Sensitivity analysis of periodic matrix population models

Demography and perturbation analyses of the coffee berry borer Hypothenemus hampei (Coleoptera: Curculionidae): Implications for management

The coffee berry borer (CBB) Hypothenemus hampei Ferrari is the most serious pest of coffee worldwide. Management of the CBB is extremely difficult because its entire life cycle occurs inside the fruit, where it is well protected. Knowing which life stages contribute most to population growth, would shed light on the population dynamics of this pest and help to improve CBB management programs. Two staged-classified matrices were constructed for CBB populations reared in the lab on artificial diets and CBB populations from artificial infestations in the field. Matrices were used to determine demographic parameters, to conduct elasticity analyses, and to perform prospective perturbation analysis. Higher values of the intrinsic rate of natural increase (r_m) and population growth rate (λ): were observed for CBB populations growing in the lab than in the field (r_m: 0.058, λ: 1.74 lab; r_m: 0.053, λ: 1.32 field). Sensitivity values for both CBB populations were highest for the transitions from larva to pupa (G₂: 0.316 lab, 0.352 field), transition from pupa to juvenile (G₃: 0.345 lab, 0.515 field) and survival of adult females (P₅: 0.324 lab, 0.389 field); these three vital rates can be important targets for CBB management. Prospective perturbation analyses indicated that an effective management for the CBB should consider multiple developmental stages; perturbations of >90% for each transition are necessary to reduce λ to <1. However, when the three vital rates with highest sensitivity are impacted at the same time, the percentage of perturbation is reduced to 25% for each transition; with these reductions in survival of larvae, pupae and adult females the value of λ was reduced from 1.32 to 0.96. Management programs for CBB should be focused on the use of biological and cultural measures that are known to affect these three important targets.

Quantifying the Contribution of Habitats and Pathways to a Spatially Structured Population Facing Environmental Change

The consequences of environmental disturbance and management are difficult to quantify for spatially structured populations because changes in one location carry through to other areas as a result of species movement. We develop a metric, G, for measuring the contribution of a habitat or pathway to network-wide population growth rate in the face of environmental change. This metric is different from other contribution metrics, as it quantifies effects of modifying vital rates for habitats and pathways in perturbation experiments. Perturbation treatments may range from small degradation or enhancement to complete habitat or pathway removal. We demonstrate the metric using a simple metapopulation example and a case study of eastern monarch butterflies. For the monarch case study, the magnitude of environmental change influences the ordering of node contribution. We find that habitats within which all individuals reside during one season are the most important to short-term network growth under complete removal scenarios, whereas the central breeding region contributes most to population growth over all but the strongest disturbances. The metric G provides for more efficient management interventions that proactively mitigate impacts of expected disturbances to spatially structured populations.

Age × stage-classified demographic analysis: a comprehensive approach

This paper presents a comprehensive theory for the demographic analysis of populations in which individuals are classified by both age and stage. The earliest demographic models were age classified. Ecologists adopted methods developed by human demographers and used life tables to quantify survivorship and fertility of cohorts and the growth rates and structures of populations. Later, motivated by studies of plants and insects, matrix population models structured by size or stage were developed. The theory of these models has been extended to cover all the aspects of age-classified demography and more. It is a natural development to consider populations classified by both age and stage. A steady trickle of results has appeared since the 1960s, analyzing one or another aspect of age × stage-classified populations, in both ecology and human demography. Here, we use the vec-permutation formulation of multistate matrix population models to incorporate age- and stage-specific vital rates into demographic analysis. We present cohort results for the life table functions (survivorship, mortality, and fertility), the dynamics of intra-cohort selection, the statistics of longevity, the joint distribution of age and stage at death, and the statistics of life disparity. Combining transitions and fertility yields a complete set of population dynamic results, including population growth rates and structures, net reproductive rate, the statistics of lifetime reproduction, and measures of generation time. We present a complete analysis of a hypothetical model species, inspired by poecilogonous marine invertebrates that produce two kinds of larval offspring. Given the joint effects of age and stage, many familiar demographic results become multidimensional, so calculations of marginal and mixture distributions are an important tool. From an age-classified point of view, stage structure is a form of unobserved heterogeneity. From a stage-classified point of view, age structure is unobserved heterogeneity. In an age × stage-classified model, variance in demographic outcomes can be partitioned into contributions from both sources. Because these models are formulated as matrices, they are amenable to a complete sensitivity analysis. As more detailed and longer longitudinal studies are developed, age × stage-classified demography will become more common and more important.

Mating, births, and transitions: a flexible two-sex matrix model for evolutionary demography

Models of sexually-reproducing populations that consider only a single sex cannot capture the effects of sex-specific demographic differences and mate availability. We present a new framework for two-sex demographic models that implements and extends the birth-matrix mating-rule approach of Pollak. The model is a continuous-time matrix model that explicitly includes the processes of mating (which is nonlinear but homogeneous), offspring production, and demographic transitions and survival. The resulting nonlinear model converges to exponential growth with an equilibrium population composition. The model can incorporate age- or stage-structured life histories and flexible mating functions. As an example, we apply the model to analyze the effects of mating strategies (polygamy or monogamy, and mated unions composed of males and females, of variable duration) on the response to sex-biased harvesting. The combination of demographic complexity with the interaction of the sexes can have major population dynamic effects and can change the outcome of evolution on sex-related characters.

Multistate matrix population model to assess the contributions and impacts on population abundance of domestic cats in urban areas including owned cats, unowned cats, and cats in shelters

Concerns over cat homelessness, over-taxed animal shelters, public health risks, and environmental impacts has raised attention on urban-cat populations. To truly understand cat population dynamics, the collective population of owned cats, unowned cats, and cats in the shelter system must be considered simultaneously because each subpopulation contributes differently to the overall population of cats in a community (e.g., differences in neuter rates, differences in impacts on wildlife) and cats move among categories through human interventions (e.g., adoption, abandonment). To assess this complex socio-ecological system, we developed a multistate matrix model of cats in urban areas that include owned cats, unowned cats (free-roaming and feral), and cats that move through the shelter system. Our model requires three inputs-location, number of human dwellings, and urban area-to provide testable predictions of cat abundance for any city in North America. Model-predicted population size of unowned cats in seven Canadian cities were not significantly different than published estimates (p = 0.23). Model-predicted proportions of sterile feral cats did not match observed sterile cat proportions for six USA cities (p = 0.001). Using a case study from Guelph, Ontario, Canada, we compared model-predicted to empirical estimates of cat abundance in each subpopulation and used perturbation analysis to calculate relative sensitivity of vital rates to cat abundance to demonstrate how management or mismanagement in one portion of the population could have repercussions across all portions of the network. Our study provides a general framework to consider cat population abundance in urban areas and, with refinement that includes city-specific parameter estimates and modeling, could provide a better understanding of population dynamics of cats in our communities.

Trait level analysis of multitrait population projection matrices

In most matrix population projection models, individuals are characterized according to, usually, one or two traits such as age, stage, size or location. A broad theory of multitrait population projection matrices (MPPMs) incorporating larger number of traits was long held back by time and space computational complexity issues. As a consequence, no study has yet focused on the influence of the structure of traits describing a life-cycle on population dynamics and life-history evolution. We present here a novel vector-based MPPM building methodology that allows to computationally-efficiently model populations characterized by numerous traits with large distributions, and extend sensitivity analyses for these models. We then present a new method, the trait level analysis consisting in folding an MPPM on any of its traits to create a matrix with alternative trait structure (the number of traits and their characteristics) but similar asymptotic properties. Adding or removing one or several traits to/from the MPPM and analyzing the resulting changes in spectral properties, allows investigating the influence of the trait structure on the evolution of traits. We illustrate this by modeling a 3-trait (age, parity and fecundity) population designed to investigate the implications of parity-fertilitytrade-offs in a context of fecundity heterogeneity in humans. The trait level analysis, comparing models of the same population differing in trait structures, demonstrates that fertility selection gradients differ between cases with or without parity-fertility trade-offs. Moreover it shows that age-specific fertility has seemingly very different evolutionary significance depending on whether heterogeneity is accounted for. This is because trade-offs can vary strongly in strength and even direction depending on the trait structure used to model the population.

Ecological modeling for the extrapolation of ecotoxicological effects measured during in situ assays in Gammarus

Evaluating the effects of chemical contamination on populations and ecological communities still constitutes a challenging necessity in environmental management. However, the toxic effects of contaminants are commonly measured by means of organism-level responses. Linking such effects measures with ecological models is a promising way to determine population-level impacts. In this way, population models are currently increasingly used in predictive risk assessment procedures, but their use in environmental diagnostic framework remains limited due to their lack of ecological realism. The present study with the crustacean Gammarus fossarum, a sentinel species in freshwater monitoring, combines a dual field and laboratory experimental approach with a population modeling framework. In this way, we developed an ecologically relevant periodic matrix population model for Gammarus. This model allowed us to capture the population dynamics in the field, and to understand the particular pattern of demographic sensitivities induced by Gammarus life-history phenology. The model we developed provided a robust population-level assessment of in situ-based effects measures recorded during a biomonitoring program on a French watershed impacted by past mining activities. Thus, our study illustrates the potential of population modeling when seeking to decipher the role of environmental toxic contamination in ecological perturbations.

In a long-term experimental demography study, excluding ungulates reversed invader's explosive population growth rate and restored natives

A major goal in ecology is to understand mechanisms that increase invasion success of exotic species. A recent hypothesis implicates altered species interactions resulting from ungulate herbivore overabundance as a key cause of exotic plant domination. To test this hypothesis, we maintained an experimental demography deer exclusion study for 6 y in a forest where the native ungulate Odocoileus virginianus (white-tailed deer) is overabundant and Alliaria petiolata (garlic mustard) is aggressively invading. Because population growth is multiplicative across time, we introduce metrics that correctly integrate experimental effects across treatment years, the cumulative population growth rate, λc, and its geometric mean, λper-year, the time-averaged annual population growth rate. We determined λc and λper-year of the invader and of a common native, Trillium erectum. Our results conclusively demonstrate that deer are required for the success of Alliaria; its projected population trajectory shifted from explosive growth in the presence of deer (λper-year = 1.33) to decline toward extinction where deer are excluded (λper-year = 0.88). In contrast, Trillium's λper-year was suppressed in the presence of deer relative to deer exclusion (λper-year = 1.04 vs. 1.20, respectively). Retrospective sensitivity analyses revealed that the largest negative effect of deer exclusion on Alliaria came from rosette transitions, whereas the largest positive effect on Trillium came from reproductive transitions. Deer exclusion lowered Alliaria density while increasing Trillium density. Our results provide definitive experimental support that interactions with overabundant ungulates enhance demographic success of invaders and depress natives' success, with broad implications for biodiversity and ecosystem function worldwide.

A seasonal, density-dependent model for the management of an invasive weed

The population effects of harvest depend on complex interactions between density dependence, seasonality, stage structure, and management timing. Here we present a periodic nonlinear matrix population model that incorporates seasonal density dependence with stage-selective and seasonally selective harvest. To this model, we apply newly developed perturbation analyses to determine how population densities respond to changes in harvest and demographic parameters. We use the model to examine the effects of popular control strategies and demographic perturbations on the invasive weed garlic mustard (Alliaria petiolata). We find that seasonality is a major factor in harvest outcomes, because population dynamics may depend significantly on both the season of management and the season of observation. Strategies that reduce densities in one season can drive increases in another, with strategies giving positive sensitivities of density in the target seasons leading to compensatory effects that invasive species managers should avoid. Conversely, demographic parameters to which density is very elastic (e.g., seeding survival, second-year rosette spring survival, and the flowering to fruiting adult transition for maximum summer densities) may indicate promising management targets.

Life-history phenology strongly influences population vulnerability to toxicants: a case study with the mudsnail Potamopyrgus antipodarum

One of the main objectives of ecological risk assessment is to evaluate the effects of toxicants on ecologically relevant biological systems such as populations or communities. However, the effects of toxicants are commonly measured on selected subindividual or individual endpoints due to their specificity against chemical stressors. Introducing these effects into population models is a promising way to predict impacts on populations. The models currently employed are very simplistic, and their environmental relevance needs to be improved to establish the ecological relevance of hazard assessment. The present study with the gastropod Potamopyrgus antipodarum combines a field experimental approach with a modeling framework. It clarifies the role played by seasonal variability of life-history traits in the population's vulnerability to the alteration of individual performance, potentially due to toxic stress. The present study comprised 3 steps: 1) characterization of the seasonal variability in life-history traits of a local population over 1 yr by using in situ experiments on caged snails, coupled with a demographic follow-up; 2) development of a periodic matrix population model that visualizes the monthly variability of population dynamics; and 3) simulation of the demographic consequences of an alteration in life-history traits (i.e., fertility, juvenile, and adult survival). The results revealed that demographic impacts strongly depend on the season when alterations of individual performance occur. Model analysis showed that this seasonal variability in population vulnerability is strongly related to the phenology of the population. The authors emphasize that improving the realism of population models is a major objective for ecological risk assessment, and that taking into account species phenology in modeling approaches should be a priority.

Impacts of climate change on avian populations

This review focuses on the impacts of climate change on population dynamics. I introduce the MUP (Measuring, Understanding, and Predicting) approach, which provides a general framework where an enhanced understanding of climate-population processes, along with improved long-term data, are merged into coherent projections of future population responses to climate change. This approach can be applied to any species, but this review illustrates its benefit using birds as examples. Birds are one of the best-studied groups and a large number of studies have detected climate impacts on vital rates (i.e., life history traits, such as survival, maturation, or breeding, affecting changes in population size and composition) and population abundance. These studies reveal multifaceted effects of climate with direct, indirect, time-lagged, and nonlinear effects. However, few studies integrate these effects into a climate-dependent population model to understand the respective role of climate variables and their components (mean state, variability, extreme) on population dynamics. To quantify how populations cope with climate change impacts, I introduce a new universal variable: the 'population robustness to climate change.' The comparison of such robustness, along with prospective and retrospective analysis may help to identify the major climate threats and characteristics of threatened avian species. Finally, studies projecting avian population responses to future climate change predicted by IPCC-class climate models are rare. Population projections hinge on selecting a multiclimate model ensemble at the appropriate temporal and spatial scales and integrating both radiative forcing and internal variability in climate with fully specified uncertainties in both demographic and climate processes.