The Nature Index: a general framework for synthesizing knowledge on the state of biodiversity.

The magnitude and urgency of the biodiversity crisis is widely recognized within scientific and political organizations. However, a lack of integrated measures for biodiversity has greatly constrained the national and international response to the biodiversity crisis. Thus, integrated biodiversity indexes will greatly facilitate information transfer from science toward other areas of human society. The Nature Index framework samples scientific information on biodiversity from a variety of sources, synthesizes this information, and then transmits it in a simplified form to environmental managers, policymakers, and the public. The Nature Index optimizes information use by incorporating expert judgment, monitoring-based estimates, and model-based estimates. The index relies on a network of scientific experts, each of whom is responsible for one or more biodiversity indicators. The resulting set of indicators is supposed to represent the best available knowledge on the state of biodiversity and ecosystems in any given area. The value of each indicator is scaled relative to a reference state, i.e., a predicted value assessed by each expert for a hypothetical undisturbed or sustainably managed ecosystem. Scaled indicator values can be aggregated or disaggregated over different axes representing spatiotemporal dimensions or thematic groups. A range of scaling models can be applied to allow for different ways of interpreting the reference states, e.g., optimal situations or minimum sustainable levels. Statistical testing for differences in space or time can be implemented using Monte-Carlo simulations. This study presents the Nature Index framework and details its implementation in Norway. The results suggest that the framework is a functional, efficient, and pragmatic approach for gathering and synthesizing scientific knowledge on the state of biodiversity in any marine or terrestrial ecosystem and has general applicability worldwide.

Geographical variation in the influence of density dependence and climate on the recruitment of Norwegian moose.

The effects of variation in climate on population dynamics are likely to differ within the distributional range of a species, yet the consequences of such regional variation on demography and population dynamics are rarely considered. Here we examine how density dependence and different climate variables affect spatio-temporal variation in recruitment rates of Norwegian moose using data collected over a large geographical area during the hunting season. After accounting for observation error by a Bayesian Markov chain Monte Carlo technique, temporal variation in recruitment rates was relatively independent of fluctuations in local population size. In fact, a positive relationship was as common as a density-dependent decrease in fecundity rates. In general, high recruitment rates were found during autumn 1 year after years with a warm February, and after a warm May or cold June in year t - 1 or in year t. Large regional variation was also found in the effects of some of the weather variables, especially during spring. These patterns demonstrate both direct and delayed effects of weather on the recruitment of moose that possibly operate through an effect of body mass on the proportion of the females that sexually mature as 1.5 or 2.5 years old.

Geographical gradients in the population dynamics of North American prairie ducks.

1. Geographic gradients in population dynamics may occur because of spatial variation in resources that affect the deterministic components of the dynamics (i.e. carrying capacity, the specific growth rate at small densities or the strength of density regulation) or because of spatial variation in the effects of environmental stochasticity. To evaluate these, we used a hierarchical Bayesian approach to estimate parameters characterizing deterministic components and stochastic influences on population dynamics of eight species of ducks (mallard, northern pintail, blue-winged teal, gadwall, northern shoveler, American wigeon, canvasback and redhead (Anas platyrhynchos, A. acuta, A. discors, A. strepera, A. clypeata, A. americana, Aythya valisineria and Ay. americana, respectively) breeding in the North American prairies, and then tested whether these parameters varied latitudinally. 2. We also examined the influence of temporal variation in the availability of wetlands, spring temperature and winter precipitation on population dynamics to determine whether geographical gradients in population dynamics were related to large-scale variation in environmental effects. Population variability, as measured by the variance of the population fluctuations around the carrying capacity K, decreased with latitude for all species except canvasback. This decrease in population variability was caused by a combination of latitudinal gradients in the strength of density dependence, carrying capacity and process variance, for which details varied by species. 3. The effects of environmental covariates on population dynamics also varied latitudinally, particularly for mallard, northern pintail and northern shoveler. However, the proportion of the process variance explained by environmental covariates, with the exception of mallard, tended to be small. 4. Thus, geographical gradients in population dynamics of prairie ducks resulted from latitudinal gradients in both deterministic and stochastic components, and were likely influenced by spatial differences in the distribution of wetland types and shapes, agricultural practices and dispersal processes. 5. These results suggest that future management of these species could be improved by implementing harvest models that account explicitly for spatial variation in density effects and environmental stochasticity on population abundance.

Estimation of population parameters from aerial counts of North American mallards: a cautionary tale.

The accuracy of population estimates strongly interferes with our ability to obtain unbiased estimates of population parameters based on analyses of time series of population fluctuations. Here we use long-term data on fluctuations in the size of Mallard populations collected as part of the May Breeding Waterfowl Survey covering a large section of North America. We assume a log-linear model of density dependence and use a hierarchical Bayesian state-space approach in which all parameters are assumed to be realizations from a common underlying distribution. Thus, parameters for different populations are not allowed to vary independently of each other. We then simulated independent time series of aerial counts, using the estimated parameters and adding various levels of observation error. These simulations showed that the estimates of stochastic population growth rate and strength of density dependence were biased even when moderate sampling errors were present. In contrast, the estimates of the environmental stochasticity and the carrying capacity were unbiased even for short time series and large observation error. Our results underline the importance of reducing the magnitude of sampling error in the design of large-scale monitoring programs of population fluctuations.

Effective size of fluctuating populations with two sexes and overlapping generations.

We derive formulas that can be applied to estimate the effective population size N(e) for organisms with two sexes reproducing once a year and having constant adult mean vital rates independent of age. Temporal fluctuations in population size are generated by demographic and environmental stochasticity. For populations with even sex ratio at birth, no deterministic population growth and identical mean vital rates for both sexes, the key parameter determining N(e) is simply the mean value of the demographic variance for males and females considered separately. In this case Crow and Kimura's generalization of Wright's formula for N(e) with two sexes, in terms of the effective population sizes for each sex, is applicable even for fluctuating populations with different stochasticity in vital rates for males and females. If the mean vital rates are different for the sexes then a simple linear combination of the demographic variances determines N(e), further extending Wright's formula. For long-lived species an expression is derived for N(e) involving the generation times for both sexes. In the general case with nonzero population growth and uneven sex ratio of newborns, we use the model to investigate numerically the effects of different population parameters on N(e). We also estimate the ratio of effective to actual population size in six populations of house sparrows on islands off the coast of northern Norway. This ratio showed large interisland variation because of demographic differences among the populations. Finally, we calculate how N(e) in a growing house sparrow population will change over time.

Predicting fluctuations of reintroduced ibex populations: the importance of density dependence, environmental stochasticity and uncertain population estimates.

1. Development of population projections requires estimates of observation error, parameters characterizing expected dynamics such as the specific population growth rate and the form of density regulation, the influence of stochastic factors on population dynamics, and quantification of the uncertainty in the parameter estimates. 2. Here we construct a Population Prediction Interval (PPI) based on Bayesian state space modelling of future population growth of 28 reintroduced ibex populations in Switzerland that have been censused for up to 68 years. Our aim is to examine whether the interpopulation variation in the precision of the population projections is related to differences in the parameters characterizing the expected dynamics, in the effects of environmental stochasticity, in the magnitude of uncertainty in the population parameters, or in the observation error. 3. The error in the population censuses was small. The median coefficient of variation in the estimates across populations was 5.1%. 4. Significant density regulation was present in 53.6% of the populations, but was in general weak. 5. The width of the PPI calculated for a period of 5 years showed large variation among populations, and was explained by differences in the impact of environmental stochasticity on population dynamics. 6. In spite of the high accuracy in population estimates, the uncertainty in the parameter estimates was still large. This uncertainty affected the precision in the population predictions, but it decreased with increasing length of study period, mainly due to higher precision in the estimates of the environmental variance in the longer time-series. 7. These analyses reveal that predictions of future population fluctuations of weakly density-regulated populations such as the ibex often become uncertain. Credible population predictions require that this uncertainty is properly quantified.

Generation time and temporal scaling of bird population dynamics.

Theoretical studies have shown that variation in density regulation strongly influences population dynamics, yet our understanding of factors influencing the strength of density dependence in natural populations still is limited. Consequently, few general hypotheses have been advanced to explain the large differences between species in the magnitude of population fluctuations. One reason for this is that the detection of density regulation in population time series is complicated by time lags induced by the life history of species that make it difficult to separate the relative contributions of intrinsic and extrinsic factors to the population dynamics. Here we use population time series for 23 bird species to estimate parameters of a stochastic density-dependent age-structured model. We show that both the strength of total density dependence in the life history and the magnitude of environmental stochasticity, including transient fluctuations in age structure, increase with generation time. These results indicate that the relationships between demographic and life-history traits in birds translate into distinct population dynamical patterns that are apparent only on a scale of generations.