Li et al submitted to Proc Roy Soc B: Reconsidering delay dependent models

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1 ELECTRONIC SUPPLEMENT ONE for: Reconsidering the importance of the past in predator-prey models: both numerical and functional responses depend on delayed prey densities Jiqiu Li 1, Andy Fenton 2, Lee Kettley 2, Phillip Roberts 2, David J. S. Montagnes 2 * 1 Laboratory of Protozoology, KLB07006, College of Life Science, South China Normal University, Guangzhou , China 2 Institute of Integrative Biology, University of Liverpool, Liverpool, UK L6 97ZB Paramecium and Didinium, a model system for the study of population dynamics Protozoa are useful model organisms, having key attributes that make them applicable to a wide range of biological disciplines [1]. Specifically, Didinium and Paramecium have been employed as models to examine population dynamics, most notably by Gause [2,3] who experimentally tested the validity of the then new Lotka- Volterra predator-prey model. Over the last 90 years, these two ciliates have continued to be instrumental and have aided in understanding ecological processes, much of which are ultimately related to population dynamics (Fig. S1, Table S1). The Paramecium-Didinium predator prey couplet, and specifically that of P. caudatum and D. nasutum that was used in the current study, has been employed to examine topics ranging from individual behaviour to metacommunity dynamics (Table S1). We, therefore, strongly support its continued application to assess population dynamics in general, not simply because of the substantial historical applications, but because of its continued utility to answer fundamental questions. 1

2 Electronic supplement figure legend Fig. S1. Publications per year on Paramecium and/or Didinium restricted to biological sciences. Data obtained from Web of Knowledge and augmented with publications that were found elsewhere. 2

3 Fig. S1 3

4 Table S1. A chronological summary of key studies that investigate the relationship between Paramecium and Didinium. The key focus or finding is made bold. Reference Details Mast & Ibara 1923 [4] Beers 1925 [5] Gause 1934 [2,3] Gause et al [6] Beers 1937 [7] Beers 1945 [8] Evans 1958 [9] Burbanck & Eisen 1960 [10] Butzel & Bolten1968 [11] Hairston et al [12] Wessenberg & Antipa 1970 [13] Luckinbill 1973 [14] Salt 1974 [15] Luckinbill 1974 [16] Salt 1975 [17] Encystment. Temperature, food, and the culture age affected Didinium encystment. Encystment. The absence of food and Paramecium waste and the presence of Didinium waste promoted Didinium encystment. Prey immigration may promote stability. Paramecium and Didinium were used to investigate processes described by Volterra s recent arguments for predator prey interactions. The Paramecium-Didinium system was self-annihilating. It was suggested that prey addition would provide stability. Prey refugia may stabilise predator-prey interaction. The equation is based on observed biological properties of the two species. Cysts viability Didinium cysts survive for 10 years. Excystment. Didinium excystment is promoted by the metabolic waste of bacteria. Predator competition is controlled by prey abundance. There was little effect of competition between two predators Didinium and Woodruffia when Paramecium is abundant due to differences in predatory behaviour. Competition increases as the Paramecium become scarce due to the greater efficiency of Didinium as a predator. Low quality prey results in reduced predator growth. Didinium fed on Paramecium that have been grown on monofloral bacteria exhibit reduced growth and persistence when compared to Didinium fed Paramecium that had been grown on a wild flora of bacteria. Growth and encystment are prey dependent Didinium fed on well-fed Paramecium reach a maximum growth when 45 Paramecium per day are consumed. Encystment only occurs if environmental conditions slowly deteriorate (not rapidly). Increased species diversity at different trophic levels alters system stability. Increasing bacterial diversity increased stability of Paramecium populations. Adding a second Paramecium species increases stability, but adding more Paramecium species reduces stability. Prey capture mechanism. Didinium s toxicysts aid in Paramecium capture and ingestion. Contact frequency between predator and prey and the environmental richness are important controls in predator-prey population s stability. Prolonged coexistence of a Paramecium and Didinium was achieved by adding a thickening agent to the medium. This reduced predator-prey contact frequency. Excess bacterial food enriched the system and resulted in the extinction of the prey followed by the predator. Reducing the bacterial food resulted in longer persistence of population oscillations. Prey density is the strongest control of the capture rate by predators. Based on observations on Paramecium and Didinium. Increased area prolongs predator-prey coexistence. Both a large habitat size and limited food supply for the Paramecium prolonged Paramecium-Didinium co-existence. Predator density dependence on predator ingestion, growth, and volume. Increased 4

5 Didinium density reduces ingestion rate and cell volume, but growth rate is constant. Maly 1978 [18] Luckinbill 1979 [19] Salt 1979 [20] Veilleux 1979 [21] Berger 1980 [22] Hewett 1980 [23] Hewett 1980 [24] Metapopulation fragmentation and prey dispersal alter system stability. Increased Paramecium dispersal improved Paramecium-Didinium stability of the system in a multicompartment system. Environmental enrichment and prey diversity alter stability of populations. Enrichment is critical to the stability of small-scale communities; prey populations are regulated by bacteria not Didinium; increasing prey diversity results in system extinction. Predators behaviour changes in response to prey availability. Didinium increased swimming speed after 30 h of starvation. This increases their dispersal to find more prey. Environmental enrichment indirectly alters predator-prey stability. The efficiency of Didinium as a predator is directly related to the nutritional adequacy of Paramecium which depends on the enrichment of the system. At low bacterial levels predator efficiency is sufficiently low to prevent the extinction of prey. Predator behaviour is affected by non-prey species through chemotaxis. A zoochlorellae endosymbiont of Paramecium reduces capture rate by Didinium. The endosymbiont may disrupt the chemicals used by the Didinium to locate the Paramecium. Predator size is influenced by prey size. Didinium size increases by increasing the size of the Paramecium species available to it. Predators encounter-rate, handling-time, and growth rate are affected by prey size. Didinium maximum ingestion rate decreases with increasing prey size; handling time increases with Paramecium size; division rate is highest on intermediate Paramecium size and lowest on smaller prey. There is an optimum Paramecium size for Didinium. Graham & Canale 1982 [25] Modelling a 4-step food chain. Full microbial food chain (organic carbon substrates Enterobacter aerogenes Paramecium primaurelia Didinium nasutum) was investigated. Antipa et al [26] Predator and prey are attracted to food of prey. Both Paramecium and Didinium are attracted to a chemical produced by bacteria (chemotaxis), illustrating an indirect mechanism of prey detection. Hewett 1987 [27] Hewett 1988 [28] Harrison 1995 [29] Spencer & Warren 1996 [31] Warren 1996 [32] Prey size effects predator-prey interaction. Didinium size increases with increasing Paramecium prey size. Didinium feeding on large Paramecium are better able to survive starvation and are more likely to form cysts. Predator and prey size effect predator-prey interaction. Larger Didinium have shorter handling times, encounter rates, and make more captures per division. Larger Paramecium need longer time to handle and ingest, and are encountered more frequently by predators. Small Didinium are more successful in initially capturing prey. Predator-prey models can qualitatively and quantitatively describe empirical predatorprey data. Luckinbill s [14] data are described by a standard predator-prey model [30]. The fit is improved by including a sigmoidal functional response (Type III) or predator mutual interference (but not both) and by including a delayed numerical response. Habitat size and productivity affect food web structure. Paramecium and Didinium are included in a microcosm study. Larger habitats support more species with more links per species and longer food chains. Enrichment has little effect on food web structure. High dispersal rate offsets species extinction in a metapopulation. Microcosm study that includes Paramecium and Didinium. 5

6 Warren 1996 [33] Dispersal and habitat destruction alter metapopulation structure. Paramecium and Didinium are included in a microcosm study. Increasing disturbance at a local level results in species extinction. Increasing dispersal between habitats moderates this effect but does not eliminate it. Dispersal rate alone has little effect on metapopulation diversity. Disturbance does not seem to increase diversity. Fox & Olsen 2000 [34] Food web structure alters predator-prey dynamics. Didinium is placed with Paramecium alone or with Paramecium and another prey, Colpidium, and an alga that only Paramecium can consume is added. Having an alternative prey enhances Didinium s response to the perturbation of Paramecium; the algae release Paramecium from competition with Colpidium. Jost & Ellner 2000 [35] Predator-prey data are used to analyse model fits. Paramecium-Didinium predator-prey data from the MSc thesis of Veilleux were analysed using a range of predator-prey models. Significantly better fits were found when predator dependence on the functional response and time-lags on the prey and predator reproductive rates were included. Kozlova et al [36] Jiang & Kulczycki 2004 [37] Functional response type affects the qualitative output of predator-prey models. Different qualitative responses were obtained using different functional responses, highlighting the importance of functional response selection. Prey competition and not predation affects the response of a microcosm to environmental change. This study examines temperature effects on Paramecium, Didinium, and Colpidium. Chakraborty et al [38] Prey-taxis is simulated using a modified predator-prey model. The model is based on Paramecium-Didinium as model organisms. Worsfold et al [39] Generalist-predator removal increases prey biomass only when a specialist-predator is present. The effect of predator removal in microcosms is investigated using Paramecium, Didinium, and Stentor. Species loss from a high trophic level is context dependent. Minter et al [40] Predator mortality is prey density dependent. There is a strong concave decline in Didinium mortality rate with increasing Paramecium abundance. Inclusion of variable mortality rate on Paramecium-Didinium alters population in models. Krivan 2011 [41] Refugia and functional response type alters population dynamics. A reanalysis of a predator-prey model (Gause et al. 1936) [6] with refuge (Type III functional response). Cooper et al [42] Habitat fragmentation influences population stability. Habitat fragmentation produced stability in a system that becomes extinct in a homogenous environment. It is concluded that fragmentation causes structural heterogeneity which effects stability of the predator-prey system. 6

7 Electronic supplement References 1 Montagnes D. J. S, Roberts E., Lukes J. & Lowe C. D The rise of model protozoa. Trends Microbiol. 20, (doi: /j.tim ) 2 Gause, G. F. 1934a Experimental analysis of Vito Volterra s mathematical theory of the struggle for existence. Science 79, (doi: /science a) 3 Gause, G. F. 1934b The Struggle for Existence. Williams & Wilkins, Baltimore, USA. 4 Mast, S. O. & Ibara, Y The effect of temperature, food, and the age of the culture on the encystment of Didinium nasutum. Biol. Bull. 45, (doi: 5 Beers, C. D Encystment and the life cycle in the ciliate Didinium nasutum. PNAS 11, (doi: 6 Gause, G. F., Smaragdova, N. P. & Witt, A. A Further studies of interactions between predators and prey. J. Anim. Ecol. 5, (doi: 7 Beers, C. D The viability of ten-year-old Didinium cysts (Infusoria). Am Nat. 71, (doi: 8 Beers, C. D The excystment process in the ciliate Didinium nasutum. J. Elisha Mitchell Sci. Soc. 61, (doi: 9 Evans, F. R Competition for food between two carnivorous ciliates. Trans. Am. Microsc. Soc. 77, (doi: 10 Burbanck, W. D. & Eisen, J. D The inadequacy of monobacterially-fed Paramecium aurelia as food for Didinium nasutum. J. Protozool. 7, (doi: /j tb00730.x) 11 Butzel, H. M. & Bolten, A. B The relationship of the nutritive state of the prey organism Paramecium aurelia to the growth and encystment of Didinium 7

8 nasutum. J. Eukaryot. Microbiol. 15, (doi: /j tb02118.x) 12 Harrison, G. W Comparing predator-prey models to Luckinbill s experiment with Didinium and Paramecium. Ecology 76, (doi: 13 Wessenberg, H. & Antipa, G Capture and ingestion of Paramecium by Didinium nasutum. J. Eukaryot. Microbiol. 17, (doi: /j tb02366.x) 14 Luckinbill, L. S Coexistence in laboratory populations of Paramecium aurelia and its predator Didinium nasutum. Ecology 54, (doi: ) 15 Salt, G. W Predator and prey densities as controls of the rate of capture by the predator Didinium nasutum. Ecology 55, (doi: http: //dx.doi.org/ / ) 16 Luckinbill, L.S The effects of space and enrichment on a predator-prey system. Ecology 55, (doi: 17 Salt, G.W Changes in the cell volume of Didinium nasutum during population increase. J. Eukaryot. Microbiol. 22, (doi: /j tb00953.x) 18 Maly, E. J Stability of the interaction between Didinium and Paramecium: effects of dispersal and predator time lag. Ecology 59, (doi: 19 Luckinbill, L. S Regulation, stability, and diversity in a model experimental microcosm. Ecology 60, (doi: 20 Salt, G.W. (1979). Density, starvation, and swimming rate in Didinium populations. Am. Nat. 113, (doi: 21 Veilleux, B. G An analysis of the predatory interaction between Paramecium and Didinium. J. Anim. Ecol. 48, (doi: 8

9 22 Berger, J Feeding behaviour of Didinium nasutum on Paramecium bursaria with normal or apochlorotic zoochlorellae. J. Gen. Microbiol. 118, (doi: / ) 23 Hewett, S. W. (1980a). Prey-dependent cell size in a protozoan predator. J. Eukaryot. Microbiol. 27, (doi: /j tb04263.x) 24 Hewett, S. W. 1980b The effect of prey size on the functional and numerical responses of a protozoan predator to its prey. Ecology 61, (doi: 25 Graham, J. M. & Canale, R. P Experimental and modelling studies of a four-trophic level predator prey system. Microbial. Ecol. 8, (doi: / BF ) 26 Antipa, G. A., Martin, K. & Rintz, M. T A note on the possible ecological significance of chemotaxis in certain ciliated protozoa. J. Eukaryot. Microbiol. 30, (doi: /j tb01033.x) 27 Hewett, S. W Prey size and survivorship in Didinium nasutum (Ciliophora: Gymnostomatida). Trans. Am. Microsc. Soc. 106, (doi: 28 Hewett, S. W Predation by Didinium nasutum: effect of predator and prey size. Ecology 69, (doi: 29 Harrison, G. W Comparing Predator-Prey Models to Luckinbill's Experiment with Didinium and Paramecium. Ecology 76, Rosenzweig, M. L. & MacArthur, R. H Graphical representation and stability conditions of predator-prey interactions. Am. Nat. 97, (doi: 31 Spencer, M. & Warren, P. H The effects of habitat size and productivity on food web structure in small aquatic microcosms. Oikos 75, (doi: / ) 32 Warren, P. H. 1996a The effects of between-habitat dispersal rate on protist communities and metacommunities in microcosms at two spatial scales. 9

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