) adults in the colony in year 2005. Had we analyzed each data set separately, we would not have been able to estimate fecundity, the estimates of survival would have been less precise, and the estimate of population growth biased. Our results demonstrate that integrated models are suitable for obtaining crucial demographic information from limited data.     

Factors Leading to Different Viability Predictions for a Grizzly Bear Data Set

Population viability analysis programs are being used increasingly in research and management applications, but there has not been a systematic study of the congruence of different program predictions based on a single data set. We performed such an analysis using four population viability analysis computer programs: GAPPS, INMAT, RAMAS/AGE, and VORTEX. The standardized demographic rates used in all programs were generalized from hypothetical increasing and decreasing grizzly bear ( Ursus arctos horribilis ) populations. Idiosyncracies of input format for each program led to minor differences in intrinsic growth rates that translated into striking differences in estimates of extinction rates and expected population size. In contrast, the addition of demographic stochasticity, environmental stochasticity, and inbreeding costs caused only a small divergence in viability predictions. But, the addition of density dependence caused large deviations between the programs despite our best attempts to use the same density-dependent functions. Population viability programs differ in how density dependence is incorporated, and the necessary functions are difficult to parameterize accurately. Thus, we recommend that unless data clearly suggest a particular density-dependent model, predictions based on population viability analysis should include at least one scenario without density dependence. Further, we describe output metrics that may differ between programs; development of future software could benefit from standardized input and output formats across different programs.     

Extinction times in experimental populations

Predicting population extinctions is a key element of quantitative conservation biology and population ecology. Although stochastic population theories have long been used to obtain theoretical distributions of population extinction times, model-based predictions have rarely been tested. Here I report results from a quantitative analysis of extinction time in 281 experimental populations of water fleas (Daphnia magna) in variable environments. To my knowledge, this is the first quantitative estimate of the shape of the distribution of population extinction times based on extinction data for any species. The finding that the distribution of population extinction times was extraordinarily peaked is consistent with theoretical predictions for density-independent populations, but inconsistent with predictions for density-dependent populations. The tail of the extinction time distribution was not exponential. These results imply that our current theories of extinction are inadequate. Future work should focus on how demographic stochasticity scales with population size and effects of nonrandom variable environments on population growth and decline.     

Predicting [corrected] extinction risk in spite of predator-prey oscillations.

Most population viability analyses (PVA) assume that the effects of species interactions are subsumed by population-level parameters. We examine how robust five commonly used PVA models are to violations of this assumption. We develop a stochastic, stage-structured predator-prey model and simulate prey population vital rates and abundance. We then use simulated data to parameterize and estimate risk for three demographic models (static projection matrix, stochastic projection matrix, stochastic vital rate matrix) and two time series models (diffusion approximation [DA], corrupted diffusion approximation [CDA]). Model bias is measured as the absolute deviation between estimated and observed quasi-extinction risk. Our results highlight three generalities about the application of single-species models to multi-species conservation problems. First, our collective model results suggest that most single-species PVA models overestimate extinction risk when species interactions cause periodic variation in abundance. Second, the DA model produces the most (conservatively) biased risk forecasts. Finally, the CDA model is the most robust PVA to population cycles caused by species interactions. CDA models produce virtually unbiased and relatively precise risk estimates even when populations cycle strongly. High performance of simple time series models like the CDA owes to their ability to effectively partition stochastic and deterministic sources of variation in population abundance.     

Double Allee Effects and Extinction in the Island Fox

Abstract:  An Allee effect (AE) occurs in populations when individuals suffer a decrease in fitness at low densities. If a fitness component is reduced (component AE), per capita population growth rates may decline as a consequence (demographic AE) and extinction risk is increased. The island fox ( Urocyon littoralis ) is endemic to six of the eight California Channel Islands. Population crashes have coincided with an increase in predation by Golden Eagles ( Aquila chrysaetos ). We propose that AEs could render fox populations more sensitive and may be a likely explanation for their sharp decline. We analyzed demographic data collected between 1988 and 2000 to test whether fox density (1) influences survival and reproductive rates; (2) interacts with eagle presence and affects fox fitness parameters; and (3) influences per capita fox population trends. A double component AE simultaneously influenced survival (of adults and pups) and proportion of breeding adult females. The adult survival AE was driven by predation by eagles. These component AEs led to a demographic AE. Multiple-component AEs, a predation-driven AE, and the simultaneous occurrence of both component and demographic AEs in a mammal are all previously unreported processes. Populations below 7 foxes/km² could have suboptimal population growth rates due to the demographic AE, and AEs may have contributed to the dramatic declines in three fox populations. Because fox densities in critically endangered populations are well below this level, removing Golden Eagles appears necessary to prevent a predation-driven AE. Conservationists should also be aware of AEs when planning the release of captive foxes. More generally, our findings highlight the danger of overlooking AEs in the conservation of populations of rare or threatened species.     

An improved formal approach to demographic loop analysis

Loop analysis is introduced to demographic analysis as a tool to compare relative contributions of different life-history types to population growth rate. In 1998, G. M. Wardle brought in basic concepts of the graph theory to demographic loop analysis and proposed a methodology to determine the loops from any life-cycle graph based on these concepts. However, the mathematics behind Wardle's methodology cannot readily be used by most population ecologists. A new methodology that is also based on graph theory concepts but both makes ecological sense in its application and is simpler to implement is proposed. Three rules of thumb serve as the basis of the proposed methodology that brings a more systematic approach to loop selection: it identifies only those loops that are ecologically meaningful (i.e., loops that are forward-flowing and with positive elasticity values). Thus, it produces a loop set that is more amenable to answer questions on comparison of different lifehistory types. It is tested on several life-cycle graphs from the literature. Three of these are presented: Vouacapoua americana, Dipsacus sylvestris, and Alcyonium sp. In each case, the methodology successfully produced a loop set that makes sense in terms of the ecology of the species. The methodology is also implemented as a couple of open-source computer codes. It is hoped that the proposed methodology will lead to wider use of loop analysis in demographic population studies.