Bimodal trait distributions with large variances question the reliability of trait-based aggregate models

Coutinho, Renato Mendes; Klauschies, Toni; Gaedke, Ursula

doi:10.1007/s12080-016-0297-9

Cited by 31 publications

(43 citation statements)

References 66 publications

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“…Given the positive sign of the second derivative of the allometric function, this implies an underestimation of the increase of v . This is in line with the overall tendency of v to decline in aggregate models previously explored in other studies (Merico et al ; Coutinho et al ). To counteract this permanent loss of functional diversity and thus adaptive potential, previous studies had to maintain v by other processes such as immigration or diffusion terms or more complex trade‐offs, all demanding additional assumptions (Wirtz and Eckhardt ; Norberg et al ; Merico et al ; Tirok et al ).…”

Section: Discussionsupporting

confidence: 91%

“…As a second approach, we consider two aggregate models which describe the temporal dynamics of B T ,

\overset{x}{true}

and v combined with a second‐order approximation of Eq. (Wirtz and Eckhardt ; Norberg et al ; Merico et al ; Coutinho et al ). These models consider additionally the dynamics of v and enable a better approximation of the non‐linearity of the fitness function by including its second derivative and of the shape of the trait distribution by accounting for potential skewness and kurtosis:

\frac{d B_{normalT}}{d t} \approx B_{normalT} \cdot true({R true(x true) |}_{_{_{x = \bar{x}}}} + v \frac{1}{2} {\frac{\partial^{2} R true(x true)}{\partial x^{2}} |}_{x = \bar{x}} true)

\frac{d \bar{x}}{d t} \approx v {\frac{\partial R true(x true)}{\partial x} |}_{_{_{x = \bar{x}}}} + M_{3} \frac{1}{2} {\frac{\partial^{2} R true(x true)}{\partial x^{2}} |}_{x = \bar{x}}

\frac{d v}{d t} \approx M_{3} {\frac{\partial R true(x true)}{\partial x} |}_{_{x = \bar{x}}} + true(M_{4} - v^{2} true) \frac{1}{2} {\frac{\partial^{2} R true(x true)}{\partial x^{2}} |}_{x = x}

…”

Section: Materials and Proceduresmentioning

confidence: 99%

“…x and v combined with a second-order approximation of Eq. 9 (Wirtz and Eckhardt 1996;Norberg et al 2001;Merico et al 2009;Coutinho et al 2016). These models consider additionally the dynamics of v and enable a better approximation of the non-linearity of the fitness function by including its second derivative and of the shape of the trait distribution by accounting for potential skewness and kurtosis:…”

Section: Characterizing Trait Distributions Based On Their Shapementioning

confidence: 99%

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Analyzing the shape of observed trait distributions enables a data‐based moment closure of aggregate models

Gaedke

Klauschies

2017

Limnology & Ocean Methods

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The shape of trait distributions may inform about the selective forces that structure ecological communities. Here, we present a new moment‐based approach to classify the shape of observed biomass‐weighted trait distributions into normal, peaked, skewed, or bimodal that facilitates spatio‐temporal and cross‐system comparisons. Our observed phytoplankton trait distributions exhibited substantial variance and were mostly skewed or bimodal rather than normal. Additionally, mean, variance, skewness und kurtosis were strongly correlated. This is in conflict with trait‐based aggregate models that often assume normally distributed trait values and small variances. Given these discrepancies between our data and general model assumptions we used the observed trait distributions to test how well different aggregate models with first‐ or second‐order approximations and different types of moment closure predict the biomass, mean trait, and trait variance dynamics using weakly or moderately nonlinear fitness functions. For weakly non‐linear fitness functions aggregate models with a second‐order approximation and a data‐based moment closure that relied on the observed correlations between skewness and mean, and kurtosis and variance predicted biomass and often also mean trait changes fairly well and better than models with first‐order approximations or a normal‐based moment closure. In contrast, none of the models reflected the changes of the trait variances reliably. Aggregate model performance was often also poor for moderately nonlinear fitness functions. This questions a general applicability of the normal‐based approach, in particular for predicting variance dynamics determining the speed of trait changes and maintenance of biodiversity. We evaluate in detail how and why better approximations can be obtained.

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Section: Discussionsupporting

confidence: 91%

“…As a second approach, we consider two aggregate models which describe the temporal dynamics of B T ,

\overset{x}{true}

\frac{d B_{normalT}}{d t} \approx B_{normalT} \cdot true({R true(x true) |}_{_{_{x = \bar{x}}}} + v \frac{1}{2} {\frac{\partial^{2} R true(x true)}{\partial x^{2}} |}_{x = \bar{x}} true)

\frac{d \bar{x}}{d t} \approx v {\frac{\partial R true(x true)}{\partial x} |}_{_{_{x = \bar{x}}}} + M_{3} \frac{1}{2} {\frac{\partial^{2} R true(x true)}{\partial x^{2}} |}_{x = \bar{x}}

\frac{d v}{d t} \approx M_{3} {\frac{\partial R true(x true)}{\partial x} |}_{_{x = \bar{x}}} + true(M_{4} - v^{2} true) \frac{1}{2} {\frac{\partial^{2} R true(x true)}{\partial x^{2}} |}_{x = x}

…”

Section: Materials and Proceduresmentioning

confidence: 99%

Section: Characterizing Trait Distributions Based On Their Shapementioning

confidence: 99%

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Analyzing the shape of observed trait distributions enables a data‐based moment closure of aggregate models

Gaedke

Klauschies

2017

Limnology & Ocean Methods

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“…Trait values are often assumed to be normally distributed and trait variances to be relatively small as a result of stabilizing selection promoting the dominance of species with very similar trait values (Enquist et al., ). Alternatively, under directional selection, trait distributions should exhibit skewness because the optimum trait values are shifting over time, while disruptive selection will promote the co‐occurrence of two very different strategies, giving rise to bimodal trait distributions with large variances (Coutinho, Klauschies, & Gaedke, ). Six scenarios are used to illustrate how only considering the first (mean) and second (variance) moment of inter‐specific trait distributions could miss important insights provided by assessing the third (skewness) and the fourth (kurtosis) moments that describe the shape of the distribution (Figure ).…”

Section: New Insights From Comparing Inter‐specific Trait Distributiomentioning

confidence: 99%

Evaluating differences in the shape of native and alien plant trait distributions will bring new insights into invasions of plant communities

Hulme

Bernard‐Verdier

2018

J Vegetation Science

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Failure to quantify differences in the shape of inter‐specific trait distributions (e.g., skew, kurtosis) when comparing co‐occurring alien and native plants hinders the integration of biological invasions and plant community ecology. Within a plant community, understanding the circumstances that lead to the shape of the inter‐specific distribution of one or more functional plant traits being unimodal, bimodal, multimodal or skewed has the potential to shed new light on community vulnerability to invasion, subsequent ecosystem impacts and the selection pressures (e.g., stabilizing, directional or disruptive) acting upon native and alien species. Ignoring differences in the shape of inter‐specific trait distributions of alien and native species could miss important insights into plant invasions, including: the existence of unsaturated native plant communities, empty niches, shifting trait optima of species as a result of environmental change and incomplete colonization–extinction processes following invasion. Future comparisons of functional trait differences between native and alien species should include assessment of the shapes of inter‐specific trait distributions since these may differ even when the mean values of traits are similar for native and alien species. The infrequent application of such approaches may explain the limited generalizations regarding the drivers and consequences of plant invasions in plant communities.

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“…This can lead to poor approximations when trait distributions are multi-modal or have large variances (Coutinho et al 2016). First, the models only track part of the trait distribution and assume that the population-level dynamics are affected solely by changes in the mean trait value.…”

Section: Eco-coevolutionary Modelmentioning

confidence: 99%

How (co)evolution alters predator responses to increased mortality: extinction thresholds and hydra effects

Cortez

Yamamichi

2019

Ecology

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Citation: Cortez, M. H., and M. Yamamichi. 2019. How (co)evolution alters predator responses to increased mortality: extinction thresholds and hydra effects. Ecology 100(10):Abstract. Population responses to environmental change depend on both the ecological interactions between species and the evolutionary responses of all species. In this study, we explore how evolution in prey, predators, or both species affect the responses of predator populations to a sustained increase in mortality. We use an eco-evolutionary predator-prey model to explore how evolution alters the predator extinction threshold (defined as the minimum mortality rate that prevents population growth at low predator densities) and predator hydra effects (increased predator abundance in response to increased mortality). Our analysis identifies how evolutionary responses of prey and predators individually affect the predator extinction threshold and hydra effects, and how those effects are altered by interactions between the evolutionary responses. Based on our theoretical results, we predict that it is common in natural systems for evolutionary responses in one or both species to allow predators to persist at higher mortality rates than would be possible in the absence of evolution (i.e., evolution increases the predator mortality extinction threshold). We also predict that evolution-driven hydra effects occur in a minority of natural systems, but are not rare. We revisited published eco-evolutionary models and found that evolution causes hydra effects and increases the predator extinction threshold in many studies, but those effects have been overlooked. We discuss the implications of these results for species conservation, predicting population responses to environmental change, and the possibility of evolutionary rescue.Notes: The terms J ij denote entries of the Jacobian in Eq. 3. All conditions assume the sign structure in Eq. 3. Coevolution conditions result in synergistic effects of prey and predator evolution, provided the conditions for only prey evolution and the conditions for only predator evolution are satisfied.

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Bimodal trait distributions with large variances question the reliability of trait-based aggregate models

Cited by 31 publications

References 66 publications

Analyzing the shape of observed trait distributions enables a data‐based moment closure of aggregate models

Analyzing the shape of observed trait distributions enables a data‐based moment closure of aggregate models

Evaluating differences in the shape of native and alien plant trait distributions will bring new insights into invasions of plant communities

How (co)evolution alters predator responses to increased mortality: extinction thresholds and hydra effects

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