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Large carnivores are expanding in Europe, and their return is associated with con- flicts that often result in policies to regulate their population size through culling. Being wide-ranging species, their populations are often distributed across several jurisdictions, which may vary in the extent to which they use lethal control. This creates the conditions for the establishment of source-sink dynamics across bor- ders, which may frustrate the ability of countries to reach their respective man- agement objectives. 2. To explore the consequences of this issue, we constructed a vec-permutation pro- jection model, applied to the case of wolverines in south-central Scandinavia, shared between Norway (where they are culled) and Sweden (where they are pro- tected). We evaluated the effect of compensatory immigration on wolverine pop- ulation growth rates, and if the effect was influenced by the distance to the national border. We assessed to what extent compensatory immigration had an influence on the number of removals needed to keep the population at a given growth rate. 3. In Norway, the model estimated a stable trend, whereas in Sweden it produced a 10% annual increase. The effect of compensatory immigration corresponded to a 0.02 reduction in population growth rate in Sweden and to a similar increase in Norway. This effect was strong closer to the Norwegian-Swedish border, but weakwhenmovingawayfromit.Anaverageof33wolverineswasshotperyear in the Norwegian part of the study area. If no compensatory immigration from Sweden had occurred, 28 wolverines shot per year would have been sufficient to achievethesamegoal.About15.5%ofalltheindividualsharvestedinNorway between 2005 and 2012 were compensated by immigrants, causing a decrease in population growth rate in Sweden. 4. Synthesis and applications. When a population is transboundary, the consequences of management decisions are also transboundary, even though the political bodies in charge of those decisions, the stakeholders who influence them, and the tax- payers who finance them are not. It is important that managers and citizens be informed that a difference in management goals can reduce the efficiency, and increase the costs, of wildlife management.

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.

1. Senescence (an increase in the mortality rate or force of mortality, or a decrease in fertility, with increasing age) is a widespread phenomenon. Theories about the evolution of senescence have long focused on the age trajectories of the selection gradients on mortality and fertility. In purely age-classified models, these selection gradients are non-increasing with age, implying that traits expressed early in life have a greater impact on fitness than traits expressed later in life. This pattern leads inevitably to the evolution of senescence if there are trade-offs between early and late performance. 2. It has long been suspected that the stage- or size-dependent demography typical of plants might change these conclusions. In this paper, we develop a model that includes both stage-and age-dependence and derive the age-dependent, stage-dependent and age × stage-dependent selection gradients on mortality and fertility. 3. We applied this model to stage-classified population projection matrices for 36 species of plants, from a wide variety of growth forms (from mosses to trees) and habitats. 4. We found that the age-specific selection gradients within a life cycle stage can exhibit increases with age (we call these contra-senescent selection gradients). In later stages, often large size classes in plant demography, the duration of these contra-senescent gradients can exceed the life expectancy by several fold. 5. Synthesis. The interaction of age- and stage-dependence in plants leads to selection pressures on senescence fundamentally different from those found in previous, age-classified theories. This result may explain the observation that large plants seem less subject to senescence than most kinds of animals. The methods presented here can lead to improved analysis of both age-dependent and stage-dependent demographic properties of plant populations.

Recent kinship models focus on the age structures of kin as a function of the age of the focal individual. However, variables in addition to age have important impacts. Generalizing age-specific models to multistate models including other variables is an important and hitherto unsolved problem. The aim is to develop a multistate kinship model, classifying individuals jointly by age and other criteria (generically, \"stages\"). The vec-permutation method is used to create multistate projection matrices including age- and stage-dependent survival, fertility, and transitions. These matrices operate on block-structured population vectors that describe the age*stage structure of each kind of kin, at each age of a focal individual. The new matrix formulation is directly comparable to, and greatly extends, the recent age-classified kinship model of Caswell (2019a). As an application, a model is derived including age and parity. It provides, for all types of kin, the joint age*parity structure, the marginal age and parity structures, and the (normalized) parity distributions, at every age of the focal individual. The age*parity distributions provide the distributions of sibship sizes of kin. As an example, the model is applied to Slovakia (1960-2014). The results show a dramatic shift in the parity distribution as the frequency of low-parity kin increased and that of high-parity kin decreased.

Despite recent advances in biodemography and metapopulation ecology, we still have limited understanding of how local demographic parameters influence short‐ and long‐term metapopulation dynamics. We used long‐term data from 17 local populations, along with the recently developed methods of matrix metapopulation modeling and transient sensitivity analysis, to investigate the influence of local demography on long‐term (asymptotic) versus short‐term (transient) dynamics of a yellow‐bellied marmot metapopulation in Colorado. Both long‐ and short‐term dynamics depended primarily on a few colony sites and were highly sensitive to changes in demography at these sites, particularly in survival of reproductive adult females. Interestingly, the relative importance of sites differed between long‐ and short‐term dynamics; the spatial structure and local population sizes, while insignificant for asymptotic dynamics, were influential on transient dynamics. However, considering the spatial structure was uninformative about the relative influence of local demography on metapopulation dynamics. The vital rates that were the most influential on local dynamics were also the most influential on both long‐ and short‐term metapopulation dynamics. Our results show that an explicit consideration of local demography is essential for a complete understanding of the dynamics and persistence of spatially structured populations.