Sensitivity Of Population Growth Rate Research Articles

Neighbor effects on population growth rate differ among populations due to variation in demographic rate sensitivities in Sedum lanceolatum

Population growth rates will respond to an environmental driver only if the driver impacts demographic rate(s) and the population is sensitive to impacted demographic rate(s). If populations vary in the sensitivity of population growth rate to demographic rates, the effect of an environmental driver on population growth rate could vary across populations, even if the effect of the driver on demographic rates does not vary across populations. Here, we use five years of demographic data of a common alpine plant, including data from a neighbor removal experiment and a climate warming experiment, to quantify the relative contribution of neighbor effects on demographic rates versus sensitivity of population growth rate to demographic rates to across‐population variation in neighbor effects on population growth rate. We find neighbor effects on population growth rate vary significantly across populations, and this effect is driven primarily by variation in sensitivity of population growth rate to demographic rates across populations. Further, results from our climate warming experiment suggests variation in sensitivity across populations is partly driven by temperature differences. Our results highlight the importance of considering changes in the sensitivity of population growth rate to demographic rates across space, and show how changes in sensitivity can contribute to spatial variation in the effects of a driver on population growth rate.

Climate change weakens the impact of disturbance interval on the growth rate of natural populations of Venus flytrap

AbstractDisturbances elicit both positive and negative effects on organisms; these effects vary in their strength and their timing. Effects of disturbance interval (i.e., the length of time between disturbances) on population growth will depend on both the timing and strength of positive and negative effects of disturbances. Climate change can modify the relative strengths of these positive and negative effects, leading to altered optimal disturbance intervals (the disturbance interval at which population growth rate is highest) and changes in the sensitivity of population growth rate to disturbance interval. While we know that climate may alter impacts of disturbance in some systems, we have a poor understanding of which effects of disturbance and which vital rates might drive an altered response to disturbance interval in a changing climate. We use demographic monitoring of natural populations of Dionaea muscipula, the Venus flytrap, that have experienced natural and managed fires, combined with realistic past and future climate projections, to construct climate‐ and fire‐driven integral projection models (IPMs). We use these IPMs to compare the effect of fire return interval (FRI) on population growth rate in past and future climates. To dissect the mechanisms driving FRI response, we then construct IPMs with demographic data from an experimental manipulation of fire effects (ash addition, neighbor removal) and an accidental fire. Our results show that an FRI of 10 years is optimal for D. muscipula in past climate conditions, but a longer FRI (12 years) is optimal in future climate conditions. Further, deviations from optimal FRI reduce population growth rate dramatically in the past climate, but this reduction is muted in a future climate (future minus past sensitivity = 0.006, 95% CI [0.002, 0.011]). Finally, our experimental work suggests that fire effects are driven in part by positive, additive effects of competitor removal and ash addition immediately following a fire; for one population, both these treatments significantly increased population growth rate. Our work suggests that climate change can alter the response of populations to disturbance, highlighting the need to consider the interacting effects of multiple abiotic drivers when projecting future population growth and geographical distributions.

Using life-history trait variation to inform ecological risk assessments for threatened and endangered plant species.

Developing population models for assessing risks to terrestrial plant species listed as threatened or endangered under the Endangered Species Act (ESA) is challenging given a paucity of data on their life histories. The purpose of this study was to develop a novel approach for identifying relatively data-rich nonlisted species that could serve as representatives for species listed under the ESA in the development of population models to inform risk assessments. We used the USDA PLANTS Database, which provides data on plants present in the US territories, to create a list of herbaceous plants. A total of 8742 species was obtained, of which 344 were listed under the ESA. Using the most up-to-date phylogeny for vascular plants in combination with a database of matrix population models for plants (COMPADRE) and cluster analyses, we investigated how listed species were distributed across the plant phylogeny, grouped listed and nonlisted species according to their life history, and identified the traits distinguishing the clusters. We performed elasticity analyses to determine the relative sensitivity of population growth rate to perturbations of species' survival, growth, and reproduction and compared these across clusters and between listed and nonlisted species. We found that listed species were distributed widely across the plant phylogeny as well as clusters, suggesting that listed species do not share a common evolution or life-history characteristics that would make them uniquely vulnerable. Lifespan and age at maturity were more important for distinguishing clusters than were reproductive traits. For clusters that were intermediate in their lifespan, listed and nonlisted species responded similarly to perturbations of their life histories. However, for clusters at either extreme of lifespan, the response to survival perturbations varied depending on conservation status. These results can be used to guide the choice of representative species for population model development in the context of ecological risk assessment. Integr Environ Assess Manag 2023;19:213-223. © 2022 The Authors. Integrated Environmental Assessment and Management published by Wiley Periodicals LLC on behalf of Society of Environmental Toxicology & Chemistry (SETAC).

Demographic Modeling Refines Assessment of Three Populations of a Long-Lived Threatened Plant

Structured demographic models can be valuable for assessing the status of at-risk plant species and for guiding efforts to protect and manage them, but they may be infrequently employed in assessments of species of conservation concern because they require data that are not often available to those charged with management. We constructed and analyzed matrix projection models for three populations of the threatened perennial plant species Euphorbia telephioides to reevaluate a prior assessment of stable status and to compare the conclusions of models based on different amounts of data. In contrast to the prior assessment, all of our models predicted population decline for all three populations. Projected growth rates were similar for models based on sparse sampling and those based on a larger more representative sample of individuals, but the models supported contrasting patterns of the sensitivity of population growth rate to individual demographic transitions. Models based on more complete data supported greater elasticity of growth rate to the demographic fates of small non-flowering plants, which had among the lowest elasticity values for models based on more sparse data. We conclude that even models based on limited data can be useful to species status assessments, but that more complete data may be necessary to identify targets for effective management.

Bridging gaps in demographic analysis with phylogenetic imputation.

Phylogenetically informed imputation methods have rarely been applied to estimate missing values in demographic data but may be a powerful tool for reconstructing vital rates of survival, maturation, and fecundity for species of conservation concern. Imputed vital rates could be used to parameterize demographic models to explore how populations respond when vital rates are perturbed. We used standardized vital rate estimates for 50 bird species to assess the use of phylogenetic imputation to fill gaps in demographic data. We calculated imputation accuracy for vital rates of focal species excluded from the data set either singly or in combination and with and without phylogeny, body mass, and life-history trait data. We used imputed vital rates to calculate demographic metrics, including generation time, to validate the use of imputation in demographic analyses. Covariance among vital rates and other trait data provided a strong basis to guide imputation of missing vital rates in birds, even in the absence of phylogenetic information. Mean NRMSE for null and phylogenetic models differed by <0.01 except when no vital rates were available or for vital rates with high phylogenetic signal (Pagel's λ > 0.8). In these cases, including body mass and life-history trait data compensated for lack of phylogenetic information: mean normalized root mean square error (NRMSE) for null and phylogenetic models differed by <0.01 for adult survival and <0.04 for maturation rate. Estimates of demographic metrics were sensitive to the accuracy of imputed vital rates. For example, mean error in generation time doubled in response to inaccurate estimates of maturation time. Accurate demographic data and metrics, such as generation time, are needed to inform conservation planning processes, for example through International Union for Conservation of Nature Red List assessments and population viability analysis. Imputed vital rates could be useful in this context but, as for any estimated model parameters, awareness of the sensitivities of demographic model outputs to the imputed vital rates is essential.

Adaptive evolution shapes the present-day distribution of the thermal sensitivity of population growth rate.

Developing a thorough understanding of how ectotherm physiology adapts to different thermal environments is of crucial importance, especially in the face of global climate change. A key aspect of an organism's thermal performance curve (TPC)-the relationship between fitness-related trait performance and temperature-is its thermal sensitivity, i.e., the rate at which trait values increase with temperature within its typically experienced thermal range. For a given trait, the distribution of thermal sensitivities across species, often quantified as "activation energy" values, is typically right-skewed. Currently, the mechanisms that generate this distribution are unclear, with considerable debate about the role of thermodynamic constraints versus adaptive evolution. Here, using a phylogenetic comparative approach, we study the evolution of the thermal sensitivity of population growth rate across phytoplankton (Cyanobacteria and eukaryotic microalgae) and prokaryotes (bacteria and archaea), 2 microbial groups that play a major role in the global carbon cycle. We find that thermal sensitivity across these groups is moderately phylogenetically heritable, and that its distribution is shaped by repeated evolutionary convergence throughout its parameter space. More precisely, we detect bursts of adaptive evolution in thermal sensitivity, increasing the amount of overlap among its distributions in different clades. We obtain qualitatively similar results from evolutionary analyses of the thermal sensitivities of 2 physiological rates underlying growth rate: net photosynthesis and respiration of plants. Furthermore, we find that these episodes of evolutionary convergence are consistent with 2 opposing forces: decrease in thermal sensitivity due to environmental fluctuations and increase due to adaptation to stable environments. Overall, our results indicate that adaptation can lead to large and relatively rapid shifts in thermal sensitivity, especially in microbes for which rapid evolution can occur at short timescales. Thus, more attention needs to be paid to elucidating the implications of rapid evolution in organismal thermal sensitivity for ecosystem functioning.

Are small fishes more sensitive to habitat loss? A generic size-based model

Habitat loss represents the greatest threat to freshwater biodiversity. The potential for life history attributes to correlate with the risks associated with habitat loss represents a possible mechanism for more effective and rapid assessments, especially in data-limited situations. Body size correlates with many other life history attributes and is a good starting point for investigating correlates with habitat loss. Here, we use a generic stage-based matrix population model, parameterized using length-based allometries, to investigate if such a mechanism exists. Our analysis revealed that small species (shorter maximum body length) were initially more sensitive to the loss of habitat. Moreover, distinct stage-based patterns exist showing an increased sensitivity of population growth rate for small species to both habitat loss and vital rate perturbations of pre-adult stages. This indicates that the pre-adult period represents a critical stage for the continued production of small species and increased importance of the conservation of habitat used by young-of-the-year and juvenile fishes.

Greater sage‐grouse juvenile survival in Utah

ABSTRACTGreater sage‐grouse (Centrocercus urophasianus; sage‐grouse) adult hen and juvenile survival have been shown to have significant influence on population growth rates. However, assessing the sensitivity of population growth rates to variability in juvenile survival has proven difficult because of limited information concerning the potentially important demographic rate. Sage‐grouse survival rates are commonly assessed using necklace‐type radio transmitters. Recent technological advances have lead to increased interest in the deployment of dorsally mounted global positioning system (GPS) transmitters for studying sage‐grouse ecology. However, the use of dorsally mounted transmitters has not been thoroughly evaluated for sage‐grouse, leading to concern that birds fitted with these transmitters may experience differential mortality rates. We evaluated the effect of transmitter positioning (dorsal vs. necklace) on juvenile sage‐grouse survival using a controlled experimental design with necklace‐style and suture‐backpack very high frequency (VHF) transmitters. To evaluate the effects of temporal variation, sex, and transmitter type on juvenile sage‐grouse survival, we monitored 91 juveniles captured in south‐central Utah from 2008 to 2010. We instrumented 19 females with backpacks, 14 males with backpacks, 39 females with necklaces, and 19 males with necklaces. We used Program MARK to analyze juvenile survival data. Although effects were only marginally significant from a statistical perspective, sex (P = 0.103) and transmitter type (P = 0.09) were deemed to have biologically meaningful impacts on survival. Dorsally mounted transmitters appeared to negatively affected daily survival (βtransmitter type = −0.55, SE = 0.32). Temporal variation in juvenile sage‐grouse daily survival was best described by a quadratic trend in time, where daily survival was lowest in late September and was high overwinter. An interaction between the quadratic trend in time and year resulted in the low point of daily survival shifting within the season between years (27 vs. 17 Sep for 2008 and 2009, respectively). Overall (15 Aug–31 Mar) derived survival ranged 0.42–0.62 for females and 0.23–0.44 for males. For all years pooled, the probability death was due to predation was 0.73, reported harvest was 0.16, unreported harvest was 0.09, and other undetermined factors was 0.02. We observed 0% and 6.8% crippling loss (from hunting) in 2008 and 2009, respectively. We recommend the adoption of harvest management strategies that attempt to shift harvest away from juveniles and incorporate crippling rates. In addition, future survival studies on juvenile sage‐grouse should use caution if implementing dorsally mounted transmitters because of the potential for experimental bias. © 2014 The Wildlife Society.

Environmental context influences both the intensity of seed predation and plant demographic sensitivity to attack

Variation in mutualistic and antagonistic interactions are important sources of variation in population dynamics and natural selection. Environmental heterogeneity can influence the outcome of interactions by affecting the intensity of interactions, but also by affecting the demography of the populations involved. However, little is known about the relative importance of environmental effects on interaction intensities and demographic sensitivity for variation in population growth rates. We investigated how soil depth, soil moisture, soil nutrient composition, and vegetation height influenced the intensity of seed predation as well as host plant demography and sensitivity to seed predation in the perennial herb Primula farinosa. Intensity of seed predation ranged from 0% to 80% of seeds damaged among the 24 study populations and was related to soil moisture in two of four years. The effect of seed predation on plant population growth rate (lambda) ranged from negligible to a reduction in lambda by 0.70. Sensitivity of population growth rate to predation explained as much of the variation in the reductions in population growth rate due to seed predation as did predation intensity. Plant population growth rate in the absence of seed predation and sensitivity to predation were negatively related to soil depth and soil moisture. Both intensity of predation and sensitivity to predation were positively correlated with potential population growth rate and, as a result, there was no significant relationship between predation intensity and realized population growth rate. We conclude that in our study system environmental context influences the effects of seed predation on plant fitness and population dynamics in two important ways: through variation in interaction intensity and through sensitivity to the effects of this interaction. Moreover, our results show that a given abiotic factor can influence population growth rate in different directions through effects on potential growth rate, intensity of biotic interactions, and the sensitivity of population growth rate to interactions.

Population Growth Rate Responses of Ceriodaphnia dubia to Ternary Mixtures of Specific Acting Chemicals: Pharmacological versus Ecotoxicological Modes of Action

When considering joint toxic apical effects at higher levels of biological organization, such as the growth of populations, the so-called pharmacological mode of action that relies on toxicological mechanistic effects on molecular target sites may not be relevant. Such effects on population growth rate will depend on the extent to which juvenile and adult survival rates and production rates (juvenile developmental rates and reproduction) are affected by toxic exposure and also by the sensitivity of population growth rates to life-history changes. In such cases, the ecotoxicological mode of action, defined as the crucial life-history trait processes and/or xenobiotic-life-history trait interactions underlying a toxicological effect on population growth rate, should be considered. Life-table response experiments with the crustacean Ceriodaphnia dubia exposed to single and ternary mixtures of nine compounds were conducted to test the hypothesis that joint effects on population growth rates could be predicted from the mixture constituent ecotoxicological mode of action. Joint effects of mixtures containing pharmacologically dissimilar compounds (cadmium, λ-cyhalothrin, and chlorpyrifos) that differentially affected life-history traits contributing to population growth rates were accurately predicted by the independent-action concept. Conversely, the concentration-addition concept accurately predicted joint effects of two different mixtures: one containing pharmacologically similar acting pyrethroids that also affected similarly life-history traits, the other one that included pharmacologically dissimilar compounds (3,4-dichloroaniline, sodium bromide, and fenoxycarb) acting mainly on reproduction rates. These results indicate that when assessing combined effects on population growth rate responses, selection of mixture toxicity conceptual models based on the ecotoxicological mode of action of mixture constituents provided more accurate predictions than those based on the pharmacological mode of action.

Response of non-native lake trout (Salvelinus namaycush) to 15 years of harvest in Yellowstone Lake, Yellowstone National Park

Introduced lake trout ( Salvelinus namaycush ) threaten to extirpate native Yellowstone cutthroat trout ( Oncorhynchus clarkii bouvieri ) in the 34 000 ha Yellowstone Lake in Yellowstone National Park, USA. Suppression (and eventual eradication) of the lake trout population is deemed necessary for the conservation of Yellowstone cutthroat trout. A US National Park Service gill-netting program removed nearly 450 000 lake trout from Yellowstone Lake from 1995 through 2009. We examined temporal variation in individual growth, body condition, length and age at maturity, fecundity, mortality, and population models to assess the efficacy of the lake trout suppression program. Population metrics did not indicate overharvest despite more than a decade of fish removal. The current rate of population growth is positive; however, it is lower than it would be in the absence of lake trout suppression. Fishing effort needs to increase above observed levels to reduce population growth rate below replacement. Additionally, high sensitivity of population growth rate to reproductive vital rates indicates that increasing fishing mortality for sexually mature lake trout may increase the effectiveness of suppression. Lake trout suppression in Yellowstone Lake illustrates the complexities of trying to remove an apex predator to restore a relatively large remote lentic ecosystem with a simple fish assemblage.

Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates

The population growth rate, or intrinsic rate of increase, measures the potential rate of growth of a population with specified and fixed vital rates.The sensitivity of population growth rate to changes in the vital rates can be written in terms of the

Linking environmental variation to population dynamics of a forest herb

Summary 1. Although necessary for understanding and predicting population dynamics, abiotic and biotic interactions have only rarely been coupled to demography and population dynamics. 2. We estimated effects of 11 environmental factors on survival, growth and fertility of the perennial herb Actaea spicata and incorporated significant factors into integral projection models to assess their effect on population dynamics. 3. Statistical models suggested that high soil potassium concentration increased individual growth and that seed predation and, to a lesser extent, canopy cover reduced seed production. 4. Demographic models showed that both soil potassium concentration and pre-dispersal seed predation could reverse population growth from positive to negative. The observed range of soil potassium concentration corresponded to growth rates ( λ ) between 0.96 and 1.07, at mean observed seed predation intensity. At observed mean potassium concentration, growth rate ranged from 0.99 to 1.02 over observed seed predation intensities. 5. Sensitivity of population growth rate to different vital rates strongly influenced the relative effects of the two factors. Elasticity analysis suggested that proportional changes in soil potassium concentration result in seven times larger effects on population growth rate than changes in seed predation. 6. Synthesis . We conclude that relatively weak associations between environmental factors and vital rates can have substantial long-term effects on population growth. Approaches based on detailed demographic models, that simultaneously assess abiotic and biotic effects on population growth rate, constitute important tools for establishing the links between the environment and dynamics of populations and communities.

Modelling the consequences of crop–wild relative gene flow: a sensitivity analysis of the effects of outcrossing rates and hybrid vigour breakdown in Lactuca

1 Hybridization between crops and their wild relatives may enhance invasiveness and change their niche dynamics. This is regarded as a major biosafety problem in terms of the development of noxious, invasive weeds and the loss of the genetic identity of native species. Modelling the consequences of hybridization is becoming an important tool for risk assessment. 2 We conducted a sensitivity analysis of a stochastic hybridization model, predicting changes in genotypic population composition. The model includes various classes of hybrids between Lactuca sativa (lettuce) and its wild relative L. serriola, and is based on empirical demographic measurements of fitness (λ). 3 We calculated the sensitivity of these transitions and of the following model parameters: outcrossing rate, the temporal frequency of crop presence, early hybrid fitness, hybrid vigour breakdown rate and assumed fitness of advanced generation hybrids. 4 In a non-stochastic simulation, the wild relative was displaced by more vigorous hybrids. The relative fitness of late generation hybrids in relation to the fitness of the wild taxon had the strongest effects on the population composition in the long term. 5 The outcrossing rate affected the estimated population composition strongly but the proportional impact of this parameter was low compared to the effect of hybrid fitness. Moreover, the stochastic simulations showed that the level of stochasticity had only a small effect on the sensitivity of population growth rates to changes in any of the model parameters, except for changes in the fitness of the wild taxon. 6 Synthesis and applications. It is essential to determine the relative fitness level of advanced generation hybrids, as this has a much stronger proportional effect than other factors. Future risk assessment should focus more on long-term fitness effects and not only on the outcrossing rate and the early establishment of hybrids. Experiments with multiple generations and analysis of hybrid vigour in modelling efforts would yield better predictions of which traits would be likely to introgress, and at what speed. This would be of benefit in the decision-making process and in future monitoring after crop release, for example of transgenes.

Thermodynamics Constrains the Evolution of Insect Population Growth Rates: “Warmer Is Better”

Diverse biochemical and physiological adaptations enable different species of ectotherms to survive and reproduce in very different temperature regimes, but whether these adaptations fully compensate for the thermodynamically depressing effects of low temperature on rates of biological processes is debated. If such adaptations are fully compensatory, then temperature-dependent processes (e.g., digestion rate, population growth rate) of cold-adapted species will match those of warm-adapted species when each is measured at its own optimal temperature. Here we show that cold-adapted insect species have much lower maximum rates of population growth than do warm-adapted species, even when we control for phylogenetic relatedness. This pattern also holds when we use a structural-equation model to analyze alternative hypotheses that might otherwise explain this correlation. Thus, although physiological adaptations enable some insects to survive and reproduce at low temperatures, these adaptations do not overcome the "tyranny" of thermodynamics, at least for rates of population increase. Indeed, the sensitivity of population growth rates of insects to temperature is even greater than predicted by a recent thermodynamic model. Our findings suggest that adaptation to temperature inevitably alters the population dynamics of insects. This result has broad evolutionary and ecological consequences.

Elasticity Analysis of Green Sturgeon Life History

I provide an analysis of a simplified life history model for green sturgeon, Acipenser medirostris, based on published and recent estimates of reproduction and growth rates and survival rates from life history theory. The deterministic life cycle models serve as a tool for qualitative analysis of the impacts of perturbations on green sturgeon, including harvest regulations based on minimum and maximum size limits (“slot limits”). Elasticity analysis of models with two alternative age–length relationships give similar results, with a high sensitivity of population growth rate to changes in the survival rate of subadult and adult fish. A dramatic increase in the survival of young of the year sturgeon or annual egg production is required to compensate for relatively low levels of fishing mortality. Peak reproductive values occur from ages 25 to 40. An increase or decrease in the maximum and minimum size limits can have a profound effect on the elasticity of population growth to changes in the annual survival rate of age classes specified by the slot, due to changes in the number of age classes of subadults and adults that are available for harvest. This analysis provides managers with a simple tool to assess the relative impacts of alternative harvest regulations. In general, green sturgeon follow life history patterns similar to other sturgeon, but species-specific demographic information is needed to produce more complex assessment and viability analysis models.

LONG-TERM CONTRASTED RESPONSES TO CLIMATE OF TWO ANTARCTIC SEABIRD SPECIES

We examined the population dynamics of two Antarctic seabirds and the influence of environmental variability over a 40-year period by coupling the estimation of demographic parameters, based on capture–recapture data, and modeling, using Leslie matrix population models. We demonstrated that the demographic parameters showing the greatest contribution to the variance of population growth rate were adult survival for both species. Breeding success showed the same contribution as adult survival for Emperor Penguins, whereas the proportion of breeders had the next stronger contribution for Snow Petrels. The sensitivity of population growth rate to adult survival was very high and the adult survival variability was weak for both species. Snow Petrel males survived better than females, whereas Emperor Penguin males had lower survival than females. These differences may be explained by the different investment in breeding. Emperor Penguin adult survival was negatively affected by air temperature during summer and winter for both sexes; male survival was negatively affected by sea ice concentration during summer, autumn, and winter. On the other hand, there was no effect of environmental covariates on Snow Petrel adult survival. The Emperor Penguin population has declined by 50% because of a decrease in adult survival related to a warming event during a regime shift in the late 1970s, whereas Snow Petrels showed their lowest numbers in 1976, but were able to skip reproduction. Indeed, the retrospective analysis of projection population matrix entries indicated that breeding abstention played a critical role in the population dynamics of Snow Petrels but not Emperor Penguins. Snow Petrels did not breed either when air temperature decreased during spring (probably reducing nest attendance and laying) or when sea ice decreased during autumn (reducing food availability). Emperor Penguin and Snow Petrel breeding population sizes were positively influenced by sea ice through its effect on adult survival for Emperor Penguins and on the proportion of breeders for Snow Petrels. Therefore, we hypothesize that the population sizes of the two species could be negatively affected by reduced sea ice in the context of global warming.

Transient population dynamics and short-term sensitivity analysis of matrix population models

Demographic analysis methodologies which consider the transient dynamics of a population promise to be highly relevant for population conservation and management, but the present methods of analysis are still in the early stages of being developed. The methods require a knowledge of a population’s initial stage-structure, and produce output which is complicated, and difficult to describe succinctly. This paper investigates whether the initial stage-structure is always required in order to obtain reliable information on the transient population dynamics. The paper also presents new methods for succinctly presenting the data from these near-term demographic analyses. The work of Fox and Gurevitch [Am. Naturalist 156 (2000) 242] is extended by deriving an analytical formula which decomposes their near-term sensitivity into two components: one which does not require the populations initial stage-structure to be measured, and one which does. This decomposition is used to estimate the sensitivity of the analysis to the initial population stage structure, without a knowledge of the population structure. The near-term sensitivity analysis is extended to look at several measures for the near-term sensitivity of population growth rate. These new measures allow the information contained in the analysis to be condensed, and for a comparison to be made between near-term and asymptotic sensitivity analyses. The methods are demonstrated by analysing empirical data on the cactus Coryphantha robbinsorum.

Partial life cycle analysis: a model for pre‐breeding census data

Matrix population models have become popular tools in research areas as diverse as population dynamics, life history theory, wildlife management, and conservation biology. Two classes of matrix models are commonly used for demographic analysis of age‐structured populations: age‐structured (Leslie) matrix models, which require age‐specific demographic data, and partial life cycle models, which can be parameterized with partial demographic data. Partial life cycle models are easier to parameterize because data needed to estimate parameters for these models are collected much more easily than those needed to estimate age‐specific demographic parameters. Partial life cycle models also allow evaluation of the sensitivity of population growth rate to changes in ages at first and last reproduction, which cannot be done with age‐structured models. Timing of censuses relative to the birth‐pulse is an important consideration in discrete‐time population models but most existing partial life cycle models do not address this issue, nor do they allow fractional values of variables such as ages at first and last reproduction. Here, we fully develop a partial life cycle model appropriate for situations in which demographic data are collected immediately before the birth‐pulse (pre‐breeding census). Our pre‐breeding census partial life cycle model can be fully parameterized with five variables (age at maturity, age at last reproduction, juvenile survival rate, adult survival rate, and fertility), and it has some important applications even when age‐specific demographic data are available (e.g., perturbation analysis involving ages at first and last reproduction). We have extended the model to allow non‐integer values of ages at first and last reproduction, derived formulae for sensitivity analyses, and presented methods for estimating parameters for our pre‐breeding census partial life cycle model. We applied the age‐structured Leslie matrix model and our pre‐breeding census partial life cycle model to demographic data for several species of mammals. Our results suggest that dynamical properties of the age‐structured model are generally retained in our partial life cycle model, and that our pre‐breeding census partial life cycle model is an excellent proxy for the age‐structured Leslie matrix model.

Partial Life-Cycle Analysis: A Model for Birth-Pulse Populations

Matrix population models have become standard tools for the demographic analysis of age- or stage-structured populations. Although age-classified (Leslie) matrix models make maximum use of age-specific demographic data, age at first reproduction, which has been suggested to be an important life-history variable, does not appear as an explicit parameter in these models. Consequently, the sensitivity of population growth rate to changes in age at first reproduction cannot be calculated using standard techniques. Age-specific demographic data to parameterize age-structured models are difficult to collect, and models that can be parameterized with partial demographic data (“partial life-cycle models”) have been developed. Partial life-cycle models are based on life-history stages, and these models can also be used to calculate sensitivity of population growth rate to changes in various life-history variables, including ages at first and last reproduction. Here, we present a partial life-cycle model appropriate for situations where demographic data are collected immediately after the birth pulse (post-breeding census). We present methods of parameterizing the partial life-cycle model, and derive formulas for calculating the sensitivity of the population growth rate to changes in model parameters, including ages at first and last reproduction. We analyzed life-table data for several species of mammals using the partial life-cycle model and found that results of our partial life-cycle model compare favorably with those obtained from the corresponding age-classified models.