Projected population persistence of eastern hellbenders (Cryptobranchus alleganiensis alleganiensis) using a stage-structured life-history model and population viability analysis

The population of eastern hellbenders (Cryptobranchus alleganiensis alleganiensis) in the Blue River, Indiana has undergone a dramatic decline over the last decade. Recruitment in these declining populations has been negligible, and populations are now composed almost entirely of older age classes (upwards of 20 years old). Given this dramatic decline, it is imperative to assess the impacts of these demographic patterns on population growth and long-term stability. Therefore, we developed a stage-structured, life-history model to examine the effects of varying levels of egg, juvenile, and adult survivorship on abundance, recruitment, and long-term population projections. We performed a sensitivity analysis of the model and determine which life-history parameters have the greatest potential to increase/stabilise hellbender population growth. Finally, we conducted a population viability analysis to determine the probability of extinction associated with varying management strategies. For eastern hellbender populations in Indiana, adults (especially females) are the most important component of long-term population viability. Sensitivity and elasticity analyses of the Lefkovitch matrix revealed that survival of adult and egg/larvae life-history stages are the most important for focused management efforts. Indeed, adults had the highest elasticity and reproductive value in the matrix model. Increasing survival by as little as 20% corresponded to the turning point at which the population ceased to decline and increased abundance (28% survival of egg/larvae). The importance of the transition from subadult to adult (transitional matrix element) was identified as an additional factor in maintaining abundance based on the relatively long period spent in this life-history stage (seven years for females). A population viability analysis was conducted to assess the likelihood and projected time frame of extinction for this population under no management (～25 years to complete extirpation; probability of extinction = 1) and if management efforts such as captive rearing and headstarting are undertaken (probability of extinction <0.2 at 25–30% survival of egg/larvae). Adult females had the greatest effect in reducing growth rate and population abundance when removed in exploitation simulations (91.3% versus 51.8% reduction in population growth rate), indicating translocation efforts should be designed to maintain females in the breeding pool. These models indicated that conservation management strategies aimed at ensuring the presence of adult females while concomitantly ameliorating survival at early life stages (population augmentation, translocations, introduction of artificial nest structures) are needed to stabilise the Indiana population of eastern hellbenders. This stage-structured model is the first to model eastern hellbenders and has broad implications for use across the geographic range where populations of eastern hellbenders are monitored and vital rates can be estimated.     

Carnivora Population Dynamics Are as Slow and as Fast as Those of Other Mammals: Implications for Their Conservation

Of the 285 species of Carnivora 71 are threatened, while many of these species fulfill important ecological roles in their ecosystems as top or meso-predators. Population transition matrices make it possible to study how age-specific survival and fecundity affect population growth, extinction risks, and responses to management strategies. Here we review 38 matrix models from 35 studies on 27 Carnivora taxa, covering 11% of the threatened Carnivora species. We show that the elasticity patterns (i.e. distribution over fecundity, juvenile survival and adult survival) in Carnivora cover the same range in triangular elasticity plots as those of other mammal species, despite the specific place of Carnivora in the food chain. Furthermore, reproductive loop elasticity analysis shows that the studied species spread out evenly over a slow-fast continuum, but also quantifies the large variation in the duration of important life cycles and their contributions to population growth rate.These general elasticity patterns among species, and their correlation with simple life history characteristics like body mass, age of first reproduction and life span, enables the extrapolation of population dynamical properties to unstudied species. With several examples we discuss how this slow-fast continuum, and related patterns of variation in reproductive loop elasticity, can be used in the formulation of tentative management plans for threatened species that cannot wait for the results of thorough demographic studies. We argue, however, that such management programs should explicitly include a plan for learning about the key demographic rates and how these are affected by environmental drivers and threats.     

Population biology of Aesculus turbinata Blume: A demographic analysis using transition matrices on a natural population along a riparian environmental gradient

Population structure and dynamics of a riparian canopy species, Aesculus turbinata (Japanese horse chestnut), were analyzed based on the census data collected for the 8 years from 1989 to 1996 in temperate deciduous forests in Ashiu, Kyoto Prefecture, Japan. The censuses were conducted in three permanently established study plots over an environmental gradient that included the lower hill slope, river terrace, and floodplain of a riparian area within a forest stand of approximately 3 ha. Transition matrix based on the data from 1989 to 1996 was provided for the total population made by pooling population data from all subpopulations in three different habitats (i.e. slope, terrace, floodplain). The total Aesculus population showed positive population growth (λ = 1.0298). From the elasticity analysis, larger elasticity values were obtained with increasing size- or stage-classes. A combined transition matrix was also constructed for the life-history processes consisting of three subpopulations developed on an environmental gradient. This whole population linked by seed flow showed an increase in population size (λ = 1.0286). The elasticity matrix showed the relative importance of the slope subpopulation, suggesting its significant role as a mainland source population. Log-linear analyses were carried out to examine spatiotemporal variations of life-history parameters; significant effects of stage and plot were recognized, while no effect of year was detected on any life-history parameters except for fecundity.     

Graph decompositions for demographic loop analysis

A new approach to loop analysis is presented in which decompositions of the total elasticity of a population projection matrix over a set of life history pathways are obtained as solutions of a constrained system of linear equations. In loop analysis, life history pathways are represented by loops in the life cycle graph, and the elasticity of the loop is interpreted as a measure of the contribution of the life history pathway to the population growth rate. Associated with the life cycle graph is a vector space -- the cycle space of the graph -- which is spanned by the loops. The elasticities of the transitions in the life cycle graph can be represented by a vector in the cycle space, and a loop decomposition of the life cycle graph is then defined to be any nonnegative linear combination of the loops which sum to the vector of elasticities. In contrast to previously published algorithms for carrying out loop analysis, we show that a given life cycle graph admits of either a unique loop decomposition or an infinite set of loop decompositions which can be characterized as a bounded convex set of nonnegative vectors. Using this approach, loop decompositions which minimize or maximize a linear objective function can be obtained as solutions of a linear programming problem, allowing us to place lower and upper bounds on the contributions of life history pathways to the population growth rate. Another consequence of our approach to loop analysis is that it allows us to identify the exact tradeoffs in contributions to the population growth rate that must exist between life history pathways.     

Transient sensitivities of non-indigenous shrub species indicate complicated invasion dynamics

As biological invasions increasingly affect natural systems, the need for methods that can quantify the processes responsible for invasion success has increased. Further, methods should be geared to the formulation of management strategies. Demographic analyses are designed to explore the causes and properties of population change. Matrix population models, a commonly used technique for demographic analysis, have been applied to the analysis of stage-structured populations. However, most commonly, analyses have focused on long-term outcomes dynamics (ergodic dynamics). The methods available for analysis of matrix population models have recently been extended to facilitate analysis of the transient dynamics most important to invasion analysis. In this paper we analyze the transient population dynamics of three invasive shrubs and compare them to ergodic dynamics. Cytisus scoparius, Clidemia hirta, and Ardisia elliptica come from different parts of the world and are all now found in the United States of America. They also have published transition matrices that measure the probabilities that any one life-history stage will transition to another over an annual time step. These matrices have been estimated from multi-year data collected from plots in various environments. Our comparative study of transient and ergodic dynamics of invasive shrubs shows that, for all the considered shrub species, there was a clear difference between the sensitivities drawn from these two approaches. The transient sensitivities of earlier life-history transitions showed magnified importance relative to ergodic sensitivities. This was especially true of A. elliptica for which the stable population structure was most different from the starting structure analyzed in detail here. For other species, as stable population structures were heavily weighted towards early stages, the differences in the importance of early transitions transiently and ergodically were less dramatic. Late life transitions showed magnified importance in areas towards the center of the invasion or in older invasion areas. Finally, populations with shorter estimated generation times show greater transient sensitivity to early life-history stages; but the pattern was complex and varied according to species, and was also observed across other life-history transitions. Overall, the ambiguity and complexity of the results highlight the power of considering transient population dynamics for invading species, as well as the importance of specific biological and ecological knowledge of the invading species. Although there may be commonalities across invasions, important decisions on control or inference on population dynamics should treat invasions as individual, unique events.     

The evolution of alternative developmental pathways: footprints of selection on life-history traits in a butterfly

Developmental pathways may evolve to optimize alternative phenotypes across environments. However, the maintenance of such adaptive plasticity under relaxed selection has received little study. We compare the expression of life-history traits across two developmental pathways in two populations of the butterfly Pararge aegeria where both populations express a diapause pathway but one never expresses direct development in nature. In the population with ongoing selection on both pathways, the difference between pathways in development time and growth rate was larger, whereas the difference in body size was smaller compared with the population experiencing relaxed selection on one pathway. This indicates that relaxed selection on the direct pathway has allowed life-history traits to drift towards values associated with lower fitness when following this pathway. Relaxed selection on direct development was also associated with a higher degree of genetic variation for protandry expressed as within-family sexual dimorphism in growth rate. Genetic correlations for larval growth rate across sexes and pathways were generally positive, with the notable exception of correlation estimates that involved directly developing males of the population that experienced relaxed selection on this pathway. We conclude that relaxed selection on one developmental pathway appears to have partly disrupted the developmental regulation of life-history trait expression. This in turn suggests that ongoing selection may be responsible for maintaining adaptive developmental regulation along alternative developmental pathways in these populations.     

Life history predicts risk of species decline in a stochastic world

Understanding what traits determine the extinction risk of species has been a long-standing challenge. Natural populations increasingly experience reductions in habitat and population size concurrent with increasing novel environmental variation owing to anthropogenic disturbance and climate change. Recent studies show that a species risk of decline towards extinction is often non-random across species with different life histories. We propose that species with life histories in which all stage-specific vital rates are more evenly important to population growth rate may be less likely to decline towards extinction under these pressures. To test our prediction, we modelled declines in population growth rates under simulated stochastic disturbance to the vital rates of 105 species taken from the literature. Populations with more equally important vital rates, determined using elasticity analysis, declined more slowly across a gradient of increasing simulated environmental variation. Furthermore, higher evenness of elasticity was significantly correlated with a reduced chance of listing as Threatened on the International Union for Conservation of Nature Red List. The relative importance of life-history traits of diverse species can help us infer how natural assemblages will be affected by novel anthropogenic and climatic disturbances.     

Stochastic demography and population dynamics in the red kangaroo Macropus rufus

1.  Many organisms inhabit strongly fluctuating environments but their demography and population dynamics are often analysed using deterministic models and elasticity analysis, where elasticity is defined as the proportional change in population growth rate caused by a proportional change in a vital rate. Deterministic analyses may not necessarily be informative because large variation in a vital rate with a small deterministic elasticity may affect the population growth rate more than a small change in a less variable vital rate having high deterministic elasticity.
2.  We analyse a stochastic environment model of the red kangaroo ( Macropus rufus ), a species inhabiting an environment characterized by unpredictable and highly variable rainfall, and calculate the elasticity of the stochastic growth rate with respect to the mean and variability in vital rates.
3.  Juvenile survival is the most variable vital rate but a proportional change in the mean adult survival rate has a much stronger effect on the stochastic growth rate.
4.  Even if changes in average rainfall have a larger impact on population growth rate, increased variability in rainfall may still be important also in long-lived species. The elasticity with respect to the standard deviation of rainfall is comparable to the mean elasticities of all vital rates but the survival in age class 3 because increased variation in rainfall affects both the mean and variability of vital rates.
5.  Red kangaroos are harvested and, under the current rainfall pattern, an annual harvest fraction of c . 20% would yield a stochastic growth rate about unity. However, if average rainfall drops by more than c . 10%, any level of harvesting may be unsustainable, emphasizing the need for integrating climate change predictions in population management and increase our understanding of how environmental stochasticity translates into population growth rate.     

Can life-history traits predict the response of forb populations to changes in climate variability?

1.  Climate change will cause changes in average temperature and precipitation as well as increased fluctuations around the mean, yet few studies have considered the impacts of altered climate variability on plant populations. We tested whether life-history traits (expected life span, generation time and seed size) can predict plant responses to increased environmental variability across similar plant species sharing the same habitat.
2.  We combined long-term demographic data on 10 prairie forb species with stochastic demography techniques to estimate the effects of potential changes in matrix element means and variances on the long-term stochastic population growth rate.
3.  For all 10 species, recruitment had higher contribution and elasticity values than survival, meaning that climate change is more likely to influence population growth through effects on recruitment than on survival for these relatively short-lived forbs. Species with longer generation times had lower elasticities to increases in matrix element variability.
4.   Synthesis. Our analysis of a unique, long-term data set suggests that longer-lived plant species will be less vulnerable to the effects of future increases in climate variability. While this relationship was previously reported for diverse taxa from many locations, our results show that it also applies within a guild of short-lived species from a single community. The generality of the pattern demonstrates the potential for using life-history traits to make predictions about which species may be the most vulnerable to climate change.     

Elasticities in variable environments: properties and implications

Elasticities in stochastic matrix models are used to understand both population and evolutionary dynamics. We examine three such elasticities: stochastic elasticity E(ij)(S) with respect to the (i, j) matrix element, the elasticity E(ij)(S mu) with respect to the mean mu(ij) of the matrix element, and the elasticity E(ij)(S sigma) with respect to the variability sigma(ij) of the matrix element. We show that the stochastic elasticity E(S) does not accurately describe the effect of variability; one should use E(S sigma) and E(S mu). We establish two general properties of these elasticities: a sum rule that connects them and a limit on the sum of the E(S sigma). We discuss the implications of these properties for the analysis of buffering and selection on the average rates versus the variability of rates.     

Population biology of two rare fern species: long life and long-lasting stability

? Premise of the study: This study describes the population dynamics of two rare fern species and evaluates the prospects of their survival. This is the first detailed demography study of ferns using transition matrix models. The study species, Asplenium adulterinum and A. cuneifolium, are restricted to serpentine rocks and differ in ploidy level and partly in habitat requirements. Both species are of interest in nature conservation. ? Methods: Single life-history traits were evaluated and transition matrix models were used to describe the dynamics of the populations. Population growth rates, elasticity values, and life-table response experiments were used to compare the dynamics between species, years, and different habitat types. Predicted population performance based on models was compared with real data on population growth. ? Key Results: All populations of both species are growing. Stable stage distribution based on stochastic simulation corresponds to current stage distribution. The most critical phase of the life cycle is stasis of large adult plants. Reproduction is of low importance. Extinction probability of small populations is low. Mean life span of individuals of both species is 30-50 yr. When compared with real data, the model successfully predicted population performance over 10 yr. ? Conclusion: Populations in the study region are not endangered, and current population dynamics are stable. Differences in life-history traits between species, probability of extinction between species and habitat, and different ploidy-and, thus, probably different dispersal ability-suggest the existence of metapopulation dynamics.     

Using elasticity analysis of demographic models to link toxicant effects on individuals to the population level: an example

1. A simple two-stage population model was applied to data from a previously published life-table response experiment (LTRE), which examined the toxicity of 4- n -nonylphenol to life-history traits of the polychaete Capitella sp. I. Population growth rates ( λ ) and the relative sensitivities (= elasticities) of λ to changes in each of the individual life-history traits were calculated.
2. In the present study, the life-history parameters measured in laboratory-reared individuals were manipulated to simulate potential effects of competition and predation on fecundity, time to reproductive maturity and juvenile survival to explore how such factors might influence the sensitivity of population growth rate to toxicant-caused changes in individual life-history traits.
3. Dramatic changes in elasticity patterns among simulations indicate that population growth rates may respond very differently to toxicant exposure depending on the extent to which other demographically limiting factors (e.g. competitors and/or predators) are operating on the population.
4. Effectively predicting the population-level consequences arising from toxicant effects measured on individuals can be improved by exploring the elasticity pattern of λ for the population over a range of realistic ecological situations.     

Elasticity analysis in epidemiology: an application to tick-borne infections

The application of projection matrices in population biology to plant and animal populations has a parallel in infectious disease ecology when next-generation matrices (NGMs) are used to characterize growth in numbers of infected hosts ( R ₀). The NGM is appropriate for multi-host pathogens, where each matrix element represents the number of cases of one type of host arising from a single infected individual of another type. For projection matrices, calculations of the sensitivity and elasticity of the population growth rate to changes in the matrix elements has generated insight into plant and animal populations. These same perturbation analyses can be used for infectious disease systems. To illustrate this in detail we parameterized an NGM for seven tick-borne zoonoses and compared them in terms of the contributions to R ₀ from three different routes of transmission between ticks, and between ticks and vertebrate hosts. The definition of host type may be the species of the host or the route of infection, or, as was the case for the set of tick-borne pathogens, a combination of species and the life stage at infection. This freedom means that there is a broad range of disease systems and questions for which the methodology is appropriate.     

Influence of density dependence on the detection of trends in unobserved life-history stages

In many species, certain life-history stages are difficult or impossible to observe directly, hampering management. Often more easily observed stages are monitored instead, but the extent to which various forms of uncertainty cloud our ability to discern trends in one critical life-history stage by observing another is poorly studied. We develop a stochastic simulation model for threatened California coho salmon Oncorhynchus kisutch to examine how well trends in one stage can be detected from observations of another. In particular, we use the model to examine the effect density dependence has on our ability to detect trends. We present a structural form for the transition between life-history stages that encompasses the common functional forms: density independence, Beverton–Holt compensatory density dependence and Ricker-type over-compensation. In small populations, such density dependence is often ignored. However, it may in fact be extremely important, for example if population decline was caused by a decrease in carrying capacity. Our results show that density dependence in any life-history transition significantly reduces the ability to detect trends in abundance; critical but inaccessible stages cannot generally be studied by monitoring more easily observed stages, especially if density dependence is present for any life-cycle transition.     

Effects of habitat fragmentation by damming on salmonid fishes: lessons from white-spotted charr in Japan

Dam construction has serious consequences, and one of the most serious concerns is the fragmentation of riverine ecosystems. We reviewed the influence of habitat fragmentation on white-spotted charr Salvelinus leucomaenis populations. First, habitat fragmentation by damming has serious consequences in terms of alternative life-history strategies. Most fish in dammed-off areas do not migrate to the sea and instead become resident forms. This loss of the anadromous form negatively affects populations through decreased spawning biomass. In addition, the smaller population sizes in dammed-off habitats can negatively affect population dynamics through demographic, environmental, and genetic stochasticity. Therefore, the population viability is reduced in small, dammed-off habitats. White-spotted charr populations also likely experience different selection pressures after damming. Many of these effects of habitat fragmentation due to damming are not immediate but rather occur gradually over several generations. Because most Japanese dams were constructed after 1970, some effects of damming may not yet be obvious. Kentaro Morita is the recipient of the 12th Denzaburo Miyadi Award.     

Using statistics to design and estimate vital rates in matrix population models for a perennial herb

Matrix population models are widely used to assess population status and to inform management decisions. Despite existing theories for building such models, model construction is often partially based on expert opinion. So far, model structure has received relatively little attention, although it may affect estimates of population dynamics. Here, we assessed the consequences of two published matrix structures (a 4 × 4 matrix based on expert opinion and a 10 × 10 matrix based on statistical modeling) for estimates of vital rates and stochastic population dynamics of the long-lived herb Astragalus scaphoides. We explored the ways in which choice of model structure alters the accuracy (i.e., mean) and precision (i.e., variance) of predicted population dynamics. We found that model structure had a negligible effect on the accuracy and precision of vital rates and stochastic stage distribution. However, the 10 × 10 matrix produced lower estimates of stochastic population growth rates than the 4 × 4 matrix, and more accurately predicted the observed trends in population abundance for three out of four study populations. Moreover, estimates of realized variation in population growth rate due to fluctuations in population stage structure over time were occasionally sensitive to matrix structure, suggesting differential roles of transient dynamics. Our study indicates that statistical modeling for choosing categories in matrix models might be preferable over expert opinion to accurately predict population trends and can provide a more objective way for model construction when the biological knowledge of the species is limited.     

Does environmental stochasticity matter? Analysis of red deer life-histories on Rum

Summary Most life-history theory assumes that short-term variation in an organism's environment does not affect the survivorships and fecundities of the organisms. This assumption is rarely met. Here we investigate the population and evolutionary biology of red deer,Cervus elephas, to see if relaxation of this assumption is likely to make significant differences to the predicted evolutionary biology of this species. To do this we used 21 years of data from a population of deer on Rum, Western Isles, Scotland. Population growth rates in a stochastic environment were estimated using Tuljapurkar's small noise approximation, confirmed by bootstrap simulation. Numerical differentiation was used to see if the selection pressures (i.e. sensitivities of population growth rate to changes in the vital rates) differ between the stochastic and deterministic cases. The data also allow the costs of reproduction to be estimated. These costs, incorporated as trade-offs into the sensitivity analysis, allow investigation of evolutionary benefits of different life-history tactics. Environmentally induced stochastic variation in the red deer vital rates causes a slight reduction ( 1%) in the predicted population growth rate and has little impact on the estimated selection pressures on the deer's life-history. We thus conclude that, even though density-independent stochastic effects on the population are marked, the deer's fitness is not markedly affected by these and they are adapted to the average conditions they experience. However, the selected life-history is sensitive to the trade-offs between current fecundity, survivorship and future fecundity and it is likely that the environmental variance will affect these trade-offs and, thus, affect the life-history favoured by selection. We also show that the current average life-history is non-optimal and suggest this is a result of selection pressures exerted by culling and predation, now much reduced. As the use of stochastic or deterministic methods provide similar estimates in this case, the use of the latter is justified. Thus,r (the annual per capita rate of population growth) is an appropriate measure of fitness in a population with stochastic numerical fluctuations. In a population of constant size lifetime reproductive success is the obvious measure of fitness to use.     

The basic reproduction number for complex disease systems: defining R(0) for tick-borne infections

Characterizing the basic reproduction number, R(0), for many wildlife disease systems can seem a complex problem because several species are involved, because there are different epidemiological reactions to the infectious agent at different life-history stages, or because there are multiple transmission routes. Tick-borne diseases are an important example where all these complexities are brought together as a result of the peculiarities of the tick life cycle and the multiple transmission routes that occur. We show here that one can overcome these complexities by separating the host population into epidemiologically different types of individuals and constructing a matrix of reproduction numbers, the so-called next-generation matrix. Each matrix element is an expected number of infectious individuals of one type produced by a single infectious individual of a second type. The largest eigenvalue of the matrix characterizes the initial exponential growth or decline in numbers of infected individuals. Values below 1 therefore imply that the infection cannot establish. The biological interpretation closely matches that of R(0) for disease systems with only one type of individual and where infection is directly transmitted. The parameters defining each matrix element have a clear biological meaning. We illustrate the usefulness and power of the approach with a detailed examination of tick-borne diseases, and we use field and experimental data to parameterize the next-generation matrix for Lyme disease and tick-borne encephalitis. Sensitivity and elasticity analyses of the matrices, at the element and individual parameter levels, allow direct comparison of the two etiological agents. This provides further support that transmission between cofeeding ticks is critically important for the establishment of tick-borne encephalitis.     

Population dynamics of Mammillaria magnimamma Haworth. (Cactaceae) in a lava-field in central Mexico

One of the habitats occupied by Mammillaria magnimamma is a 2000-year old lava-field, in Mexico City. The great ecological interest on this lava-field and the little knowledge there is regarding cacti population ecology have compelled us to analyse the demography of this species to evaluate its present conservation status at this site. We studied two populations of this species within the lava-field: one in a disturbed site (i.e., recently burned) and another one in a well preserved site. For each population we built two size-based population projection matrices (1996/97 and 1997/98). Demographic data were gathered directly from observations of plant fates from one year to the next. Additionally, seed germination and seedling establishment experiments were carried out in the field to estimate fecundity values and seedling survival probabilities. The four matrices built were used to perform numerical analyses simulating yearly stochastic demographic variation to project the overall population's long-term behaviour under these changing conditions. Three of the four matrices showed λ values slightly below unity. In these cases elasticity values were highest for matrix entries corresponding to plants remaining in their same category. The matrix that showed a λ value above unity (well preserved site, 1997/98) had higher elasticity values for entries referring to seedling survival and growth. The numerical simulations of demographic stochasticity showed that the population appears to be growing at a slow rate. According to the simulation results, the variation in overall population size over time may be accounted for by yearly variation in seed germination and seedling survival. Population persistence probability might decrease significantly if fire frequency increases. This revised version was published online in August 2006 with corrections to the Cover Date.