水生食物網網絡中的寄生關係

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(1)國立臺灣師範大學生命科學系博士論文. 水生食物網網絡中的寄生關係 Parasitism in the Network of Aquatic Food Web. 研究生：陳宣汶 Hsuan-Wien Chen. 指導教授：邵廣昭博士 Dr. Kwang-Tsao Shao 指導教授：李壽先博士 Dr. Shou-Hsien Li 中華民國九十九年十月.

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(3) ACKNOWLEDGEMENTS. First, I like to thank two of my co-advisors who offered me the second change to fulfil the dream. Dr. Kwang-Tsao Shao opens a door for me to explore the marvellous world of ocean. I like to thank you for all the opportunities you have been giving to me. The doors you opened is not just one but rather a variety of paths to be a professional. Your generosity to junior scientists and enormous endeavours to the general public are both qualities that I will always strive for.. Dr. Li is another academia role model of mine. I like to thank you for admitting me into the program and allowing me to share my out-of-tone ideas in the meeting. Your devotion to science and productivity on IF will set a high standard for me to pursue in the future.. I also like to thanks my long time collaborator and a great friend, Dr. Wei-Chung Liu. I thank you for bring me into the world of networks when I was ready to give up science. You magic ability to turn the complexity into simple phrase has saved me many sleepless nights. Without your helps, my time with my dissertation would definitely go doubled or trebled. Thanks also go to my co-authors and extended collaborators all over the world. They are Andrew Davis, Ferenc Jordán, Robert Poulin, Ross Thompson, Kevin Lafferty, Armand Kuris, Alex Hernandez, Mark Huxham and Per-Arne Amundsen.. I.

(4) My committee, Drs. Hsing-Juh Lin, Mau-Hsiang Shih and Yuying Hsu, has been provided valuable assistance throughout my graduate studies. I am grateful for all you did for me. Members in Shao lab and Li lab have supported me in various ways. While it is impractical to spell out all your English names herein, you know I am thanking you. Thanks to those who attend the lunch meeting in B311 and the dinner meeting in Z640. Thanks to those who were onboard with me in ORV-3 and 4. Without your smiles and laughs, I won‟t be able to reach the finish line in this graduation marathon.. Finally, I have to thank my family for their endless love and encourages. Thanks to my mom because she never asks why her son spends twice as much time to get one degree while others can get two (or three). Thanks to my wife since she never asks for diamonds or roses even it is the ten year anniversary. Thanks to my kids because their ages consistently remind me how long I have been the graduate program. And, my biggest thanks to my dad because I believe if he knows my graduation he will be smiling at me in heaven.. II.

(5) ABSTRACT. Parasites are ubiquitous in ecological communities but they haven‟t been routinely included in food web studies until very recent. Using recently published data and the tool of network analysis, I elucidated features associated with the pattern of parasitism in food web networks. First, I showed that parasites are not only occurring in non-random fashion in food webs but also positively associated with the prominent network positions occupied by their hosts. Meanwhile, a host species with high parasite diversity tends to have a wide diet range, occupy a network position close to many prey species, or occupy a network position that can better accumulate resources from species at lower trophic levels, whereas a host species with higher vulnerability to predators, being at a network position close to many predatory species, or being involved in many different food chains, tends to serve as a good intermediate host in parasite transmission. Second, by conducting simulation experiments with different food web models and extinction scenarios, I demonstrated that the reduction in food web robustness after considering parasites is mainly contributed by the life cycle constrain of parasites. The finding further demonstrates that parasites are prone to secondary extinctions and their extinctions occur earlier than those involving non-parasite species. The evident vulnerability nature of parasite to species loss designates parasite a proper leading indicators of food web integrity. Lastly, with the extension of a previously developed methodology, a new approach is presented and used to quantify the interaction structure of a food web and III.

(6) consequently the topological importance of species when the food web is viewed as a signed digraph. This method is also capable to quantify the strength of inter-specific interaction as well as in what way species interact with each other after counting both direct and indirect cascades in both top-down and bottom-up directions. As it has the potential to quantify a wide range of ecological interactions, its further application on revealing the interaction structures between parasites and other functional groups in food web with parasites is evidently achievable.. Keyword: parasitism, food web, ecological network, trophic cascade, robustness, topological index, signed graph. IV.

(7) 摘要寄生蟲是生態群聚中重要的一部分；但是直到最近，寄生蟲才較常被納入食物網的研究中。利用最近發表的文獻資料與相關的網絡分析工具，我的研究嘗試釐清寄生蟲在水生生態系的食物網網路中所扮演的角色。首先，本研究闡明寄生蟲在食物網中並非隨機分布的，而是與其宿主在食物網的位置有關。宿主在食物網的位置如果擁有較多的獵物種類、較靠近所有的獵物、或是能從食物網的底層往上累積較多的資源，其寄生蟲之種類多樣性便較高。相對的，若是宿主在食物網的位置有較多的掠食者、較靠近所有的掠食者、或是位在許多食物鏈路徑的必經之處，則此宿主的寄生蟲往上傳遞的比例越高。再者，本研究利用生態模式模擬食物網加入寄生蟲後，其網絡強固性之變化。首次將寄生蟲所造成之網絡強固性減少，分成網路的結構複雜性改變與寄生蟲特性兩個成因來探討；研究結果顯示造成食物網強固性減少的主因在於寄生蟲對宿主資源利用的可替代性較低。本研究建議利用寄生蟲對次級滅絕特別敏感的特性，可將寄生蟲當成食物網功能是否完整之領先指標。最後，本研究以過去食物網中物種的拓樸重要性指標為基礎，延伸加入食性營養關係中能量流動方向性的正負符號概念，發展出一套新的具正負符號的拓樸重要性指標。此一指標涵括食物網中的上行與下行效應、直接與間接作用，可用來定量物種間彼此的交 V.

(8) 互作用。應用此一新指標在包含寄生蟲的食物網資料上，可幫助我們進一步釐清寄生蟲在食物網中的角色與和其他功能群間的交互關係。. 關鍵字: 寄生關係、食物網、生態網絡、營養遞延、強固性、拓樸指標、符號圖形. VI.

(9) TABLE OF CONTENTS. ACKNOWLEDGEMENTS ..................................................................... I ABSTRACT ............................................................................................ III TABLE OF CONTENTS ......................................................................VII LIST OF FIGURES ............................................................................... IX LIST OF TABLES.................................................................................... X CHAPTER 1: AN OVERVIEW ..............................................................1 CHAPTER 2: NETWORK POSITION OF HOSTS IN FOOD WEBS AND THEIR PARASITE DIVERSITY..................................................4 INTRODUCTION .................................................................................4 MATERIAL AND METHODS.............................................................8 RESULTS .............................................................................................16 DISCUSSION.......................................................................................20 CHAPTER 3: THE REDUCTION OF FOOD WEB ROBUSTNESS BY PARASITISM ...................................................................................29 INTRODUCTION ...............................................................................29 MATERIAL AND METHODS...........................................................33 RESULTS .............................................................................................38 DISCUSSION.......................................................................................41 CHAPTER 4: QUANTIFYING THE INTERACTION STRUCTURE AND THE TOPOLOGICAL IMPORTANCE OF SPECIES IN FOOD WEBS: A SIGNED DIGRAPH APPROACH ..........................55 VII.

(10) INTRODUCTION ...............................................................................55 MATERIAL AND METHODS...........................................................58 RESULTS .............................................................................................63 DISCUSSION AND CONCLUSION .................................................69 CHAPTER 5: CONCLUSION REMARKS AND PERSPECTIVES 84 REFERENCES........................................................................................89 APPENDIX 1: QUANTIFYING INTERACTION STRUCTURE AMONG FUNCTIONAL GROUPS OF FOOD WEB WITH PARASITES ..........................................................................................105 APPENDIX 2: REPRINT OF PUBLISHED CHAPTERS ............... 111. VIII.

(11) LIST OF FIGURES. FIG. 2-1 .....................................................................................................27 FIG. 2-2. ....................................................................................................28 FIG. 3-1. ....................................................................................................51 FIG. 3-2. ....................................................................................................52 FIG. 3-3. ....................................................................................................53 FIG. 3-4 .....................................................................................................54 FIG. 4-1 .....................................................................................................74 FIG. 4-2. ....................................................................................................75 FIG. 4-4. ....................................................................................................77 FIG. 4-5. ....................................................................................................78 FIG. 4-6. ....................................................................................................79 FIG. 4-8 .....................................................................................................81 FIG. 4-9. ....................................................................................................82. IX.

(12) LIST OF TABLES. TABLE 2-1..................................................................................................25 TABLE 2-2..................................................................................................26 TABLE 3-1..................................................................................................48 TABLE 3-2..................................................................................................49 TABLE 4-1..................................................................................................73. X.

(13) CHAPTER 1: AN OVERVIEW. Parasitism is a widespread life-history strategy practiced by parasites (Price 1980). More than half of the world‟s species behave as a parasite at some point of their life cycle and most organisms are parasitized (Poulin and Morand 2000, Dobson et al. 2008). Parasites present not only a substantial portion of the species diversity (Poulin and Morand 2000) and biomass (Kuris et al. 2008), but also the functional importance in shaping natural communities (Poulin 1999, 2007). Past studies on ecological significances of parasites have emphasised the interplays among different parasite species (Pedersen and Fenton 2007) and their strong effects on their host community (Mouritsen and Poulin 2010). Current endeavours to elucidate the functional roles that parasites played in the complex food webs has posed a great challenge in both ecology and parasitology (Lafferty et al. 2008, Beckerman and Petchey 2009, Byers 2009, Poulin 2010). Although recent advances in network analysis have proven invaluable in entangling the complexity of biological networks, the majority of their ecological applications have focused on predator-prey, plant-herbivore and plant-pollinator interactions (Bascompte 2007, Bascompte 2009, Bascompte and Stouffer 2009). Food webs with parasites are clearly missing and neglected in both main-stream ecology and parasitology. Recent increasing, but still limited, numbers of food webs with parasites (Huxham and Raffaelli 1995, Thompson et al. 2005, Lafferty et al. 2006, Hernandez and Sukhdeo 2008, Amundsen et al. 2009) 1.

(14) has been making great inroads in gaining feedbacks from fellow scientists (Lafferty et al. 2008, Beckerman and Petchey 2009, Byers 2009, Ings et al. 2009, Poulin 2010). While more food web datasets from variety of ecosystems are clearly needed, new emerging patterns and analytical tools are equally desired for clutching the new complexity introduced by parasites.. The main goal of this dissertation is to reveal new insights of parasitism in food web using network analysis. To fulfil such purposes, I began with describing the aggregation pattern of parasites in several food webs collected in Chapter 2. Furthermore, I intend to explain such variations on parasite diversity with a number of indices programmed to quantify the topological importance of network positions where hosts occupied in the real food webs.. Following the long standing debate on interplays between complexity and stability in ecosystem (McCann 2000, Montoya et al. 2006, Uchida and Drossel 2007), I hence investigate whether the inclusions of parasites in food webs alter the network robustness. By extending a recent work published by Lafferty and Kuris (Lafferty and Kuris 2009), I propose a series of food web models, each focus on an individual factor that may cause changes on network complexity (i.e. size, connectance, preferential attachment and life stage constrains). The endeavours are meant to elucidate the alternation of network robustness is due to the change of food web complexity or unique attributes of 2.

(15) parasitism.. During the robustness modelling, I become aware the imperfection of commonly employed robustness analysis (Dunne et al. 2002b, 2004, Dunne and Williams 2009) which counts only cascading effect from resource supplying end. Considering parasites often insert strong impacts from top-down (Hatcher et al. 2006), a new method is urgently needed to overcome the existing shortage. The signed digraph approach presented in Chapter 4 is intended to count for the effects of species loss from both bottom-up and top-down directions over the entire food web. The methodology developed in Chapter 4 is akin to the methodology of Jordán et al. (2003), but viewing the food web as a signed digraph.. Following the three main chapters, major conclusions and future directions of study will be outlined in the last chapter. In particular, investigating the interaction patterns between parasites and other functional groups in food web with the newly developed methods (see Appendix 1) suggests another potential rewarding topic which one must go further in due course.. 3.

(16) CHAPTER 2: NETWORK POSITION OF HOSTS IN FOOD WEBS AND THEIR PARASITE DIVERSITY1. INTRODUCTION Parasites are organisms that live in other organisms, hosts, from which they obtain nutrients (Poulin and Morand 2000, Bush et al. 2001). More than half of the world‟s species behave as a parasite at some point of their life cycle and most organisms are parasitized(Poulin and Morand 2000, Dobson et al. 2008). Parasites constitute a substantial proportion of the entire biomass of an ecosystem (Kuris et al. 2008) and have very strong community effects (Poulin 1999, Mouritsen and Poulin 2002, Torchin et al. 2002, Pedersen and Fenton 2007). However, despite their importance, the relationships of parasites to food webs have been neglected due, in part, to practical problems.. The small size of parasites compared to their hosts (Lafferty and Kuris 2002) has traditionally led to several practical and theoretical problems in ecology (Warren et al. 2010). The small size makes them difficult to detect and invasive techniques are often required to study parasites inside their hosts. Small parasites consuming their much larger hosts (Leaper and Huxham 2002) is also distinct from the majority of trophic interactions where species at high trophic levels are on average 1. This chapter has published and cited as Chen, H. W., W. C. Liu, A. J. Davis, F. Jordan, M. J. Hwang, and K. T. Shao. 2008. Network position of hosts in food webs and their parasite diversity. Oikos 117:1847-1855 (see Appendix 2). Author‟ contributions: HWC proposed the study, WCL, FJ, MJH performed simulations, HWC, AJD, KTS analyzed data and HWC, WCL wrote the paper in principle with contributions from AJD and FJ. 4.

(17) larger (predator-prey) or similar (parasitoid-host) in size to those at lower trophic levels (Cohen et al. 2003, Woodward et al. 2005). This difference also makes problematic the use of body size as one of the criteria to establish trophic hierarchies (although body size is not the only criteria used) in food web models such as the cascade model (Cohen and Newman 1985, Cohen et al. 1993), the niche model (Williams and Martinez 2000) and the nested hierarchy model (Cattin et al. 2004). Moreover, many parasites possess several distinct life stages and each stage may occur in different hosts or environments making it difficult to compile a comprehensive host list for the parasite life cycle (Parker et al. 2003). Different stages may thus also have different trophic positions in the food web raising the question of whether a parasite species is a single trophic component or several tropho-species in a food web (Huxham and Raffaelli 1995, Huxham et al. 1996).. Given these difficulties, it is not surprising that many ecological studies have practically ignored parasites (Marcogliese and Cone 1997), and new general models are needed to explain the observed patterns of parasitism in food webs (Lafferty et al. 2006, Lafferty et al. 2008, Byers 2009). Recent field studies have, however, provided an increasing amount of food web data involving parasites (Huxham and Raffaelli 1995, Thompson et al. 2005, Arias-Gonzalez and Morand 2006, Lafferty et al. 2006, Hernandez and Sukhdeo 2008, Amundsen et al. 2009). In addition, the neglect of parasites in traditional food web studies is being remedied by studies of what happens when parasites are included in food webs to 5.

(18) fundamental web properties (Huxham et al. 1996, Thompson et al. 2005, Hernandez and Sukhdeo 2008, Lafferty et al. 2008, Byers 2009, Lafferty and Kuris 2009).. A food web is essentially a network of nodes; in this paper, rather than treating parasite species as individual nodes in food webs, we simply regard parasite diversity as a nodal attribute of a host species. We address a simple question of what determines the parasite diversity of host species in food webs. Our investigation of food webs goes a step further than the observation that parasitism tends to be concentrated at higher trophic levels (Lafferty et al. 2006). We first investigate whether parasitism is randomly distributed across all non-parasite species in a food web and second, use the tool of network analysis to investigate the issue of parasite diversity in food webs.. As networks, food webs can be analysed using network analysis, tools that have proven invaluable in several different fields of biological research from ecology to molecular biology (Newman 2003, Barabasi 2009). Each node occupies a position in a network, and one particular aspect of network analysis is how to characterise a network position. There exist different network indices that can characterise a network position from different perspectives (Jordan et al. 2006). By considering species as nodes, the importance of a species is its ability to affect others in the web by virtue of its network position; therefore, different network indices reflect different aspects of its importance in the web. For instance, 6.

(19) a species with many direct interactors is important as it can affect many different species; and a species might be important if it is at a network position that serves as a bridge linking species at lower trophic levels to those at higher ones (e.g. a wasp-waist species in marine ecosystems)(Jordan et al. 2005). Network position can be expected to influence the number of parasite species a host species harbours because a host species can acquire parasites via predator-prey interactions and parasites seem to increase trophic transmission (Lafferty 1999, Choisy et al. 2003, Mouritsen and Poulin 2003). Furthermore, many parasite species have complex life cycles where different developmental stages require different host species. A host species in a parasite‟s life cycle in which the parasite species reaches sexual maturity is called a definitive host whereas those involved in earlier stages are called intermediate hosts (Chubb et al. 2010). We therefore also investigate whether there are differences in network positions between definitive and intermediate hosts.. The paper is organised as follows. We first describe the data used in our study. This is followed by a description of methods, including (1) randomisation tests; (2) network indices quantifying different aspects of importance of a network position; and (3) quantifying the propensity of being an intermediate host. We then present the results and discuss their implication in terms of the mechanism that might lead to the observed patterns of parasitism.. 7.

(20) MATERIAL AND METHODS Data We used three datasets: “Car”, the Carpinteria salt marsh community near Santa Barbara, USA (Lafferty et al. 2006); “COM”, the intertidal mudflat community of Company Bay in Otago Harbour, New Zealand (Thompson et al. 2005); and “YTH”, the Ythan Estuary in Scotland, United Kingdom (Huxham and Raffaelli 1995). Since we are only interested in parasite diversity of non-parasite species and their network positions in food webs, we only considered predator-prey links (i.e. the conventional food webs) and numbers of parasite species per host species (i.e. parasitism) for all three datasets. Included in the Car dataset but not in the other two are micropredators (leech and two mosquitoes) and microparasites (virus and malaria); we therefore initially omitted them from the analysis but subsequently analysed how retaining them (Car+) might affect the results. Bacteria can function both as food sources and decomposers, and we treated them as food sources in our analysis here. The COM and YTH food web data include a small number of loops (i.e. species A consumes species B, and species B consumes species A). Two of the network indices used rely on the partitioning of species into distinct trophic levels and this is impossible if there are loops. When we calculated these two network indices we therefore removed predator-prey links that create loops but used all the data otherwise. Details of the three food webs can be found in the original sources (Huxham and Raffaelli 1995, Thompson et al. 2005, Lafferty et al. 2006).. 8.

(21) The Car and COM datasets give clear definitions of intermediate and definitive hosts (Thompson et al. 2005, Lafferty et al. 2006), but the original YTH data does not. We therefore derived this information from Yamaguti (1975) and labelled all host species as either intermediate or definitive hosts for the YTH dataset. However, the YTH data is missing, in a few cases, the hosts required for a particular parasite to complete its life cycle. Thus, some host species occupy the final position in all identifiable transmission pathways but do not harbour sexually mature parasites. We refer to these hosts as „final hosts‟ and reserve „definitive host‟ for species containing the sexually mature stage of the parasite species.. Descriptive statistics For each web, we determined the number of non-parasite species (Hos), the number of parasite species (Par), the number of predator-prey links (LT) and the number of parasite-host interactions (LP). For each non-parasite species (i), we determined the number of parasite species it harbours (i.e. parasite diversity, Pi) and for each parasite species (i), the number of different host species it uses (i.e. host specificity, Hi).. Randomisation of parasitism For each original web, we generated 10,000 simulations. In each simulation only parasitism were randomised but the predator-prey links remained intact. For a parasite species i, this was achieved by randomly choosing Hi different host species from the total Hos non-parasite species 9.

(22) in the web. The process was repeated for all the web‟s parasite species. An expected distribution of Pi was then obtained from those simulations and we used a modified chi-square test (to avoid low expected values and for continuity) to compare the observed and expected distributions of Pi.. For each web, we also determined the trophic position (Levine 1980) of each non-parasite species. We then determined for each web the mean trophic position of host species with parasites. Using the same procedure as before we again generated 10,000 simulations for each of which we then calculated the mean trophic position of hosts. The data mean should be well within the 95% confidence intervals of the model mean distribution if parasitism is indeed random.. Network indices for measuring the importance of a network position We selected and used twelve network indices that, together, cover different aspects of importance of a network position (Jordan et al. 1999, Jordan et al. 2006). Broadly speaking, these indices fall into two groups: centrality measures (Wasserman and Faust 1994) and keystone measures (Jordan et al. 2006, Jordan et al. 2007).. Centrality measures Degree (Di) is the number of nodes directly linked to a given node i. For a non-parasite species it is simply the number of its prey and predator 10.

(23) species. The degree of a non-parasite species i can be decomposed into in-degree (Din,i) and out-degree (Dout,i) to account for the direction of the links. In-degree is the number of species preyed upon and out degree is the number of predator species a species has. A species with high degree, in-degree or out-degree centralities is important because it directly interacts with many others.. Closeness centrality (Ci) measures how close node i is to all others in the network: Ci . N. d. j 1, i  j. ij. ,. (1). where dij is the length of the shortest path (distance) between nodes i and j, and N is the number of nodes in the network (i.e. N=Hos). Closeness centrality is small if a node is very close to other nodes in the same network. Thus, the importance of such a node is that it can rapidly affect others and be affected quickly by others. Including the direction of links allows quantification of in-closeness (Cin,i) and out-closeness (Cout,i) for a given node i. These are different because, when links have direction, a pair of nodes may be linked in one direction but not in the other. In-closeness is calculated using equation (1) but replacing dij by di→j which is the length of the shortest path from node i to node j. Out-closeness is calculated similarly but dij is replaced by dj→i, the length of the shortest path from node j to node i. The quantities di→j and dj→i are always greater than or equal to dij, and not necessarily equal to each other. In-closeness centrality measures how quickly food and energy can reach 11.

(24) node i through predator-prey interactions. Similarly, out-closeness centrality measures how fast such resources from node i can reach all other nodes.. Betweenness centrality (Bi) measures how frequently node i lies on all shortest paths between all other pairs of nodes in the network: Bi   g jk i  g ik j k. ,. (2). where i≠j and k; gjk is the number of equally shortest paths between nodes j and k, and gjk(i) is the number of these shortest paths that include node i. A node with high betweenness centrality is important in that it mediates many indirect interactions between pairs of nodes. To include the direction of interaction, directed betweenness centrality (Bdir,i) is calculated using equation (2) but replacing gjk by gj→k and gjk(i) by gj→k(i). The quantity gj→k is the number of directed equally shortest paths from node j to k, and gj→k(i) is the number of these shortest directed paths that include node i. Thus the importance of a node with high directed betweenness centrality is that it mediates many of the shortest food chains. All these centrality based-indices were calculated using UCINET (Borgatti et al. 2002).. Keystone measures The second type of network indices includes the keystone indices that quantify the bottom-up and top-down effects within a food web (Jordan et al. 1999). Defining these two network indices require non-parasite species to be partitioned into clear trophic levels without 12.

(25) loops.. From the bottom-up direction, the keystone index of a species i (Kbu,i) is defined as: n. 1 1  K bc  c 1 d c ,. K bu,i  . (3). where n is the number of predatory species eating species i (i.e. n=Dout,i), dc is the number of prey species of its cth predator and Kbc is the bottom-up keystone index of the cth predator. The bottom-up keystone index of a given species measures its importance in terms of the diet range of its predators and of other species at higher trophic levels. It measures how well the efforts of predatory species are focused on a particular prey species. Symmetrically, from the top-down direction, the keystone index of a species i (Ktd,i) is defined as: m. 1 (1  K te ) e 1 f e ,. K td,i  . (4). where m is the number of prey eaten by species i (i.e. m=Din,i), fe is the number of predators of its eth prey and Kte is the top-down keystone index of the eth prey. The top-down keystone index measures the importance of a given species by taking into account its diet range, that of its prey, and those of species at lower trophic levels. It thus measures how well resources are channelled into the focal species.. Measure of trophic position We also quantified the trophic position of every non-parasite species 13.

(26) in each of the three webs. Trophic position is defined as the averaged path length over which a species obtains energy from basal species (Levine 1980). This energy budget-based measure differs from the conventional trophic level in allowing loops in food webs. It measures the trophic function of a focal species by considering all paths leading to this species.. We determined trophic position by first creating a square matrix R for each web where the i,jth element represents the fraction of energy of species i that is from species j. We then rearranged R to create a new matrix, S, in which all species to be considered basal come first. Basal species have a trophic position of zero by definition. Embedded in S is a sub-matrix W, which describes the energy flow between non-basal species. From W we then calculated the trophic position of non-basal species as: y  (I - W) -1 ,. (5). where I is the identity matrix and y is a vector containing the trophic position of non-basal species. We determined the trophic position of non-parasite species for all three webs from the bottom-up (Tbu,i) and top-down (Ttd,i) directions.. The propensity of being an intermediate host Parasites often have a definitive host in which they reproduce sexually and intermediate hosts in which they grow or reproduce asexually. A non-parasite species may thus be a definitive host for one 14.

(27) parasite species and an intermediate host for another. We quantified the propensity of being an intermediate host (Qi) for a non-parasite species i as: Qi . hi Hi. ,. (6). where Hi is the number of parasite species in host species i while hi is the number of parasite species passed onto at least one predator of the focal species i via predator-prey interaction. Some parasites are not transmitted by trophic interactions but, like the free living cercariae of some trematodes, use non-predator-prey interactions (Yamaguti 1975). We therefore identified and excluded such parasites when determining hi. If a non-parasite species is the intermediate host for all of its parasite species, Qi=1. If it is the final host for all of its parasite species, then Qi=0. The index is undefined for non-parasite species in the web that are not a host for at least one parasite species.. Statistical tests We tested the correlation between parasite diversity (P) and each network index calculated for the non-parasite species (D, Din, Dout, C, Cin, Cout, B, Bdir, Kbu, Ktd, Tbu and Ttd). We used the Spearman rank correlation coefficient because the distributions of these indices are not suitable for the Pearson correlation tests. We also determined the Spearman rank correlation coefficient between the propensity of being an intermediate host (Q) and each of those twelve network indices. To avoid the family-wise error rate during the multiple pairwise comparisons, we apply Bonferroni corrections to adjust the p values at different levels of 15.

(28) significance. The adjusted p value equals the original p value multiplied by twelve since there are twelve network indices.. RESULTS In the CAR web there are 83 non-parasite and 40 parasite species, with 496 predator-prey links and 515 parasite-host interactions. In COM, there are 67 non-parasite and 9 parasite species, with 428 predator-prey links and 71 parasite-host interactions. In YTH, there are 92 non-parasite and 42 parasite species, with 417 predator-prey links and 177 parasite-host interactions. Among the parasite-host interactions realised, 82% of them in CAR transfer parasites to their definitive hosts while only 56% do so in COM and 55% in YTH.. Parasitism is not a random process The random model of the number of non-parasite species having a given number of parasite species produces Poisson–like expected frequency distributions, whereas the observed frequency distributions are overly dispersed (Fig. 2-1). There are significant differences between the expected and observed frequency distributions for all three webs (CAR: X2=204.59, df=7, χ2α=0.001=24.32, p<<<0.001; COM: X2=47.96, df=3, χ2α=0.001=16.27, p<<<0.001; YTH: X2=132.81, df=5, χ2α=0.001=20.52, p<<<0.001). Thus, in the three webs, the pattern of parasite-host interactions is not consistent with their being formed at random.. For the CAR web, the average bottom-up trophic position of host 16.

(29) species participating in parasite-host interactions is 2.10, for COM it is 2.47 and for YTH 1.98. The mean for the random CAR web is 1.61 (95% confidence intervals=1.55-1.67), for COM 1.60 (1.43-1.77) and for YTH 1.68 (1.57-1.80). Thus species that are hosts to parasites tend to be in higher trophic positions than expected in the random model. From the top-down direction, the average trophic position is 0.43 for the CAR web, 0.77 for COM and 0.87 for YTH. The expected values derived from the random model are CAR 0.91 (0.85-0.97), COM 1.54 (1.35-1.73) and YTH 1.28 (1.13-1.43). This suggests that there are more parasite species on hosts near the end of food chains than would be expected by chance. Parasitism is thus evidently not random and there is great heterogeneity in the number of parasite species a host species harbours.. Network indices and parasite diversity Of the twelve network indices calculated, five are significantly correlated with parasite diversity (P) for all three webs (Table 1-1). These five indices are in-degree centrality (Din), in-closeness centrality (Cin), top-down keystone index (Ktd), bottom-up trophic position (Tbu), and top-down trophic position (Ttd). Degree centrality (D) and betweenness centrality (B) show significant correlation with parasite diversity for COM and YTH webs. Out-degree centrality (Dout), out-closeness centrality (Cout) and bottom-up keystone index (Kbu) only significantly correlate with parasite diversity for the CAR web. Closeness centrality (C) only shows significant correlation with parasite diversity for the COM web. Directed betweenness centrality (Bdir) is the only centrality measure 17.

(30) that is not significantly correlated with parasite diversity for any of the three webs. Across all three webs, Din, Cin and Ktd show strong correlation with parasite diversity. Thus parasite diversity is associated with having a wide diet range (Din), being at a network position close to many prey species (Cin), or occupying a network position that can accumulate resources from species at lower trophic levels (Ktd).. Some network indices show similar correlations with parasite diversity (Table 2-1). This might be the result of some indices being intrinsically related as they quantify similar characteristics of a network position. PCA (principal component analysis) was then performed on those indices in order to determine their interrelationships. In the PCA (Fig. 2-2), the first and the second principal axes together explain 77.89% of the variance in the CAR data, 76.32% of that for COM and 75.66% for YTH. The centrality measures D, B and Bdir form a small cluster for all three webs (Fig. 2-2) indicating they measure similar characteristics of a network position. Other indices seem to be relatively far from this cluster but there are two loose clusters. One of these is Din, Ktd, Tbu and Cout and the other is Dout, Kbu, Ttd and Cin, with C as an outlier. The three clusters and C represent four moderately different qualities of a network position.. Network indices and the propensity of being an intermediate host In all three webs, six of the twelve network indices, D, Dout, Cout, Bdir, Kbu and Ttd, are significantly correlated with Q (Table 2-2). Two indices, 18.

(31) C and B, show significant correlations with Q for two of the three webs. CAR is the only web in which Din, Cin, Ktd, and Tbu all show significant correlation with Q. Across all three webs, Dout, Cout, Kbu and Bdir persistently show strong correlation with Q. Thus, in general, being an intermediate host for several species is linked with higher vulnerability to predators (Dout), being at network positions close to predatory species (Cout and Kbu) or being involved in many different food chains (Bdir).. The effect of retaining parasite links previously omitted from the Carpinteria data In the CAR+ web there are 83 non-parasite and 45 parasite species, with 496 predator-prey links and 630 parasite-host interactions. The average bottom-up trophic position of host species participating in parasite-host interactions is 2.13 while the mean for the random CAR+ web is 1.61 (95% confidence intervals=1.55-1.65), and their top-down counterparts are 0.39 and 0.91 (0.86-0.96) respectively. Therefore the results for the CAR+ data still suggest that parasitism is not a random process. The replacement of the five parasite species does not alter the correlation between parasite diversity and network indices too drastically (Table 2-1). The same applies to the correlation between the propensity of being an intermediate hosts and network indices despite that the correlation with Din is now non-significant while that with C is now significant (Table 2-2).. 19.

(32) DISCUSSION It is clear from our results that parasite diversity, the number of parasite species using each host species, is very different from random and consistently over dispersed in all three food webs. Only a few host species harbour many parasite species and many have few or no parasite species. It is thus probable that there are common factors influencing the parasite diversity of host species in our three webs and, therefore, potentially in all food webs. There are non-random patterns in parasitism of individuals and of communities (Poulin 2007). The significant covariation in parasite richness of different parasite taxa across vertebrate hosts suggests that common underlying mechanisms may operate (Poulin and Morand 2000). Non-randomness is congruent with previous findings in the comparative study of parasite diversity at the macroecological scale (Poulin 1995) and in host-parasite interaction networks (Vazquez et al. 2005). Parasitism therefore fits the general rule that interaction ties in ecology, for instance predator-prey links and plant-pollinator interactions, tend to be non-random (Jordano et al. 2003, Vazquez 2005, Poulin 2007).. There have been repeated studies of factors contributing to non-randomness in parasitism. These have included life history traits (i.e. body size, geographic range and diet) and epidemiological parameters (i.e. host density, host longevity and parasite transmission rate) (Poulin 1995, Poulin and Morand 2000). Our study examines parasite diversity from a different perspective by looking at the network position of host species in the food web. A large part of the non-randomness in parasite diversity is, 20.

(33) as we have demonstrated, strongly related to the network position of host species. The importance of a species is its ability to affect others in the web by virtue of its network position. We used different network indices to emphasize different aspects of a network position. High parasite diversity is associated with species having a wide diet range, occupying a network position close to many prey species, and species to which many resources are efficiently channelled. Thus the better a species can acquire or accumulate resources from species at lower trophic levels, the more parasite species it is likely to have. Factors such as “what you eat” and the “feeding habit of your prey” importantly affect the likelihood of a host species acquiring many parasite species (Marcogliese 2002).. The three webs do not have exactly the same parasite diversity-network position relationships. In particular, only in the CAR web is there a significant relationship between parasite diversity and host species with few predators. At this stage, with only three webs, it is not possible to say whether CAR is unusual. Such a decision awaits the examination of many more webs. The discrepancy might be due simply to the uniqueness of the Carpinteria salt marsh system. Alternatively, the difference may relate to CAR having a much larger proportion (82%) of parasite-host interactions connecting parasites to their definitive hosts than do the other two webs. Parasites at the final stage of their life cycle might prefer a stable host environment in which to fully complete their development; and host species that are free from predation might just be good targets for those parasites. Theoretical models illustrate that 21.

(34) selective predation on prey with many macroparasites can rapidly drive extinct the parasite species (Packer et al. 2003, Hatcher et al. 2006), and macroparasites are usually highly aggregated on certain individuals of a host population (Poulin 2007). Extending this idea to the ecosystem raises the expectation that parasites may persist if they exploit host species that suffer low predation, and this may be the case in CAR.. One reason why high parasite diversity is associated with important or prominent network positions may be that a non-parasite species at a more peripheral position may be prone to extinction. This is because such a species relies on only a few species for its survival (Allesina and Bodini 2004). Therefore, over time, parasites of such a host species will experience more fluctuations in host availability and be at a greater risk of extinction. Host species occupying prominent network positions, in contrast, have many interacting partners and the associated parasite species are therefore buffered against fluctuations in host availability. If an interacting partner goes extinct the parasite can use others to continue its life-cycle and survive. The correlation with important network positions might be counteracted, however, by competition between parasite species (Holt and Lawton 1994). The correlations between parasite diversity and network indices do not, of course, exclude other factors that might influence the pattern of parasitism. These factors include the abundance of host species (Vazquez et al. 2005, Vazquez et al. 2007) and phylogenetic constraints (Mouillot et al. 2008).. 22.

(35) Species serving as intermediate hosts tend to lie in different food web positions to that for host species in general. Species occupying these positions tend to have many different predators, are the focus of many predatory effects from species at higher-trophic levels, or mediate many food chains. Such properties favour frequent and stable predator-prey interactions between host species that can ensure successful completion of parasite life cycles. Our finding that the network position of intermediate hosts is associated closely with material accumulation and transmission is therefore similar to the notion of “PITT”, Parasite Increased Trophic Transmission (Lafferty 1999, Mouritsen and Poulin 2002).. The study of food webs with parasites is a new challenge in ecology. There are two dimensions of complexity. The first is the interaction between parasites and their definitive hosts (Vazquez 2005, Vazquez et al. 2007). The second is that of how parasites are intertwined with food webs such that parasites can be transmitted from one host species to another via predator-prey links (Marcogliese 2001, Mouritsen and Poulin 2003, Lafferty et al. 2008). The existing food web models (Cohen and Newman 1985, Williams and Martinez 2000, Cattin et al. 2004) do not portray the interplay between parasitism and food webs, and we argue there is a need for a new food web model with parasites. Such a new model has to capture the characteristics of the underlying food web as well as the pattern of parasitism; and our results indicate that the network position of hosts is an important factor influencing the pattern of parasitism. 23.

(36) Our results make a substantial contribution to a general law for food web models by demonstrating two important features of parasitism in food webs. The first of these is that parasitism is not random within food webs. The second is that parasite diversity is positively related to the network position of the host species. Parasites preferentially exploit highly connected hosts species at higher trophic positions as well as those with wide diet range. There are also more parasite species using hosts mediating many food chains and those vulnerable to many predators. Considering parasitism from a network perspective as we have done reveals strong general patterns of parasitism in food webs.. 24.

(37) Table 2-1 Spearman rank correlations between parasite diversity (P) and different network indices (as identified by the top row; D: total degree, Din: in-degree, Dout: out degree, C: closeness; Cin: in closeness; Cout: out closeness, B: betweenness, Bdir: directional betweenness, Kbu: bottom-up keystone, Ktd: top-down keystone, Tbu: bottom-up trophic position, Ttd: top-down trophic position) for each of the webs studied (as identified by the left column). In each cell the value is the Spearman rank correlation. Entries in bold indicate significant correlations at the 0.05 level after Bonferroni corrections.. D. Din. Dout. C. Cin. Cout. B. Bdir. Kbu. Ktd. Tbu. Ttd. CAR. 0.185. 0.745. -0.446. -0.232. -0.695. 0.616. 0.083. -0.105. -0.509. 0.645. 0.634. -0.663. COM. n.s. 0.422. *** 0.527. ** -0.022. n.s. -0.348. *** -0.590. *** 0.336. n.s. 0.403. n.s. 0.020. *** -0.151. *** 0.529. *** 0.508. *** -0.431. YTH. ** 0.413. *** 0.411. n.s -0.002. * -0.262. *** -0.390. n.s 0.142. ** 0.375. n.s 0.182. n.s -0.013. *** 0.415. *** 0.323. ** -0.432. CAR+. *** 0.077. *** 0.777. n.s -0.576. n.s. -0.126. ** -0.769. n.s 0.733. ** -0.009. n.s -0.204. n.s -0.634. *** 0.718. * 0.732. *** -0.774. n.s.. ***. ***. n.s.. ***. ***. n.s.. n.s.. ***. ***. ***. ***. 25.

(38) Table 2-2 Spearman rank correlation between the propensity of being an intermediate host (Q) and different network indices (as identified by the top row; D: total degree, Din: in-degree, Dout: out degree, C: closeness; Cin: in closeness; Cout: out closeness, B: betweenness, Bdir: directional betweenness, Kbu: bottom-up keystone, Ktd: top-down keystone, Tbu: bottom-up trophic position, Ttd: top-down trophic position) for each of the webs studied (as identified by the left column). In each cell the value is the Spearman rank correlation. Entries in bold indicate significant correlations at the 0.05 level after Bonferroni corrections.. D. Din. Dout. C. Cin. Cout. B. Bdir. Kbu. Ktd. Tbu. Ttd. CAR. 0.463. -0.436. 0.862. -0.358. 0.635. -0.843. 0.399. 0.683. 0.866. -0.459. -0.707. 0.785. COM. ** 0.636. ** 0.024. *** 0.783. n.s. -0.680. *** 0.364. *** -0.732. * 0.458. *** 0.823. *** 0.814. ** -0.444. *** -0.506. *** 0.683. YTH. * 0.607. n.s. -0.020. *** 0.719. ** -0.567. n.s. 0.169. ** -0.679. n.s 0.657. *** 0.784. *** 0.716. n.s. -0.144. n.s. -0.320. ** 0.665. CAR+. *** 0.500. n.s. -0.335. *** 0.919. *** -0.361. n.s. 0.635. *** -0.894. *** 0.489. *** 0.826. *** 0.920. n.s. -0.405. n.s. -0.707. *** 0.854. ***. n.s.. ***. *. ***. ***. ***. ***. ***. *. ***. ***. 26.

(39) CAR. COM. YTH. Parasite diversity (P). Fig. 2-1. The distribution of the number of parasite species (parasite diversity) for the Carpinteria (CAR), Company Bay (COM), and Ythan Estuary (YTH) ecosystems. The observed distributions (Data) are shown in filled bars and the expected distributions according to a random model (Random) are in open bars. 27.

(40) -15. -10. -5. 0. 5. -5. 0. -5. 5. 0. 5. 0.2. -20. 6. 14. 5. 0.1. 0.3. C 28. 7. 41. COM. 0.3. CAR. YTH C. 24 2. 31. 8. 16. 27. Cin. C. 54. 29 36 22 21. 51 53 39. 19. 60. 42. 32. 5. 40. 5 4. 17. 35 26. 37. 82. 25. 45 44. 10 13 12. 76 80 79. 61 65 64 63 68. 66. 9 34. Kbu. Cout. 74. 71. 59 78. 67 55. 11. 0. 0.0. Ttd. Car. 5. 70. 0.2. 30. 15. 60 49. 33. 77. 60 49. Cin. 81 23. 0.2. 3. Cin. 33. 41. 41. 20 69. 8 21. Cout. 38. 2. 40 15 14. 25 24. 0. 62 46 45 34. 65. 59. 54. 56. 53. 22 10 42 12 11 9. 39 25 24 26. 5. 62 46 45 34. 65. 59. 54. 30. 57 30. 57. 55 1. Tbu. 55 1. 58. -0.1. Ktd 37 36. Bdir. -5. Kbu 52. 61. Dout. 32. 35. Ktd 37 36. Bdir. Dout. Din. Din. 47. Kbu 52. 61. -5. 32. 35. -0.2. -0.1. 58. -0.2. -10 -15. Ttd. 29 28 27 31. Ttd. 29 28 27 31. 13. Tbu. 0. 10. 39 26. 13. -0.4. 51. 22. 12 11 9. 5. Comp.2. 73. 7 6. 42. 0.0. -0.2. DBBdir. 57. 17. 7 6. 44 43. 4 3. 20 19 18 23. 56. 53. 17. 40 15 14. Comp.2. Din. 48 47 20 19 18 23. 44 43 51. Ktd. 38. 2. 48 47 63 4 3. 58. 52 72. 8 21. Cout. 63. 38. 43. -5. -0.1. Tbu. -0.3. Comp.2. Dout. 0.1. 75. 62 48 50. 0.1. 83 49 33. 18. 0.0. 1. 50 50. -0.5. -0.3. -0.3. -20. 46 16. B. 64. 16. B. -0.5. -0.4. -0.3. -0.2. -0.1. Comp.1. 0.0. 0.1. 0.2. -0.3. -0.2. -0.1. 0.0 Comp.1. 64. 66. 66. D. 56. D. 67. 0.1. 0.2. 0.3. -0.3. -0.2. -0.1. 0.0. 67. 0.1. 0.2. 0.3. Comp.1. Fig. 2-2. PCA plots of the twelve network indices measuring different characteristics of a network position (D: total degree, Din: in-degree, Dout: out degree, C: closeness; Cin: in closeness; Cout: out closeness, B: betweenness, Bdir: directional betweenness, Kbu: bottom-up keystone, Ktd: top-down keystone, Tbu: bottom-up trophic position, Ttd: top-down trophic position) for the Carpinteria (CAR), Company Bay (COM), and Ythan Estuary (YTH) ecosystems. There are four visible clusters. The first consists of degree, betweenness and directed betweenness centralities that form a tightly packed cluster. Closeness centrality stands out from other network indices while the remaining ones form two loosely packed clusters.. 28.

(41) CHAPTER 3: THE REDUCTION OF FOOD WEB ROBUSTNESS BY PARASITISM2 INTRODUCTION All species of an ecosystem are embedded within an intricate web of trophic interactions (Pimm et al. 1991). Due to the structural complexity arising from the direct and indirect trophic linkages among species, it is not always a simple problem to predict how changes in the abundances of some species may affect the entire food web (Yodzis 2000). One pressing issue in food web research is to investigate the response of a web to species losses (Duffy 2002, Dunne et al. 2002b, Ebenman et al. 2004, Eklof and Ebenman 2006) as some human activities, such as over-fishing, habitat destruction and alien species invasion, may cause the extinction of native species and indirectly trigger the collapse of an ecosystem (Grosholz et al. 2000, Dobson et al. 2006, Baum and Worm 2009).. One strategy for understanding the response of a food web to species losses is to study its robustness (Dunne et al. 2002b, 2004). Such a methodology has its root in network science where the integrity of a network under random errors and targeted attacks was first investigated by Albert, Jeong & Barabasi (2000). Network robustness in the traditional sense mainly focuses on how structural properties of a network change 2. This chapter has submitted to International Journal for Parasitology in the title “The Reduction of Food Web Robustness by Parasitism: Fact and Artefact” and coauthor with K.-T. Shao, C. W.-J. Liu, W.-H. Lin and W.-C. Liu. Author‟ contributions: HWC proposed the study, WCL, WHL coded programs, HWC, CWJL,WCL performed simulation and data analysis, HWC, WCL, KTS wrote the paper. 29.

(42) when nodes are progressively removed from it (Albert et al. 2000); a network starts to disintegrate into isolated parts when the proportion of removed nodes passes a certain threshold (Callaway et al. 2000). In ecology, the issue of food web robustness takes a different approach. With the exception of producers, all species in a food web rely on at least one other species for survival; thus the loss of a species, in particular a prey species, will reduce the diet range of its predator species. When all prey species consumed by a predator species become extinct, this then drives the predator‟s own extinction, which in turn might cause the extinction of other species at higher trophic levels (Dunne et al. 2002b). Thus the study of food web robustness concerns here the cascading secondary extinctions of species caused by primary species losses. Quantitatively speaking, the robustness of a food web can be defined as the number of primary extinctions required in order to result in a total loss of species beyond a pre-determined threshold (Dunne and Williams 2009). To date, most studies of food web robustness have focused on the relationship between robustness and network properties such as the degree distribution, food web size and connectance (Dunne et al. 2002b, Melian and Bascompte 2002, Estrada 2007, Gilbert 2009). More recently, through a systematic study on a variety of food web models, it has been demonstrated that a food web is less likely to collapse if it has higher species richness and connectance (Dunne and Williams 2009).. One practical issue regarding food web robustness is whether there exist leading indicators that can signal the integrity or the health state of 30.

(43) an ecosystem (Carpenter et al. 2008, Petchey et al. 2008b). Potential candidates for such indicators include parasites. Parasites are ubiquitous in nature (Poulin 1999), and several species have complex life cycles in which different developmental stages require different host species. Parasites are often transmitted from one host species to another through trophic interactions between their hosts (Lafferty 1999), and the absence of parasite species with complex life cycles sends a strong signal indicating the possible breakage of food chains (Marcogliese 2002, Hernandez et al. 2007, Valtonen et al. 2010). Therefore, it has been suggested that the presence of certain parasite species can be regarded as an indicator of ecosystem integrity (Bhuthimethee et al. 2005, Marcogliese 2005, Palm and Ruckert 2009). More recently, by adopting the approach of Dunne et al. (2002), Lafferty & Kuris (2009) have demonstrated that a Californian salt marsh ecosystem is less robust to species losses with the inclusion of parasite species than without. The authors suspect this is probably due to the nature of the parasites‟ complex life cycles making them more prone to secondary extinction than non-parasite species.. Although the reliance of parasites on specific host species at different stages of their life cycle can be a risk factor contributing to their sensitivity to secondary extinction, the addition of parasites into a food web may change the structure of the web and might potentially affect its robustness. For example, the inclusion of new species can change the link (or degree) distribution and the connectance of a food web (Dunne et al. 31.

(44) 2002a, Montoya and Sole 2003, Jordan and Osvath 2009), and it is well known that food web robustness is closely-related to those two structural properties (Dunne et al. 2002b, Estrada 2007, Dunne and Williams 2009). Furthermore, it has been shown recently that parasitism does not occur at random locations within a food web (see Chapter 2); in particular, intermediate hosts utilised by the larval or juvenile stages of many parasite species tend to occupy important positions in a food web. Thus, we suspect that the reduction in robustness of a food web that includes parasites might also be due to host species occupying peculiar network positions within the web such that they are more prone to secondary extinction than other parasite-free species.. In this paper, we conduct a series of simulation experiments to demonstrate the influence of parasitism on food web robustness; by doing so, factors contributing to changes in food web robustness will be elucidated. Whether parasites are indeed good indicators of food web robustness will be determined by examining how sensitive they are to species losses in comparison with non-parasite species. We perform our analysis on five published food webs in order to test the generality of our findings. First, we describe the data used in this study, followed by an account of methods used, including: (1) a definition of food web robustness; (2) a detailed description of the simulation procedure for various extinction scenarios that teases apart factors that may or may not affect food web robustness; and (3) how to assess the sensitivity of parasites to secondary extinction. The results are followed by a discussion 32.

(45) on whether the inclusion of parasites can reduce food web robustness and how this may be achieved. We then conclude with comments on parasites as indicators of ecosystem integrity.. MATERIAL AND METHODS Food web data Five published food webs that incorporate parasites were used in this study: “CAR”, the Carpinteria salt marsh community near Santa Barbara, USA (Lafferty et al. 2006); “COM”, the intertidal mudflat community of Company Bay in Otago Harbor, New Zealand (Thompson et al. 2005); “MUS”, the forest stream community of Muskingum Brook in the New Jersey Pinelands, USA (Hernandez and Sukhdeo 2008); “TAK”, the pelagic community of the subarctic Lake Takvatn in Norway (Amundsen et al. 2009); and “YTH”, the Ythan River estuary community in Scotland, UK (Huxham and Raffaelli 1995, Huxham et al. 1996). Each dataset contains predator-prey (i.e. who eats whom) and parasite-host interactions (i.e. who parasitises whom). The CAR, COM and TAK data also contain extra information on parasites as food sources for non-parasite species and we define those as predator-parasite interactions. The size of those food webs and the number of different trophic links they include are summarised in Table 3-1.. Extinction simulation and food web robustness An extinction simulation consists of a sequence of events, with T 33.

(46) denoting the Tth event. Initially we set T=0 and we start with an intact food web. The simulation then proceeds by repeating the following steps: (1) set T=T+1; (2) during the Tth event, a species is selected randomly and then deleted from the food web, which we denote as the Tth primary extinction; (3) the remaining food web is then checked for species (bar producers) that are left with no prey species following the primary extinction, and those species are then deleted from the food web (here we assume a species becomes extinct when all of its food sources are absent); (4) step (3) is repeated until there are no further species losses; and (5) we denote those species deleted following the Tth primary extinction as the Tth secondary extinctions. Following Dunne & Williams (2009), the simulation then stops when the number of species remaining in the food web is less than half of the number of species in the original food web. If N and M represent the number of species in the original food web and the required number of primary extinctions, respectively, then the robustness of a food web, R50, is defined as M/N.. An extinction sequence is also recorded for each simulation, and it contains information on: (1) in which Tth event an extinction occurs; (2) whether a particular extinction involves a non-parasite species or a parasite species; and (3) whether a particular extinction is a primary or secondary extinction. This information is then used to investigate whether parasites are more prone to secondary extinction than non-parasite species. This can be done in two ways. First, the numbers of parasite species involved in primary extinctions, YP, and secondary extinctions, XP, 34.

(47) are determined; similarly, the equivalent numbers are also obtained for non-parasite species and denoted as YNP and XNP respectively. If ZP is the number of parasite species in a food web, then ZP - YP represents the number of parasite species that could potentially be lost as secondary extinctions; thus the quantity XP%= XP /(ZP - YP) denotes the proportion of parasite species involved in secondary extinctions out of the available pool of parasite species. ZNP and XNP% are similarly defined for non-parasite species. If parasites are more sensitive to secondary extinction than non-parasite species, then XP% should be significantly larger than XNP%. Second, we argue that if parasite species are more sensitive to species losses, then generally speaking their extinctions should occur earlier than those of non-parasite species. In terms of T, secondary extinctions involving parasite species should have smaller T values than those involving non-parasite species. Since the values of T are not normally distributed, the median T can serve as a measure of central tendency of where in the event sequence secondary extinctions involving parasite species occur, and we denote this as TP. We then standardise TP by dividing it with the maximum T, TP,Max, to obtain TP% (i.e. TP%= TP / TP,Max). Likewise, the equivalent statistics can also be defined for non-parasite species (i.e. TNP and TNP%). If parasites are more sensitive to species losses than non-parasite species, then TP% should be significantly smaller than TNP%.. Extinction experiments For each of the 5 food webs, a series of extinction experiments were 35.

(48) conducted in order to investigate whether and how parasites affect food web robustness. Different extinction experiments consider different modifications of a food web, and for simplicity we refer to those as food web models; they are described in more detail in the next section. Each extinction experiment consisted of 1000 extinction simulations; thus there are 1000 values of R50, XP%, XNP%, TP% and TNP%, which in turn form their respective distributions.. Food web models In order to elucidate the effect of parasitism on food web robustness, we performed extinction experiments using different food web models that account for changes in food web size, degree distribution, connectance and preferential parasitism. These models were:. Predation only (H): this model only considers the interactions between non-parasitic species, namely the conventional predator-prey interactions.. Parasitism with (HPLC) or without (HP) the life cycle constraints of parasites: here, both models include predator-prey and parasite-host interactions. In model HPLC, a parasite species becomes extinct when all host species for any one of its developmental stages have gone extinct; whereas in model HP, this constraint is relaxed by assuming that a parasite species goes to extinction if and only if all of its host species have gone extinct regardless of developmental stages.. 36.

(49) Additional random predation (HHR): one difference between food webs with and without parasitism is the increase in the numbers of nodes and links when parasites are included, resulting in changes in network complexity (e.g. degree distribution). In order to ascertain whether the change in food web robustness after adding parasites is indeed caused by factors that are different from those resulting from the simple addition of more predators, we must consider the following food web model (i.e. HHR). First, the number of parasite species, A, is determined from model HP; model HHR is then constructed by adding A new species to model H, with each of those newly added species having its number of prey species sampled from the in-degree distribution of model H (in-degree here refers to the number of prey species consumed by a predator species). For each of those new A species, all predator-prey links are connected to random positions in the food web model H. Moreover, each simulation was carried out by using a separately generated model HHR.. Random parasitism with (HPR,LC) or without (HPR) the life cycle constraints of parasites: in order to investigate whether the change in food web robustness is due to the sensitivity of the host species‟ network positions to species losses, we must consider a model setting with random parasitism. Both models HPR,LC and HPR are essentially the same as HPLC and HP, respectively; the only difference here is that models HPR,LC and HPR consider random parasitism by randomizing the host species in all parasite-host interactions. Again, for those models involving randomization, namely HPR,LC and HPR, each simulation was carried out 37.

(50) by using a newly generated food web model.. Parasites as food resources with (HPF,LC) or without (HPF) the life cycle constraints of parasites: of the five food webs used in this paper, three (CAR, COM and TAK) contain information on predator-parasite interactions (i.e. parasites serving as food resources for some non-parasite species). Here, models HPF,LC and HPF are essentially the same as models HPLC and HP, respectively, except that the new models also consider predator-parasite links. These two new models thus provide an opportunity to assess the impact of predation-on-parasites on food web robustness.. Table 3-2 summarises the similarities and differences among the above-mentioned food web models. Note that each parasite species is considered as a distinct node in a food web, and we do not consider a parasite species with different developmental stages as different tropho-species.. RESULTS Food web robustness By comparing the median robustness value (or median R50 for short) of model H with those of the other models, we can observe that increasing food web size, by including parasites or additional predators, often reduces food web robustness (Fig. 3-1A). On average, adding more top predators in a random manner reduces median R50 by 3.0% (i.e. 38.

(51) compare model H with model HHR), whereas adding parasites with no lifecycle constraints only reduces median R50 by 1.4%, 1.5% and 0.7% for models HP, HPR, and HPF respectively. The largest reductions in food web robustness are observed in models with parasite lifecycle constraints: on average, median R50 drops by 7.3%, 7.5% and 5.4% for models HPLC, HPR,LC and HPF,LC respectively.. To rule out the effect of unequal food web sizes and changing network complexity (e.g. degree distribution) on food web robustness, we have to compare median R50 of model HHR with that of models involving parasitism (i.e. models HPLC, HPR,LC, HPF,LC, HP, HPR and HPF). On average, median R50 drops by 4.3%, 4.4% and 3.4% for models HPLC, HPR,LC and HPF,LC respectively, but it increases respectively by 1.7%, 1.5% and 1.4% for models HP, HPR and HPF.. The difference in R50 is less obvious between models with random and non-random parasitism. Median R50 drops by 1.7% from models HP to HPR and marginally by 0.1% from models HPR,LC to HPLC when averaged across all five datasets. As for including parasites as food sources for non-parasitic predators, median R50 increases by 0.7% from models HP to HPF and by 0.9% from models HPLC to HPF,LC after averaging the results from the CAR, COM and TAK datasets.. Our study also shows the negative correlation between species number in a food web and its network connectance 39.

(52) (Fig.3-2; N = 36, r = 0.622, P < 0.001). Therefore, increasing food web size may result in lower connectance and thus leads to lower network robustness. Furthermore, our results suggest two separate logarithmic relationships between network robustness and connectance (Fig 3-3). One regression line is made up by data points from food web models with parasite life cycle constraints (the solid line in Fig.3; R50 = 0.034*ln(Connectance) + 0.497, r2 = 0.692, P < 0.001), whereas the other line is for data points from models with the parasite life cycle constraints relaxed (the dash line in Fig. 3; R50 = 0.016*ln(Connectance) + 0.508, r2 = 0.183, P < 0.05).. The proportion of non-parasite and parasite species involved in secondary extinction On average, 3.5% of non-parasite species out of the available pool suffered secondary extinction, while this number was much higher, i.e. 29.8%, for parasite species (Fig. 3-1B). When parasite lifecycle constraints were relaxed, XP% was 10.7% after averaging the results from models HP, HPR and HPF; however, when these constraints were in place, XP% achieved a value of 51.8% after averaging over models HPLC, HPR,LC, HPF,LC. For non-parasite species, a noticeable difference existed in the 40.

(53) TAK web whether or not parasites were treated as food sources for non-parasite species: XNP% for models without parasites as food sources were lower than those for models with this additional complexity, and on average those figures differed by as much as 8.9%.. The observed sequence of secondary extinctions involving non-parasite and parasite species Fig. 3-1C summarises the standardised median T for secondary extinctions involving non-parasite and parasite species. The averaged median values of TNP% and TP% over all models are 85.7% and 66.5% respectively (note that a smaller percentage implies extinctions occurring at earlier stages in the extinction sequence). Food web models with parasite lifecycle constraints (i.e. models HPLC, HPR,LC, HPF,LC) have an averaged median TP% of 54.1%; once such constraints were relaxed, this value increased to 79.4% (i.e. models HP, HPR and HPF), a value not very different from its counterpart for non-parasite species (i.e. the averaged median TNP% =85.7%). However, there were cases not following this general trend: for the COM dataset, non-parasite species often became extinct before parasite species in food web models without the parasite lifecycle constraints (Fig. 3-1C).. DISCUSSION Based on the results from a previous study (Lafferty and Kuris 2009) and those presented here, it is clear that food webs with parasitism are 41.

(54) less robust to species loss than those without. Comparing the results from models H, HHR and HPR suggests that simply adding more species, no matter whether they are parasites or top predators, can reduce food web robustness. It has been shown that adding parasites to a food web can change its network complexity (Huxham and Raffaelli 1995, Huxham et al. 1996, Thompson et al. 2005, Lafferty et al. 2006, Hernandez and Sukhdeo 2008), which can consequently alter its robustness (Dunne et al. 2002b, Gilbert 2009). One measure of network complexity is connectance, and it has been shown that food webs with high connectance tend to be robust structurally (Dunne and Williams 2009). We found that this was indeed the case as models H tended to have higher connectance and food web robustness than models HHR and HPR (Fig. 3-2). In light of this, it is therefore important to understand and clarify whether the reduction in food web robustness after the inclusion of parasitism is due to factors associated with the characteristics of parasites, or simply an inevitable artefact of the addition of new nodes and links to an existing network. Those arguments motivated us to develop several extinction experiments to elucidate the factors responsible for reduction in food web robustness. Based on the reasons above, we argue that the difference made by parasitism in food web robustness can only be revealed meaningfully by comparisons with results derived from food webs of similar sizes and complexity. Hence, in this study, we explored several unique aspects of parasitism and their effects on food web robustness, including: (1) the life cycle constraints of parasites, (2) the preferential host use by parasites, and (3) treating parasites as food sources for non-parasite species. 42.

(55) Starting with the life cycle constraints of parasites, our results show that substantial reductions in food web robustness occur only when food web models consider such constraints (i.e. models HPLC, HPR,LC, and HPR,LC). Even for food webs having similar network connectance, models consider parasite life cycle constraints are less robust than those without such constraint (Fig. 3-3). Parasites are four times more vulnerable to random species loss in food web models with parasite lifecycle constraints than in those without. Furthermore, parasites appear much earlier in the extinction sequence in models with parasite lifecycle constraints than in those without. All these findings suggest that lifecycle constraints contribute substantially to the sensitivity of parasites to species loss and to reduced food web robustness. Moreover, we suggest that future studies on food web robustness should consider the effect of lifecycle constraints for non-parasite species if they have well-defined developmental stages with noticeable ontogenetic diet shifts between different stages(Yodzis and Winemiller 1999). We suspect this additional complexity will further reduce food web robustness to a level lower than those reported here or in previous studies.. Parasitism has been demonstrated to occur at non-random positions in food webs (see Chapter 2). However, it is surprising that food web robustness for models with non-random parasitism (models HPR and HPR,LC) did not differ significantly from those with random parasitism (models HP and HPLC). A possible explanation is that parasites tend to 43.