A general understanding of biological invasions will provide insights into fundamental ecological and evolutionary problems and contribute to more efficient and effective prediction, prevention and control of invasions. We review recent papers that have proposed conceptual frameworks for invasion biology. These papers offer important advances and signal a maturation of the field, but a broad synthesis is still lacking. Conceptual frameworks for invasion do not require invocation of unique concepts, but rather should reflect the unifying principles of ecology and evolutionary biology. A conceptual framework should incorporate multicausality, include interactions between causal factors and account for lags between various stages. We emphasize the centrality of demography in invasions, and distinguish between explaining three of the most important characteristics by which we recognize invasions: rapid local population increase, monocultures or community dominance, and range expansion. As a contribution towards developing a conceptual synthesis of invasions based on these criteria, we outline a framework that explicitly incorporates consideration of the fundamental ecological and evolutionary processes involved. The development of a more inclusive and mechanistic conceptual framework for invasion should facilitate quantitative and testable evaluation of causal factors, and can potentially lead to a better understanding of the biology of invasions.

No abstract

Various ecological mechanisms influence the forms of species richness relationships (SRRs). These mechanisms can be gathered under five general categories: more individuals, environmental heterogeneity, dispersal limitations, biotic interactions, and multiple species pools. Often only the first two categories are discussed. In contrast, we examine all five and explore how they can influence the form of SRRs. We discuss how various sampling schemes and methods of SRR construction can be used to gain insight about how various processes influence species richness patterns. The field is ripe for probing these effects through more complex simulation models or more sophisticated mathematical approaches. To facilitate deeper understanding, we need to embrace the full spectrum of SRRs and reconsider the assumed common knowledge about the functional form of SRRs. The relationship between species richness and the space or time over which it is sampled has received increasing attention over the past decade, resulting in extensive debates about terminology and methods of construction. These debates reflect deep conceptual issues; to resolve them we discuss the long history of species richness relationships (SRRs) and the connections among different methodological and terminological approaches. We reinforce recent calls to organize the variety of methods used to construct SRRs into a cohesive structure. SRRs are descriptors of various aspects of inventory (α‐ and γ‐) diversity and the various types of SRRs serve different purposes. Contrary to most claims, SRRs do not provide a direct measure of differentiation (β‐) diversity.

Population viability analysis (PVA) is a technique that employs stochastic demographic models to predict extinction risk. All else being equal, higher variance in a demographic rate leads to a greater extinction risk. Demographic stochasticity represents variance due to differences among individuals. Current implementations of PVAs, however, assume that the expected fates of all individuals are identical. For example, demographic stochasticity in survival is modeled as a random draw from a binomial distribution. We developed a simple conceptual model showing that if there is variation among individuals in expected survival, then existing PVA models overestimate the variance due to demographic stochasticity in survival. This is a consequence of Jensen's inequality and the fact that the binomial demographic variance is a concave function of mean survival. The effect of variation among individuals on demographic stochasticity in fecundity depends on the mean-variance relationship for individual reproductive success, which is not presently known. If fecundity patterns mirror those of survival, then variation among individuals will reduce the extinction risk of small populations. Variación entre Individuos y Estocasticidad Demográfica ReducidaResumen: El análisis de viabilidad poblacional (AVP) es un técnica que emplea modelos demográficos estocásticos para predecir el riesgo de extinción. Todo lo demás siendo igual, mayor variación en la tendencia demográfica conduce a un mayor riesgo de extinción. La estocasticidad demográfica representa variación debido a diferencias entre individuos. Sin embargo, los AVP actualmente asumen que el destino esperado para cada individuo es idéntico. Por ejemplo, la estocasticidad demográfica en la supervivencia es modelada como una muestra aleatoria de una distribución binomial. Desarrollamos un modelo conceptual simple que muestra que si hay variación entre individuos en la supervivencia esperada, entonces los modelos de AVP existentes sobrestiman la variación debida a la estocasticidad demográfica en la supervivencia. Esto es una consecuencia de la desigualdad de Jensen y del hecho de que la variación demográfica binomial es una función cóncava de la supervivencia promedio. El efecto de la variación entre individuos sobre la estocasticidad demográfica en la fecundidad depende de la relación media-varianza del éxito reproductivo individual, que actualmente es desconocida. Si los patrones de fecundidad son un reflejo de los de supervivencia, entonces la variación entre individuos reducirá el riesgo de extinción de poblaciones pequeñas.

How do unit or proportional changes in vital rates affect populations in the short term? We present a new extension to standard methods of matrix model analysis that allows us to answer this question for the first time. By using the sensitivities of all the eigenvalues/vectors, rather than just the leading eigenvalue/vector pair, we can predict the consequences of unit or proportional changes in vital rates to population size and structure at any arbitrary time, not just when populations have neared their stable distribution. These extensions are particularly important in studying populations subject to frequent disturbance, where stable growth rate and stable distribution do not provide sufficient information about the effects of changes in the vital rates; managed populations in which short-term goals are defined; and the adequacy of the underlying matrix model for either short- or long-term understanding. We use analysis of empirical data on the cactus Coryphantha robbinsorum to demonstrate this approach and show that short-term predictions can differ substantially from those based on standard, asymptotic, analysis.