570 Biowissenschaften; Biologie
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Predator-prey oscillations are expected to show a 1/4-phase lag between predator and prey. However, observed dynamics of natural or experimental predator-prey systems are often more complex. A striking but hardly studied example are sudden interruptions of classic 1/4-lag cycles with periods of antiphase oscillations, or periods without any regular predator-prey oscillations. These interruptions occur for a limited time before the system reverts to regular 1/4-lag oscillations, thus yielding intermittent cycles. Reasons for this behaviour are often difficult to reveal in experimental systems. Here we test the hypothesis that such complex dynamical behaviour may result from minor trait variation and trait adaptation in both the prey and predator, causing recurrent small changes in attack rates that may be hard to capture by empirical measurements. Using a model structure where the degree of trait variation in the predator can be explicitly controlled, we show that a very limited amount of adaptation resulting in 10-15% temporal variation in attack rates is already sufficient to generate these intermittent dynamics. Such minor variation may be present in experimental predator-prey systems, and may explain disruptions in regular 1/4-lag oscillations.
The green microalga Chlamydomonas acidophila is an important primary producer in very acidic lakes (pH 2.0-3.5), characterized by high concentrations of ferric iron (up to 1 g total Fe L-1) and low rates of primary production. It was previously suggested that these high iron concentrations result in high iron accumulation and inhibit photosynthesis in C. acidophila. To test this, the alga was grown in sterilized lake water and in medium with varying total iron concentrations under limiting and sufficient inorganic phosphorus (Pi) supply, because Pi is an important growth limiting nutrient in acidic waters. Photosynthesis and growth of C. acidophila as measured over 5 days were largely unaffected by high total iron concentrations and only decreased if free ionic Fe3+ concentrations exceeded 100 mg Fe3+ L-1. Although C. acidophila was relatively rich in iron (up to 5 mmol Fe: mol C), we found no evidence of iron toxicity. In contrast, a concentration of 260 mg total Fe L-1 (i.e. 15 mg free ionic Fe3+ L-1), which is common in many acidic lakes, reduced Pi-incorporation by 50% and will result in Pi-limited photosynthesis. The resulting Pi-limitation present at high iron and Pi concentrations was illustrated by elevated maximum Pi-uptake rates. No direct toxic effects of high iron were found, but unfavourable chemical Pi-speciation reduced growth of the acidophile alga.
Ecoevolutionary feedbacks in predator-prey systems have been shown to qualitatively alter predator-prey dynamics. As a striking example, defense-offense coevolution can reverse predator-prey cycles, so predator peaks precede prey peaks rather than vice versa. However, this has only rarely been shown in either model studies or empirical systems. Here, we investigate whether this rarity is a fundamental feature of reversed cycles by exploring under which conditions they should be found. For this, we first identify potential conditions and parameter ranges most likely to result in reversed cycles by developing a new measure, the effective prey biomass, which combines prey biomass with prey and predator traits, and represents the prey biomass as perceived by the predator. We show that predator dynamics always follow the dynamics of the effective prey biomass with a classic 1/4-phase lag. From this key insight, it follows that in reversed cycles (i.e., -lag), the dynamics of the actual and the effective prey biomass must be in antiphase with each other, that is, the effective prey biomass must be highest when actual prey biomass is lowest, and vice versa. Based on this, we predict that reversed cycles should be found mainly when oscillations in actual prey biomass are small and thus have limited impact on the dynamics of the effective prey biomass, which are mainly driven by trait changes. We then confirm this prediction using numerical simulations of a coevolutionary predator-prey system, varying the amplitude of the oscillations in prey biomass: Reversed cycles are consistently associated with regions of parameter space leading to small-amplitude prey oscillations, offering a specific and highly testable prediction for conditions under which reversed cycles should occur in natural systems.
Ecological communities are complex adaptive systems that exhibit remarkable feedbacks between their biomass and trait dynamics. Trait-based aggregate models cope with this complexity by focusing on the temporal development of the community’s aggregate properties such as its total biomass, mean trait and trait variance. They are based on particular assumptions about the shape of the underlying trait distribution, which is commonly assumed to be normal. However, ecologically important traits are usually restricted to a finite range, and empirical trait distributions are often skewed or multimodal. As a result, normal distribution-based aggregate models may fail to adequately represent the biomass and trait dynamics of natural communities. We resolve this mismatch by developing a new moment closure approach assuming the trait values to be beta-distributed. We show that the beta distribution captures important shape properties of both observed and simulated trait distributions, which cannot be captured by a Gaussian. We further demonstrate that a beta distribution-based moment closure can strongly enhance the reliability of trait-based aggregate models. We compare the biomass, mean trait and variance dynamics of a full trait distribution (FD) model to the ones of beta (BA) and normal (NA) distribution-based aggregate models, under different selection regimes. This way, we demonstrate under which general conditions (stabilizing, fluctuating or disruptive selection) different aggregate models are reliable tools. All three models predicted very similar biomass and trait dynamics under stabilizing selection yielding unimodal trait distributions with small standing trait variation. We also obtained an almost perfect match between the results of the FD and BA models under fluctuating selection, promoting skewed trait distributions and ongoing oscillations in the biomass and trait dynamics. In contrast, the NA model showed unrealistic trait dynamics and exhibited different alternative stable states, and thus a high sensitivity to initial conditions under fluctuating selection. Under disruptive selection, both aggregate models failed to reproduce the results of the FD model with the mean trait values remaining within their ecologically feasible ranges in the BA model but not in the NA model. Overall, a beta distribution-based moment closure strongly improved the realism of trait-based aggregate models.
Resisting annihilation
(2018)
Allelopathic species can alter biodiversity. Using simulated assemblages that are characterised by neutrality, lumpy coexistence and intransitivity, we explore relationships between within-assemblage competitive dissimilarities and resistance to allelopathic species. An emergent behaviour from our models is that assemblages are more resistant to allelopathy when members strongly compete exploitatively (high competitive power). We found that neutral assemblages were the most vulnerable to allelopathic species, followed by lumpy and then by intransitive assemblages. We find support for our modeling in real-world time-series data from eight lakes of varied morphometry and trophic state. Our analysis of this data shows that a lake's history of allelopathic phytoplankton species biovolume density and dominance is related to the number of species clusters occurring in the plankton assemblages of those lakes, an emergent trend similar to that of our modeling. We suggest that an assemblage's competitive power determines its allelopathy resistance.
Phenotypic plasticity in prey can have a dramatic impact on predator-prey dynamics, e.g. by inducible defense against temporally varying levels of predation. Previous work has overwhelmingly shown that this effect is stabilizing: inducible defenses dampen the amplitudes of population oscillations or eliminate them altogether. However, such studies have neglected scenarios where being protected against one predator increases vulnerability to another (incompatible defense). Here we develop a model for such a scenario, using two distinct prey phenotypes and two predator species. Each prey phenotype is defended against one of the predators, and vulnerable to the other. In strong contrast with previous studies on the dynamic effects of plasticity involving a single predator, we find that increasing the level of plasticity consistently destabilizes the system, as measured by the amplitude of oscillations and the coefficients of variation of both total prey and total predator biomasses. We explain this unexpected and seemingly counterintuitive result by showing that plasticity causes synchronization between the two prey phenotypes (and, through this, between the predators), thus increasing the temporal variability in biomass dynamics. These results challenge the common view that plasticity should always have a stabilizing effect on biomass dynamics: adding a single predator-prey interaction to an established model structure gives rise to a system where different mechanisms may be at play, leading to dramatically different outcomes.
Parasites, such as bacterial viruses (phages), can have large effects on host populations both at the ecological and evolutionary levels. In the case of cyanobacteria, phages can reduce primary production and infected hosts release intracellular nutrients influencing planktonic food web structure, community dynamics, and biogeochemical cycles. Cyanophages may be of great importance in aquatic food webs during large cyanobacterial blooms unless the host population becomes resistant to phage infection. The consequences on plankton community dynamics of the evolution of phage resistance in bloom forming cyanobacterial populations are still poorly studied. Here, we examined the effect of different frequencies of a phage-resistant genotype within a filamentous nitrogen-fixing Nodularia spumigena population on an experimental plankton community. Three Nodularia populations with different initial frequencies (0%, 5%, and 50%) of phage-resistant genotypes were inoculated in separate treatments with the phage 2AV2, the green alga Chlorella vulgaris, and the rotifer Brachionus plicatilis, which formed the experimental plankton community subjected to either nitrogen-limited or nitrogen-rich conditions. We found that the frequency of the phage-resistant Nodularia genotype determined experimental community dynamics. Cyanobacterial populations with a high frequency (50%) of the phage-resistant genotype dominated the cultures despite the presence of phages, retaining most of the intracellular nitrogen in the plankton community. In contrast, populations with low frequencies (0% and 5%) of the phage-resistant genotype were lysed and reduced to extinction by the phage, transferring the intracellular nitrogen held by Nodularia to Chlorella and rotifers, and allowing Chlorella to dominate the communities and rotifers to survive. This study shows that even though phages represent minuscule biomass, they can have key effects on community composition and eco-evolutionary feedbacks in plankton communities.
The shapes of phytoplankton units (unicellular organisms and colonies) are extremely diverse, and no unique relationship exists between their volume, V, and longest linear dimension, L. However, an approximate scaling between these parameters can be found because the shape variations within each size class are constrained by cell physiology, grazing pressure, and optimality of resource acquisition. To determine this scaling and to test for its seasonal and interannual variation under changing environmental conditions, we performed weighted regression analysis of time-dependent length-volume relations of the phytoplankton community in large deep Lake Constance from 1979 to 1999. We show that despite a large variability in species composition, the V(L) relationship can be approximated as a power law, V similar to L-alpha, with a scaling exponent alpha = 3 for small cells (L < 25 mu m) and alpha = 1.7 if the fitting is performed over the entire length range, including individual cells and colonies. The best description is provided by a transitional power function describing a regime change from a scaling exponent of 3 for small cells to an exponent of 0.4 in the range of large phytoplankton. Testing different weighted fitting approaches we show that remarkably the best prediction of the total community biovolume from measurements of L and cell density is obtained when the regression is weighted with the squares of species abundances. Our approach should also be applicable to other systems and allows converting phytoplankton length distributions (e.g., obtained with automatic monitoring such as flow cytometry) into distributions of biovolume and biovolume-related phytoplankton traits.
Estimating parameters from multiple time series of population dynamics using bayesian inference
(2019)
Empirical time series of interacting entities, e.g., species abundances, are highly useful to study ecological mechanisms. Mathematical models are valuable tools to further elucidate those mechanisms and underlying processes. However, obtaining an agreement between model predictions and experimental observations remains a demanding task. As models always abstract from reality one parameter often summarizes several properties. Parameter measurements are performed in additional experiments independent of the ones delivering the time series. Transferring these parameter values to different settings may result in incorrect parametrizations. On top of that, the properties of organisms and thus the respective parameter values may vary considerably. These issues limit the use of a priori model parametrizations. In this study, we present a method suited for a direct estimation of model parameters and their variability from experimental time series data. We combine numerical simulations of a continuous-time dynamical population model with Bayesian inference, using a hierarchical framework that allows for variability of individual parameters. The method is applied to a comprehensive set of time series from a laboratory predator-prey system that features both steady states and cyclic population dynamics. Our model predictions are able to reproduce both steady states and cyclic dynamics of the data. Additionally to the direct estimates of the parameter values, the Bayesian approach also provides their uncertainties. We found that fitting cyclic population dynamics, which contain more information on the process rates than steady states, yields more precise parameter estimates. We detected significant variability among parameters of different time series and identified the variation in the maximum growth rate of the prey as a source for the transition from steady states to cyclic dynamics. By lending more flexibility to the model, our approach facilitates parametrizations and shows more easily which patterns in time series can be explained also by simple models. Applying Bayesian inference and dynamical population models in conjunction may help to quantify the profound variability in organismal properties in nature.