Density dependence plays an important role in population regulation and is known to generate temporal fluctuations in population density. However, the ways in which density dependence affects spatial population processes, such as species invasions, are less understood. Although classical ecological theory suggests that invasions should advance at a constant speed, empirical work is illuminating the highly variable nature of biological invasions, which often exhibit nonconstant spreading speeds, even in simple, controlled settings. Here, we explore endogenous density dependence as a mechanism for inducing variability in biological invasions with a set of population models that incorporate density dependence in demographic and dispersal parameters. We show that density dependence in demography at low population densities—i.e., an Allee effect—combined with spatiotemporal variability in population density behind the invasion front can produce fluctuations in spreading speed. The density fluctuations behind the front can arise from either overcompensatory population growth or density-dependent dispersal, both of which are common in nature. Our results show that simple rules can generate complex spread dynamics and highlight a source of variability in biological invasions that may aid in ecological forecasting.

The rate at which a population grows and spreads can depend on individual behaviour and interactions with others. In many species with two sexes, males and females differ in key life history traits (e.g. growth, survival, dispersal), which can scale up to affect population rates of growth and spread. In sexually reproducing species, the mechanics of locating mates and reproducing successfully introduce further complications for predicting the invasion speed (spread rate), as both can change nonlinearly with density. Most models of population spread are based on one sex, or include limited aspects of sex differences. Here we ask whether and how the dynamics of finding mates interact with sex-specific life history traits to influence the rate of population spread. We present a hybrid approach for modelling invasions of populations with two sexes that links individual-level mating behaviour (in an individual-based model) to population-level dynamics (in an integrodifference equation model). We find that limiting the amount of time during which individuals can search for mates causes a demographic Allee effect which can slow, delay or even prevent an invasion. Furthermore, any sex-based asymmetries in life history or behaviour (skewed sex ratio, sex-biased dispersal, sex-specific mating behaviours) amplify these effects. In contrast, allowing individuals to mate more than once ameliorates these effects, enabling polygynandrous populations to invade under conditions where monogamously mating populations would fail to establish. We show that details of individuals’ mating behaviour can impact the rate of population spread. Based on our results, we propose a stricter definition of a mate-finding Allee effect, which is not met by the commonly used minimum mating function. Our modelling approach, which links individual and population-level dynamics in a single model, may be useful for exploring other aspects of individual behaviour that are thought to impact the rate of population spread.

Climate affects the timing and magnitude of phytoplankton blooms that fuel marine food webs and influence global biogeochemical cycles. Changes in bloom timing have been detected in some cases, but the underlying mechanisms remain elusive, contributing to uncertainty in long-term predictions of climate change impacts. Here we describe a 13-year hourly time series from the New England shelf of data on the coastal phytoplankter Synechococcus, during which the timing of its spring bloom varied by 4 weeks. We show that multiyear trends are due to temperature-induced changes in cell division rate, with earlier blooms driven by warmer spring water temperatures. Synechococcus loss rates shift in tandem with division rates, suggesting a balance between growth and loss that has persisted despite phenological shifts and environmental change.