Loss of species will directly change the structure and potentially the dynamics of ecological communities, which in turn may lead to additional species loss (secondary extinctions) due to direct and/or indirect effects (e.g. loss of resources or altered population dynamics). Furthermore, the vulnerability of food webs to repeated species loss is expected to be affected by food web topology, species interactions, as well as the order in which species go extinct. Species traits such as body size, abundance and connectivity might determine a species vulnerability to extinction and, thus, the order in which species go primarily extinct. Yet, the sequence of primary extinctions, and their effects on the vulnerability of food webs to secondary extinctions, when species abundances are allowed to respond dynamically, has only recently become the focus of attention. Here, we analyse and compare topological and dynamical robustness to secondary extinctions of model food webs, in the face of 34 extinction sequences based on species traits. Although secondary extinctions are frequent in the dynamical approach and rare in the topological approach, topological and dynamical robustness tends to be correlated for many bottom-up directed, but not for top-down directed deletion sequences. Furthermore, removing species based on traits that are strongly positively correlated to the trophic position of species (such as large body size, low abundance, high net effect) is, under the dynamical approach, found to be as destructive as removing primary producers. Such top-down oriented removal of species are often considered to correspond to realistic extinction scenarios, but earlier studies, based on topological approaches, have found such extinction sequences to have only moderate effects on the remaining community. Thus, our result suggests that the structure of ecological communities, and therefore the integrity of important ecosystem processes could be more vulnerable to realistic extinction sequences than previously believed.

Recent studies predict elevated and accelerating rates of species extinctions over the 21st century, due to climate change and habitat loss. Considering that such primary species loss may initiate cascades of secondary extinctions and push systems towards critical tipping points, we urgently need to increase our understanding of if certain sequences of species extinctions can be expected to be more devastating than others Most theoretical studies addressing this question have used a topological (non-dynamical) approach to analyse the probability that food webs will collapse, below a fixed threshold value in species richness, when subjected to different sequences of species loss. Typically, these studies have neither considered the possibility of dynamical responses of species, nor that conclusions may depend on the value of the collapse threshold. Here we analyse how sensitive conclusions on the importance of different species are to the threshold value of food web collapse. Using dynamical simulations, where we expose model food webs to a range of extinction sequences, we evaluate the reliability of the most frequently used index, R-50, as a measure of food web robustness. In general, we find that R-50 is a reliable measure and that identification of destructive deletion sequences is fairly robust, within a moderate range of collapse thresholds. At the same time, however, focusing on R-50 only hides a lot of interesting information on the disassembly process and can, in some cases, lead to incorrect conclusions on the relative importance of species in food webs.

Most of the world’s ecosystems suffer from stress caused by human activities such as habitat destruction, fragmentation, overexploitation of species and climate change. These factors affect the reproduction and/or survival of individual species as well as interactions between species in ecological communities. Forthcoming effects of this are altered abundances, direct species loss, and indirect cascading extinctions, with yet largely unknown consequences on community structure and functioning. Today, biodiversity loss is of global concern since human society and welfare depend upon resources and services provided by ecosystems. The importance of considering entire ecological communities as a target for conservation and management has been increasingly recognized due to the interdependencie  of species. Our ability to make predictions of the response of ecological communities to stress and biodiversity loss is in need of a deeper understanding of how structure and dynamical processes contributes to the functioning and stability of a community. In this thesis I use mathematical theory and dynamical models to study the response of community structure and resilience to a variety of disturbances affecting species and species interactions, ranging from small perturbations (Papers I-II) to large perturbations (species extinctions, Papers IIIIV).

In Paper I we develop Community Sensitivity Analysis (CSA) as an analytical tool to study how a small permanent perturbation to the intrinsic growth rate, or mortality rate, of species is expected to affect i) the resilience (return rate) and ii) the structure (distribution of species equilibrium abundances) of an ecological community. Species interactions are described using Lotka-Volterra predator-prey dynamics. We apply CSA on the pelagic food webs of Lake Vättern and the Baltic Sea, respectively, and find that a change in the mortality rate of large-bodied species has a higher impact on community resilience and structure, compared to a perturbation to small-bodied species. However, analyzing the effect of a proportional change to the growth or mortality rate of species (elasticity analysis) shows that smallbodied species have proportionally larger effects on species equilibrium abundances, but not on resilience. CSA can also be used to study the effect of permanent (absolute or proportional) changes to inter- and intraspecific interaction strengths. For the two pelagic systems used in this study, CSA reveal that changes in the effect of a prey on its consumer tend to affect community structure and resilience significantly more than changes in the effect of a predator on its prey.

In Paper II we assess the importance of rare species for the structure and resilience of ecological communities. First we show analytically, for a two species predator-prey system, that a change in the intrinsic growth rate of the rare species affect resilience more than a change in the growth rate of the common species. To test the generality of these results we next apply CSA on complex model food webs. In the analysis we distinguish between four trophic groups, each including only species with a similar trophic position, to separate the effect of abundance from the trophic position of species. Using mixed effect models we find support for our analytical predictions. More precisely, we find a strong negative relationship between the importance (sensitivity) of a species and its equilibrium abundance within all consumer groups and a weaker, but significant, relationship for producer species. The results from this study suggest that rare species can act as keystones through their effect on both community resilience and community structure, regardless of its trophic position.

In Paper III we evaluate the risk of food web collapse caused by different trait-based extinction scenarios. In previous studies, groups of species, e.g. rare species, large-bodied species and top predators, have been identified to be relatively more prone to extinctions and other studies have found that extinctions of such species have comparably small effects on the remaining community. Using mathematical models of species dynamics we study the response of ecological communities to species removal (i.e. the proportion of species needed to be primarily removed to cause a 50% reduction in species richness, R⁵⁰) when species are sequentially removed from the food web based on eight different traits. We show, contrary to some previous studies of sequential extinction simulations, that communities can be very vulnerable to realistic species loss. We furthermore find that the response of communities seems to depend on whether the extinction sequence follows a bottom-up or top-down direction, making it difficult to identify one particular extinction sequence as the most important/severe sequence.

Finally, in Paper IV we aim to identify traits of species that can be used to identify keystone species, in terms of causing the highest proportion of secondary extinctions following their loss, in food webs with different degree of disassembly. Moreover, we analyze if the loss of a species that triggers a cascade of many secondary extinctions are the same species being identified as a keystones using Community Sensitivity Analysis. To answer these questions we randomly remove species from a set of 100 model communities. We analyze the relationship between the number of secondary extinctions following the randomly removed species and a range of species traits in communities where i) 75-100% of the initial number of species remain, ii) 50-75% of all species remain, iii) 25-50% of all species remain and iv) only 0-25% of all species remain. We find that the variation in secondary extinctions explained using species traits increases when the degree of food web disassembly and food web connectance are taken into account. The most important trait varies for different degrees of food web disassembly and also depends on whether basal species can go primarily extinct or not. However, due to correlation between most important traits, we conclude that the key status of different traits is rather robust against structural changes in the model food webs. Interestingly, food webs seem to be most sensitive to a random species loss after the loss of more than 25% of all initial species, suggesting that there is a threshold from which secondary extinctions increases. We also conclude that species being identified as keystones, based on the effect of their loss, are to some extent the same species being identified as having the largest effect on community structure and resilience, respectively, following a small perturbation.

Global warming leads to increased intensity and frequency of weather extremes. Such increased environmental variability might in turn result in increased variation in the demographic rates of interacting species with potentially important consequences for the dynamics of food-webs. Using a theoretical approach we here explore the response of food-webs to a highly variable environment. We investigate how species richness and correlation in the responses of species to environmental fluctuations affect the risk of extinction cascades. We find that the risk of extinction cascades increases with increasing species richness, especially when correlation among species is low. Initial extinctions of primary producer species unleash bottom-up extinction cascades, especially in webs with specialist consumers. In this sense, species-rich ecosystems are less robust to increasing levels of environmental variability than species-poor ones. Our study thus suggests that highly species-rich ecosystems like coral reefs and tropical rainforests might be particularly vulnerable to increased climate variability.

Human-induced alterations in the birth and mortality rates of species and in the strength of interactions within and between species can lead to changes in the structure and resilience of ecological communities. Recent research points to the importance of considering the distribution of body sizes of species when exploring the response of communities to such perturbations. Here, we present a new size-based approach for assessing the sensitivity and elasticity of community structure (species equilibrium abundances) and resilience (rate of return to equilibrium) to changes in the intrinsic growth rate of species and in the strengths of species interactions. We apply this approach on two natural systems, the pelagic communities of the Baltic Sea and Lake Vättern, to illustrate how it can be used to identify potential keystone species and keystone links. We find that the keystone status of a species is closely linked to its body size. The analysis also suggests that communities are structurally and dynamically more sensitive to changes in the effects of prey on their consumers than in the effects of consumers on their prey. Moreover, we discuss how community sensitivity analysis can be used to study and compare the fragility of communities with different body size distributions by measuring the mean sensitivity or elasticity over all species or all interaction links in a community. We believe that the community sensitivity analysis developed here holds some promise for identifying species and links that are critical for the structural and dynamic robustness of ecological communities.

Loss of species will directly change the structure of ecological communities, which in turn may cause additional species loss (secondary extinctions) due to indirect effects (e.g. loss of resources or altered population dynamics). The vulnerability of food webs to repeated species loss is expected to be affected by food web topology, species interactions and the order in which species go extinct. Species traits such as body size, abundance and connectivity probably determine the vulnerability to extinction of species and, thus, the order in which species go primarily extinct. However, how different sequences of primary extinctions affect the vulnerability of food webs to secondary extinctions, when species abundances are allowed to respond dynamically, is not well understood. So far, only one study has incorporated species dynamics when assessing the effect of different extinction sequences on community structure, and only a limited number of extinction sequences have been evaluated. Here, using complex model food webs and including population dynamics, we analyze the effect of 33 extinction sequences on community structure using R50 (the proportion of primarily removed species needed to cause a 50% reduction in species richness) as a measure of community robustness to secondary extinctions. As expected, we find community structure to be highly vulnerable to removal of primary producers. More surprisingly, removing species based on traits that are strongly linked to the trophic position of species (such as large-bodied species, rare species, species with a high net effect, species with a high trophic position) are found to be as destructive as removing only primary producers. Such top-down oriented removal of species are often considered to correspond to realistic primary extinctions of species, but earlier studies, based on topological approaches, have not found such realistic extinction sequences to have any drastic effect on the remaining community. Thus, our result suggests that ecological communities could be more vulnerable to realistic extinction sequences than previously believed.

The majority of species in the ecosystems of the world are rare. Because the contributions to community biomass and productivity of many of these species are small it has been suggested that loss of rare species should have relatively small ecological consequences. However, the extent to which rare species affect the structure and stability of ecosystems is largely unknown. Using a theoretical approach, based on analytical methods, we here   investigate how perturbations to rare as well as common species affect the structure (distribution of equilibrium abundances of species) and resilience (recovery rate) of complex ecological communities. We show that, contrary to expectation, resilience and structure of ecological communities are generally more sensitive to perturbations to rare than to common species. We find the explanation for this to lie in the cause of rarity: rare species tend to interact strongly, on a per capita basis, with other species. Our results suggest that many rare species are likely to fill important ecological roles in ecosystems.

Global change keeps pushing species towards extinction which results in altered structures of ecological communities. Consequently, the loss of certain species can trigger a cascade of secondary extinctions resulting in further degradation of the system. The importance of species for upholding the structure of communities may be linked to the traits of species. However, due to the altered structure of communities following species loss, the importance of species (and species traits) may change as the structure of the food web change. Using a dynamical approach and simulating species loss in complex model communities we analyze the potential importance of 11 species traits. We find that the most important trait varies for different degree of food web collapse and food web connectance. Though, as the most important traits of species usually are correlated we conclude that the importance of species traits is rather robust against structural changes in the communities (especially when only consumer species are targets of primarily extinctions). Interestingly, food webs display a collapse threshold (after the initial loss of approximately 25% of all species) from which secondary extinctions increases. Finally, consider only the loss of consumer species, the effect (number of secondary extinctions) on community structure caused by a large perturbation (species loss) is positively correlated to the response of food webs resulting from a small perturbation to the same species.