Scaling population responses to spatial environmental variability in advection‐dominated systems

Regulation of open populations of a stream insect through larval density-dependence

In organisms with complex life cycles, the various stages occupy different habitats creating demographically open populations. The dynamics of these populations will depend on the occurrence and timing of stochastic influences relative to demographic density dependence, but understanding of these fundamentals, especially in the face of climate warming, has been hampered by the difficulty of empirical studies.

Using a logically feasible organism, we conducted a replicated density‐perturbation experiment to manipulate late‐instar larvae of nine populations of a stream caddisfly, Zelandopsyche ingens, and measured the resulting abundance over 2 years covering the complete life cycle of one cohort to evaluate influences on dynamics.

Negative density feedback occurred in the larval stage, and was sufficiently strong to counteract variation in abundance due to manipulation of larval density, adult caddis dispersal in the terrestrial environment as well as downstream drift of newly hatched and older larvae in the current. This supports theory indicating regulation of open populations must involve density dependence in local populations sufficient to offset variability associated with dispersal, especially during recruitment, and pinpoints the occurrence to late in the larval life cycle and driven by food resource abundance.

There were large variations in adult, egg mass and early instar abundance that were not related to abundance in the previous stage, or the manipulation, pointing to large stochastic influences. Thus, the results also highlight the complementary nature of stochastic and deterministic influences on open populations. Such density dependence will enhance population persistence in situations where variable dispersal and transitioning between life stages frequently creates mismatches between abundance and the local availability of resources, such as might become more common with climate warming.

Advection exacerbates population decline from habitat loss: maintaining threatened taxa while restoring natural river flow regimes

Modification of flow regimes and habitat degradation are the strongest, most common, and often co-occurring human activities affecting riverine populations. Ongoing efforts to restore peak flow events found under pristine flow regimes could increase advection-driven dispersal for many species. In rivers with extensive habitat loss, increased advection could transport individuals from remnant populations into degraded downstream areas, causing restored flow regimes to decrease persistence of threatened species. To demonstrate such possible 'washout' effects across imperiled taxa, we evaluate population growth in spatial models of insect, fish, and mollusc taxa that experience advective dispersal and either long-term habitat loss or temporary drought disturbances. As a case study to quantify advective dispersal in threatened species, we use intensive mark-recapture methods in a Rio Grande population of the endangered mussel Popenaias popeii belonging to the Unionida order, the most threatened faunal taxa worldwide. Our mark-recapture models estimate high levels of annual downstream emigration (16-51%) and immigration from upstream habitats (32-48%) of adult P. popeii, a result consistent with hydrodynamic experiments. Across taxa where such advective dispersal occurs in specific life stages, our population model suggests that washout effects might strongly reduce population recovery under high levels of habitat loss, especially for sessile or shorter lived species. Averting this potential negative consequence of restoring hydrology requires simultaneously restoring or protecting long, contiguous stretches of suitable habitats. In heavily impacted systems, we suggest integrating hydrodynamic studies and field surveys to detect the presence of advective dispersal and prioritize areas for habitat restoration to enhance population persistence.

Longitudinal patterns and response lengths of algae in riverine ecosystems: A model analysis emphasising benthic-pelagic interactions

In riverine ecosystems primary production is principally possible in two habitats: in the benthic layer by sessile algae and in the surface water by planktonic algae being transported downstream. The relevance of these two habitats generally changes along the rivers' continuum. However, analyses of the interaction of algae in these two habitats and their controlling factors in riverine ecosystems are, so far, very rare. We use a simplified advection-diffusion model system combined with ecological process kinetics to analyse the interaction of benthic and planktonic algae and nutrients along idealised streams and rivers at regional to large scales. Because many of the underlying processes affecting algal dynamics are influenced by depth, we focus particularly on the impact of river depth on this interaction. At constant environmental conditions all state variables approach stable spatial equilibria along the river, independent of the boundary conditions at the upstream end. Because our model is very robust against changes of turbulent diffusion and stream velocity, these spatial equilibria can be analysed by a simplified ordinary differential equation (ode) version of our model. This model variant reveals that at shallower river depths, phytoplankton can exist only when it is subsidised by detaching benthic algae, and in turn, at deeper river depths, benthic algae can exist only in low biomasses which are subsidised by sinking planktonic algae. We generalise the spatial dynamics of the model system using different conditions at the upstream end of the model, which mimic various natural or anthropogenic factors (pristine source, dam, inflow of a waste water treatment plant, and dilution from e.g. a tributary) and analyse how these scenarios influence different aspects of the longitudinal spatial dynamics of the full spatial model: the relation of spatial equilibrium to spatial maximum, the distance to the spatial maximum, and the response length. Generally, our results imply that shallow systems recover within significantly shorter distances from spatially distinct disturbances when compared to deep systems, independent of the type of disturbance.

Assessing recovery of stream insects from pesticides using a two-patch metapopulation model

Pesticides can exert lethal and sublethal effects on streams organisms. Field studies have shown that non-polluted upstream patches promote population recovery from such effects. Nevertheless, the dynamics and potential carryover effects on the upstream patch are largely unknown. We used a metapopulation model with 2 patches to simulate lethal and sublethal effects on the downstream population of an insect with one generation per year, which was structured into early and late instars aquatic life stages, and an adult terrestrial life stage. We examined the implications for the recovery time of a range of scenarios covering different pesticide effect combinations, migration and exposure types. We found that recovery time responded most strongly to a reduction in reproduction in terms of the reduction of the intrinsic growth rate during the early instar aquatic life stage. For 60 of 96 scenarios with pesticide exposure in consecutive years, no recovery occurred within one year if the intrinsic growth rate was reduced by 50% or more. Without migration between patches (32 scenarios), the polluted downstream population went extinct in 5 of these scenarios. Migration lead overall to slightly faster recovery, albeit this was scenario dependent, but also to a carryover of the pesticide effect from the polluted downstream to the non-polluted upstream patch (up to 25% reduction in the minimal population size). A sensitivity analysis revealed that recovery time was most sensitive to the parameters length of the intrinsic growth phase during early instar aquatic life stage and to migration mortality of the late instar aquatic larvae, and least sensitive to the adult emigration rate and timing of pesticide application. Our study highlights the important role of sublethal effects for population responses to pesticides and that migration buffers against effects, but also carries effects over to non-polluted patches.

Geometric indicators of population persistence in branching continuous-space networks

We study population persistence in branching tree networks emulating systems such as river basins, cave systems, organisms on vegetation surfaces, and vascular networks. Population dynamics are modeled using a reaction-diffusion-advection equation on a metric graph which provides a continuous, spatially explicit model of network habitat. A metric graph, in contrast to a standard graph, allows for population dynamics to occur within edges rather than just at graph vertices, subsequently adding a significant level of realism. Within this framework, we stochastically generate branching tree networks with a variety of geometric features and explore the effects of network geometry on the persistence of a population which advects toward a lethal outflow boundary. We identify a metric (CM), the distance from the lethal outflow point at which half of the habitable volume of the network lies upstream of, as a promising indicator of population persistence. This metric outperforms other metrics such as the maximum and minimum distances from the lethal outflow to an upstream boundary and the total habitable volume of the network. The strength of CM as a predictor of persistence suggests that it is a proper "system length" for the branching networks we examine here that generalizes the concept of habitat length in the classical linear space models.

Applications of step-selection functions in ecology and conservation

Recent progress in positioning technology facilitates the collection of massive amounts of sequential spatial data on animals. This has led to new opportunities and challenges when investigating animal movement behaviour and habitat selection. Tools like Step Selection Functions (SSFs) are relatively new powerful models for studying resource selection by animals moving through the landscape. SSFs compare environmental attributes of observed steps (the linear segment between two consecutive observations of position) with alternative random steps taken from the same starting point. SSFs have been used to study habitat selection, human-wildlife interactions, movement corridors, and dispersal behaviours in animals. SSFs also have the potential to depict resource selection at multiple spatial and temporal scales. There are several aspects of SSFs where consensus has not yet been reached such as how to analyse the data, when to consider habitat covariates along linear paths between observations rather than at their endpoints, how many random steps should be considered to measure availability, and how to account for individual variation. In this review we aim to address all these issues, as well as to highlight weak features of this modelling approach that should be developed by further research. Finally, we suggest that SSFs could be integrated with state-space models to classify behavioural states when estimating SSFs.

A mathematical biologist's guide to absolute and convective instability

Mathematical models have been highly successful at reproducing the complex spatiotemporal phenomena seen in many biological systems. However, the ability to numerically simulate such phenomena currently far outstrips detailed mathematical understanding. This paper reviews the theory of absolute and convective instability, which has the potential to redress this inbalance in some cases. In spatiotemporal systems, unstable steady states subdivide into two categories. Those that are absolutely unstable are not relevant in applications except as generators of spatial or spatiotemporal patterns, but convectively unstable steady states can occur as persistent features of solutions. The authors explain the concepts of absolute and convective instability, and also the related concepts of remnant and transient instability. They give examples of their use in explaining qualitative transitions in solution behaviour. They then describe how to distinguish different types of instability, focussing on the relatively new approach of the absolute spectrum. They also discuss the use of the theory for making quantitative predictions on how spatiotemporal solutions change with model parameters. The discussion is illustrated throughout by numerical simulations of a model for river-based predator-prey systems.

Spatiotemporal population distributions and their implications for species coexistence in a variable environment

A population experiences environmental variation both directly, through effects on life history parameters such as fecundity, and indirectly, through effects on the population distributions of competitors and thus on the distribution of competition. Which spatial and temporal scales of environmental variation most influence the coexistence of two species thus depends in part on the degree to which the resident population responds to different scales of variation. In this paper, I calculate an approximation for a spatiotemporal population distribution as the result of a filter function convolved with the environmental variation. I find that there is no straightforward connection between spatial or temporal scales inherent to an organism's life history, such as mean lifetime or dispersal distance, and the population's sensitivity to variation at different scales. Rather, life history traits interact sensitively with the way environmental variation affects the organism. I comment on the implications for variation-mediated coexistence.

A Short Note on Short Dispersal Events

We study how the speed of spread for an integrodifference equation depends on the dispersal pattern of individuals. When the dispersal kernel has finite variance, the central limit theorem states that convolutions of the kernel with itself will approach a suitably chosen Gaussian distribution. Despite this fact, the speed of spread cannot be obtained from the Gaussian approximation. We give several examples and explanations for this fact. We then use the kurtosis of the kernel to derive an improved approximation that shows a very good fit to all the kernels tested. We apply the theory to one well-studied data set of dispersal of Drosophila pseudoobscura and to two one-parameter families of theoretical dispersal kernels. In particular, we find kernels that, despite having compact support, have a faster speed of spread than the Gaussian kernel.

Spatial scaling of consumer-resource interactions in advection-dominated systems

Ecologists studying consumer-resource interactions in advection-dominated systems such as streams and rivers frequently seek to link the results of small-scale experiments with larger-scale patterns of distribution and abundance. Accomplishing this goal requires determining the characteristic scale, termed the response length, at which there is a shift from local dynamics dominated by advective dispersal to larger-scale dynamics dominated by births and deaths. Here, we model the dynamics of consumer-resource systems in a spatially variable, advective environment and show how consumer-resource interactions alter the response length relative to its single-species value. For one case involving a grazer that emigrates in response to high predator density, we quantify the changes using published data from small-scale experiments on aquatic invertebrates. Using Fourier analysis, we describe the responses of advection-dominated consumer-resource systems to spatially extended environmental variability in a way that involves explicit consideration of the response length. The patterns we derive for different consumer-resource systems exhibit important similarities in how component populations respond to spatial environmental variability affecting dispersal as opposed to demographic parameters.