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Robust permanence for ecological equations with internal and external feedbacks.
Species experience both internal feedbacks with endogenous factors such as trait evolution and external feedbacks with exogenous factors such as weather. These feedbacks can play an important role in determining whether populations persist or communities of species coexist. To provide a general mathematical framework for studying these effects, we develop a theorem for coexistence for ecological models accounting for internal and external feedbacks. Specifically, we use average Lyapunov functions and Morse decompositions to develop sufficient and necessary conditions for robust permanence, a form of coexistence robust to large perturbations of the population densities and small structural perturbations of the models. We illustrate how our results can be applied to verify permanence in non-autonomous models, structured population models, including those with frequency-dependent feedbacks, and models of eco-evolutionary dynamics. In these applications, we discuss how our results relate to previous results for models with particular types of feedbacks
Biodiversity in model ecosystems, II: Species assembly and food web structure
This is the second of two papers dedicated to the relationship between
population models of competition and biodiversity. Here we consider species
assembly models where the population dynamics is kept far from fixed points
through the continuous introduction of new species, and generalize to such
models thecoexistence condition derived for systems at the fixed point. The
ecological overlap between species with shared preys, that we define here,
provides a quantitative measure of the effective interspecies competition and
of the trophic network topology. We obtain distributions of the overlap from
simulations of a new model based both on immigration and speciation, and show
that they are in good agreement with those measured for three large natural
food webs. As discussed in the first paper, rapid environmental fluctuations,
interacting with the condition for coexistence of competing species, limit the
maximal biodiversity that a trophic level can host. This horizontal limitation
to biodiversity is here combined with either dissipation of energy or growth of
fluctuations, which in our model limit the length of food webs in the vertical
direction. These ingredients yield an effective model of food webs that produce
a biodiversity profile with a maximum at an intermediate trophic level, in
agreement with field studies
Persistence of complex food webs in metacommunities
Metacommunity theory is considered a promising approach for explaining
species diversity and food web complexity. Recently Pillai et al. proposed a
simple modeling framework for the dynamics of food webs at the metacommunity
level. Here, we employ this framework to compute general conditions for the
persistence of complex food webs in metacommunities. The persistence conditions
found depend on the connectivity of the resource patches and the structure of
the assembled food web, thus linking the underlying spatial patch-network and
the species interaction network. We find that the persistence of omnivores is
more likely when it is feeding on (a) prey on low trophic levels, and (b) prey
on similar trophic levels
Biodiversity in model ecosystems, I: Coexistence conditions for competing species
This is the first of two papers where we discuss the limits imposed by
competition to the biodiversity of species communities. In this first paper we
study the coexistence of competing species at the fixed point of population
dynamic equations. For many simple models, this imposes a limit on the width of
the productivity distribution, which is more severe the more diverse the
ecosystem is (Chesson, 1994). Here we review and generalize this analysis,
beyond the ``mean-field''-like approximation of the competition matrix used in
previous works, and extend it to structured food webs. In all cases analysed,
we obtain qualitatively similar relations between biodiversity and competition:
the narrower the productivity distribution is, the more species can stably
coexist. We discuss how this result, considered together with environmental
fluctuations, limits the maximal biodiversity that a trophic level can host
Risk-driven behaviour in the African leopard:how is leopard behaviour mediated by lion presence?
Agricultural expansion is restricting many carnivore species to smaller tracts of land, potentially forcing increased levels of overlap between competitors by constraining spatial partitioning. Understanding encounters between competitors is important because competition can influence species densities, distributions, and reproductive success. Despite this, little is known of the mechanisms that mediate coexistence between the African leopard (Panthera pardus) and its competitors. This project used GPS radiocollar data and playback experiments to understand risk-driven changes in the leopard’s behaviour and movement during actual and perceived encounters with lions (Panthera leo). Targeted playbacks of lion roars were used to elucidate immediate and short-lived behavioural responses in leopards when lions were perceived to be within the immediate area. To investigate the post-encounter spatial dynamics of leopard movements, the project used datasets from high-resolution GPS radiocollars deployed on leopards and lions with overlapping territories in the Okavango Delta, Botswana. Leopards were found to adapt behaviours and movements when lions were perceived to be nearby. Specifically, roar playbacks elicited longer periods of vigilance than controls, and movement directions were influenced by speaker locations. Further, leopard movements were quicker and more directional after encountering lions. However, adjustments in behaviour and movement were short-lived. The results provide insights into mechanisms used by the leopard to coexist with its competitors and are a useful case study of the methods that could be used to investigate encounter dynamics within other systems
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