André M. de Roos

Self-organization of vegetation in arid ecosystems

Scientists are still searching for possible unifying mechanisms to explain this range of spatial patterns (Tongway and Ludwig 2001), and an important question of this research is whether this range is the result of preexisting environmental heterogeneity, the result of spatial selforganization, or both (Klausmeier 1999; Couteron and Lejeune 2001; HilleRisLambers et al. 2001; Von Hardenberg et al. 2001). Here, we contribute to the ongoing debate about vegetation pattern formation in arid ecosystems by presenting novel, spatially explicit model analyses and results, extending on the work of HilleRisLambers et al. (2001). Our results show that these different vegetation patterns observed in arid ecosystems might all be the result of spatial self-organization, caused by one single mechanism: water infiltrates faster into vegetated ground than into bare soil, leading to net displacement of surface water to vegetated patches. This model differs from earlier model results (Klausmeier 1999; Couteron and Lejeune 2001; HilleRisLambers et al. 2001; Von Hardenberg et al. 2001) primarily in two ways: it is fully mechanistic, and it treats the lateral flow of water above and below the soil as separate, not independent, variables. Although the current model greatly simplifies the biophysics of arid systems, it can reproduce the whole range of distinctive vegetation patterns as observed in arid ecosystems, indicating that the proposed mechanism might be generally applicable. We further show that self-organized vegetation patterns can persist far into regions of high aridity, where plants would become extinct if homogeneously distributed, pointing to the importance of this mechanism for maintaining productivity of arid ecosystems (Noy-Meir 1973). Our analyses are based on the model first developed in HilleRisLambers et al. (2001)

Size-dependent life-history traits promote catastrophic collapses of top predators

Catastrophic population collapses such as observed in many exploited fish populations have been argued to result from depensatory growth mechanisms (i.e., reduced reproductive success at low population densities, also known as Allee effect). Empirical support for depensation from population-level data is, however, hard to obtain and inconclusive. Using a size-structured, individual-based model we show that catastrophic population collapses may nonetheless be an intrinsic property of many communities, because of two general aspects of individual life history: size- and food-dependent individual growth and individual mortality decreasing with body size. Positive density dependence, characteristic for depensatory growth mechanisms and catastrophic behavior, results as a direct and robust consequence of the interplay between these individual life-history traits, which are commonly found in many species.

Synchronous and asynchronous updating in cellular automata

We analyze the properties of a synchronous and of various asynchronous methods to iterate cellular automata. Asynchronous methods in which the time variable is not explicitly defined, operate by specifying an updating order of the cells. The statistical properties of this order have significant consequences for the dynamics and the patterns generated by the cellular automata. Stronger correlations between consecutive steps in the updating order result in more, artificial structure in the patterns. Among these step-driven methods, using random choice with replacement to pick the next cell for updating, yields results that are least influenced by the updating method. We also analyse a time-driven method in which the state transitions of single cells are governed by a probability per unit time that determines an exponential distribution of the waiting time until the next transition. The statistical properties of this method are completely independent of the size of the grid. Consecutive updating steps therefore show no correlation at all. The stationary states of a cellular automaton do not depend on whether a synchronous or asynchronous updating method is used. Their basins of attraction might, however, be vastly different under synchronous and asynchronous iteration. Cyclic dynamics occur only with synchronous updating.

Population dynamic theory of size-dependent cannibalism

Cannibalism is characterized by four aspects: killing victims, gaining energy from victims, size–dependent interactions and intraspecific competition. In this review of mathematical models of cannibalistic populations, we relate the predicted population dynamic consequences of cannibalism to its four defining aspects. We distinguish five classes of effects of cannibalism: (i) regulation of population size; (ii) destabilization resulting in population cycles or chaos; (iii) stabilization by damping population cycles caused by other interactions; (iv) bistability such that, depending on the initial conditions, the population converges to one of two possible stable states; and (v) modification of the population size structure. The same effects of cannibalism may be caused by different combinations of aspects of cannibalism. By contrast, the same combination of aspects may lead to different effects. For particular cannibalistic species, the consequences of cannibalism will depend on the presence and details of the four defining aspects. Empirical evidence for the emerged theory of cannibalism is discussed briefly. The implications of the described dynamic effects of cannibalism are discussed in the context of community structure, making a comparison with the community effects of intraguild predation.

Demographic analysis of continuous‐time life‐history models

I present a computational approach to calculate the population growth rate, its sensitivity to life-history parameters and associated statistics like the stable population distribution and the reproductive value for exponentially growing populations, in which individual life history is described as a continuous development through time. The method is generally applicable to analyse population growth and performance for a wide range of individual life-history models, including cases in which the population consists of different types of individuals or in which the environment is fluctuating periodically. It complements comparable methods developed for discrete-time dynamics modelled with matrix or integral projection models. The basic idea behind the method is to use Lotkas integral equation for the population growth rate and compute the integral occurring in that equation by integrating an ordinary differential equation, analogous to recently derived methods to compute steady-states of physiologically structured population models. I illustrate application of the method using a number of published life-history models.

Culling prey promotes predator recovery - Alternative states in a whole-lake experiment

Many top-predator fish stocks in both freshwater and marine systems have collapsed as a result of overharvesting. Consequently, some of these communities have shifted into seemingly irreversible new states. We showed, for predators feeding on prey that exhibit food-dependent growth, that culling of fish prey may promote predator recovery. We removed old stunted individuals of a prey-fish species in a large, low-productive lake, which caused an increase in the availability of small-sized prey and allowed the predator to recover. The shift in community state has been sustained for more than 15 years after the cull ended and represents an experimental demonstration of an alternative stable state in a large-scale field system. Because most animals exhibit food-dependent growth, shifts into alternative stable states resulting from overcompensating prey growth may be common in nature and may require counterintuitive management strategies.

Evolutionary regime shifts in age and size at maturation of exploited fish stocks

Worldwide declines of fish stocks raise concerns about deleterious consequences of harvesting for stock abundances and individual life histories, and call for appropriate recovery strategies. Fishes in exploited stocks mature earlier at either larger or smaller sizes due to both genetic and plastic responses. The latter occur commonly when reduced competition for food leads to faster growth. Using a size-structured consumer–resource model, which accounts for both genetic and plastic responses, we show that fisheries-induced evolutionary changes in individual life history and stock properties can easily become irreversible. As a result of annual spawning, early maturation at small sizes and late maturation at large sizes can become alternative, evolutionarily and ecologically stable states under otherwise identical environmental conditions. Exploitation of late-maturing populations can then induce an evolutionary regime shift to smaller maturation sizes associated with stepwise, 1-year decreases in age at first reproduction. Complete and early fishing moratoria slowly reverse this process, but belated or partial closure of fisheries may accelerate or even instigate further evolution to smaller sizes at maturation. We suggest that stepwise decreases in maturation age can be used as early warnings of upcoming evolutionary changes, and should inspire timely restrictions of fisheries.

Food‐Dependent Growth Leads to Overcompensation in Stage‐Specific Biomass When Mortality Increases: The Influence of Maturation versus Reproduction Regulation

We analyze a stage‐structured biomass model for size‐structured consumer‐resource interactions. Maturation of juvenile consumers is modeled with a food‐dependent function that consistently translates individual‐level assumptions about growth in body size to the population level. Furthermore, the model accounts for stage‐specific differences in resource use and mortality between juvenile and adult consumers. Without such differences, the model reduces to the Yodzis and Innes (1992) bioenergetics model, for which we show that model equilibria are characterized by a symmetry property that reproduction and maturation are equally limited by food density. As a consequence, biomass production rate exactly equals loss rate through maintenance and mortality in each consumer stage. Stage‐specific differences break up this symmetry and turn specific stages into net producers and others into net losers of biomass. As a consequence, the population in equilibrium can be regulated in two distinct ways: either through total population reproduction or through total population maturation as limiting process. In the case of reproduction regulation, increases in mortality may lead to an increase of juvenile biomass. In the case of maturation regulation, increases in mortality may increase adult biomass. This overcompensation in biomass occurs with increases in both stage‐independent and stage‐specific mortality, even when the latter targets the stage exhibiting overcompensation.

Intraguild Predation Usually does not Disrupt Biological Control

Intraguild predation is claimed to be ubiquitous in nature. It also occurs among natural enemies in biological control systems, where one natural enemy (the intraguild predator) attacks another species of natural enemy (the intraguild prey), whereas they also compete for the same pest. We review the theory of intraguild predation and its consequences for biological control for two different scenarios. 1. The intraguild predator is the superior natural enemy (

Competition in size-structured populations: mechanisms inducing cohort formation and population cycles

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