Jörgen Ripa

Noise Colour and the Risk of Population Extinctions

A recurrent problem in ecology and conservation biology is to estimate the risk of population extinctions. Extinction probabilities are not only imperative for conservation and management, but may also elucidate basic mechanisms of the regulation of natural populations (Burgman et al. 1993; Pimm 1994). The usual way of modelling stochastic influence on population dynamics has been to assume that the external noise is uncorrelated. This means that each and every randomly drawn noise value is totally independent on previous ones. This is what is generally called ‘white’ noise. However, the noise itself can be temporally autocorrelated. That is, the values of the random numbers used in the noise process will depend on previous ones. Here we show that the autocorrelation, or colour, of the external noise assumed to influence population dynamics strongly modifies estimated extinction probabilities. For positively autocorrelated (‘red’) noise, the risk of extinction clearly decreases the stronger the autocorrelation is, Negatively autocorrelated (‘blue’) noise is more ambiguously related to extinction probability. Thus, the commonly assumed white noise in population modelling will severely bias population extinction risk estimates. Moreover, the extinction probability estimates are also significantly dependent on model structure which calls for a cautious use of traditional discrete-time models.

Bet-hedging as an evolutionary game: the trade-off between egg size and number

Bet-hedging theory addresses how individuals should optimize fitness in varying and unpredictable environments by sacrificing mean fitness to decrease variation in fitness. So far, three main bet-hedging strategies have been described: conservative bet-hedging (play it safe), diversified bet-hedging (don’t put all eggs in one basket) and adaptive coin flipping (choose a strategy at random from a fixed distribution). Within this context, we analyse the trade-off between many small eggs (or seeds) and few large, given an unpredictable environment. Our model is an extension of previous models and allows for any combination of the bet-hedging strategies mentioned above. In our individual-based model (accounting for both ecological and evolutionary forces), the optimal bet-hedging strategy is a combination of conservative and diversified bet-hedging and adaptive coin flipping, which means a variation in egg size both within clutches and between years. Hence, we show how phenotypic variation within a population, often assumed to be due to non-adaptive variation, instead can be the result of females having this mixed strategy. Our results provide a new perspective on bet-hedging and stress the importance of extreme events in life history evolution.

Food web dynamics in correlated and autocorrelated environments

The densities of populations in a community or food web vary as a consequence of both population interactions and environmental (e.g. weather) fluctuations. Populations often respond to the same kinds of environmental fluctuations, and therefore experience correlated environments. Furthermore, some environmental factors change slowly over time, thereby producing positive environmental autocorrelation. We show that the effects of environmental correlation and autocorrelation on the dynamics of the populations in a food web can be large and unintuitive, but can be understood by analyzing the eigenvectors of the community (system) matrix of interactions among populations. For example, environmental correlation and autocorrelation may either obscure or enhance the cyclic dynamics that generally characterize predator-prey interactions even when there is no direct effect of the environment on how species interact. Thus, understanding the population dynamics of species in a food web requires explicit attention to the correlation structure of environmental factors affecting all species.

A general theory of environmental noise in ecological food webs.

We examine the effects of environmental noise on populations that are parts of simple two‐species food webs. We assume that the species are strongly interacting and that one or the other population is affected by the noise signal. Further assuming that a stable equilibrium with positive population densities exists, we are able to perform a complete frequency analysis of the system. If only one of the populations is subject to noise, the relative noise response by both populations is fully determined by the sign of a single element of the Jacobian matrix. The analysis is readily extended to cases when both species are affected by noise or when the food web has more than two species. The general conclusion about relative responses to noise is then less unambiguous, but the power spectra describing the frequency composition of the population variabilities are nevertheless completely determined. These results are entirely independent on the exact nature of the interaction (i.e., predation, competition, mutualism) between the populations. The results show that the interpretation of the “color” of ecological time series (i.e., the frequency composition of population variability over time) may be complicated by species interactions. The propagation of noise signals through food webs and the importance of web structure for the expected response of all parts of the web to such signals is a challenging field for future studies.

Primary assembly of soil communities: disentangling the effect of dispersal and local environment

It has long been recognised that dispersal abilities and environmental factors are important in shaping invertebrate communities, but their relative importance for primary soil community assembly has not yet been disentangled. By studying soil communities along chronosequences on four recently emerged nunataks (ice-free land in glacial areas) in Iceland, we replicated environmental conditions spatially at various geographical distances. This allowed us to determine the underlying factors of primary community assembly with the help of metacommunity theories that predict different levels of dispersal constraints and effects of the local environment. Comparing community assembly of the nunataks with that of non-isolated deglaciated areas indicated that isolation of a few kilometres did not affect the colonisation of the soil invertebrates. When accounting for effects of geographical distances, soil age and plant richness explained a significant part of the variance observed in the distribution of the oribatid mites and collembola communities, respectively. Furthermore, null model analyses revealed less co-occurrence than expected by chance and also convergence in the body size ratio of co-occurring oribatids, which is consistent with species sorting. Geographical distances influenced species composition, indicating that the community is also assembled by dispersal, e.g. mass effect. When all the results are linked together, they demonstrate that local environmental factors are important in structuring the soil community assembly, but are accompanied with effects of dispersal that may “override” the visible effect of the local environment.

A Theory of Stochastic Harvesting in Stochastic Environments

We investigate how model populations respond to stochastic harvesting in a stochastic environment. In particular, we show that the effects of variable harvesting on the variance in population density and yield depend critically on the autocorrelation of environmental noise and on whether the endogenous dynamics of the population display over‐ or undercompensation to density. These factors interact in complicated ways; harvesting shifts the slope of the renewal function, and the net effect of this shift will depend on the sign and magnitude of the other influences. For example, when environmental noise exhibits a positive autocorrelation, the relative importance of a variable harvest to the variance in density increases with overcompensation but decreases with undercompensation. For a fixed harvesting level, an increasing level of autocorrelation in environmental noise will decrease the relative variation in population density when overcompensation would otherwise occur. These and other intricate interactions have important ramifications for the interpretation of time series data when no prior knowledge of demographic or environmental details exists. These effects are important whenever the harvesting rate is sufficiently high or variable, conditions likely to occur in many systems, whether the harvesting is caused by commercial exploitation or by any other strong agent of density‐independent mortality.

What is bet-hedging, really?

Bet-hedging is defined as a strategy that reduces the temporal variance in fitness at the expense of a lowered arithmetic mean fitness. After a few technical points, we will here argue that this definition of bet-hedging is badly suited for models with density- and/or frequency-dependent fitness. A strict interpretation cannot be employed; possibly, a modified definition is necessary.

Hamilton's rule confronts ideal free habitat selection

If individuals occupy habitats in a way that maximizes their fitness, if they are free to occupy the habitats they choose and if fitness declines with population density, then their abundance across habitats should follow an ideal free distribution. But, if individuals are genetically related, this simple fitness–maximization mechanism breaks down. Habitat occupation should obey Hamiltons rule (natural selection favours traits causing a loss in individual fitness as long as they result in an equal or greater gain in inclusive fitness) and depends more on inclusive fitness than it does on individual fitness.We demonstrate that the resulting inclusive–fitness distribution inflates the population density in habitats of poorer inherent quality, creating pronounced source–sink dynamics.Wealso show that density–dependent habitat selection among relatives reinforces behaviours such as group defence and interspecific territoriality, and that it explains many anomalies in dispersal and foraging.

The Coupling Between Grazing and Detritus Food Chains and the Strength of Trophic Cascades Across a Gradient of Nutrient Enrichment

A minimal food web model was constructed comprising one grazing and one detritus food chain coupled by nutrient cycling and generalist carnivores to investigate how prey preference by carnivores may affect the strength of trophic cascades across a gradient of nutrient enrichment. The equilibrium or mean abundance of each food web component and the magnitude of the carnivore effect on lower trophic levels were calculated for different values of the prey preference and nutrient input parameters. Our model predicts that nutrient enrichment increases the mean abundances of carnivores, autotrophs and detritus, but the magnitude of this effect is dependent on the prey preference term. On the other hand, herbivores and detritivores are relatively unaffected by enrichment but are strongly affected by carnivore preference. Carnivores have a negative effect on herbivores and a positive effect on autotrophs and detritus, whereas the effect on detritivores can be both positive and negative. At high preference for herbivores, carnivores have a positive effect on detritivores, because the positive effect of increased detritus availability due to reduced herbivore grazing outweighs the negative effect of predation. At high preference for detritivores, the balance is changed in the other direction. We argue that in systems where authochtonous primary production is the major source of detritus, herbivores can control the rates of detritus production and have indirect effects on detritivores, which may feed back into effects on herbivores through their shared enemies. This positive feedback is probably one mechanism affecting the resilience of alternative stable states in shallow lakes.

When is sympatric speciation truly adaptive? An analysis of the joint evolution of resource utilization and assortative mating

The plausibility of sympatric speciation has long been debated among evolutionary ecologists. The process necessarily involves two key elements: the stable coexistence of at least two ecologically distinct types and the emergence of reproductive isolation. Recent theoretical studies within the theoretical framework of adaptive dynamics have shown how both these processes can be driven by natural selection. In the standard scenario, a population first evolves to an evolutionary branching point, next, disruptive selection promotes ecological diversification within the population, and, finally, the fitness disadvantage of intermediate types induces a selection pressure for assortative mating behaviour, which leads to reproductive isolation and full speciation. However, the full speciation process has been mostly studied through computer simulations and only analysed in part. Here I present a complete analysis of the whole speciation process by allowing for the simultaneous evolution of the branching ecological trait as well as a continuous trait controlling mating behaviour. I show how the joint evolution can be understood in terms of a gradient landscape, where the plausibility of different evolutionary paths can be evaluated graphically. I find sympatric speciation unlikely for scenarios with a continuous, unimodal, distribution of resources. Rather, ecological settings where the fitness inferiority of intermediate types is preserved during the ecological branching are more likely to provide opportunity for adaptive, sympatric speciation. Such scenarios include speciation due to predator avoidance or specialization on discrete resources.