Predator-prey persistence is thought to be enhanced by spatial heterogeneity. Theory predicts that metacommunity size, spatial connectivity, network synchrony, predator identity, and productivity influence predator-prey persistence, through a variety of mechanisms such as statistical stabilization, colonization-extinction dynamics, and trophic interactions. However, comparative tests and synthesis of the multiple factors and mechanisms across different spatial networks are needed to understand which factors and mechanisms of spatial network structure promote predator-prey persistence. To address this gap between theory and empirical work, we synthesized data from 22 microcosm experiments of protist predator-prey communities differing the productivity, connectivity, and size of spatial habitat structure. Prey time to extinction was better explained by productivity and spatial factors than predator time to extinction. At the local and regional scale, metacommunity size and productivity had positive effects on prey occupancy, whereas connectivity negatively influenced prey occupancy. For predators, metacommunity size and connectivity had positive effects on predator occupancy, network synchrony had negative influences, and productivity showed a hump-shaped relationship with predator occupancy. Further, trophic interactions drove variation in the way species were spatially structured, where the strength and direction of predator and prey occupancy relationships varied among productivity levels and predator-prey combinations. In predator-prey interactions that were stronger, prey occupancy showed negative relationship with predator occupancy regardless of productivity. However, in predator-prey interactions that were weaker, prey occupancy was positively related to predator occupancy at low productivity, and this relationship disappeared at higher productivity treatments where prey occupancy was high regardless of predator occupancy. Predictions from metapopulation theory explained predator occupancy, while prey were better explained by trophic dynamics. Taken together, these results highlight that spatial network structure has a complex, spatially contingent relationship with predator-prey dynamics.

We conducted a data synthesis on experimental studies that manipulated aspects of spatial network structure (i.e. connectivity and metacommunity size) and measured this effect on predator-prey dynamics. We focused our data synthesis on protist microcosm experiments that were conducted with predator-prey species in spatially connected metacommunities that allowed for active dispersal of protozoa (rather than passive dispersal via pipetting) and sampled at high temporal frequencies. We utilized a suite of previously unpublished experiments through our laboratory at UC Riverside (Anderson Lab, unpublished; Green et al. in press) and also through publicly available data (Holyoak, 2000; Holyoak & Lawler, 1996). A total of 22 experiments representing 16 unique spatial network structures were included in this analysis (Figure 1; Table 1).

Experimental Methods: Full details of methods conducted for the data used in this synthesis can be found in the original papers (Holyoak and Lawler 1996, Holyoak 2000, Green et al. in press), but we summarize these methods below. We studied the predator-prey dynamics of three groups of predators and prey in a spatial context: 1) Euplotes eurystomus and Tetrahymena pyriformis, 2) Didinium nasutum and Colpidium striatum, 3) Didinium nasutum and Paramaecium aurelia. E. eurystomus is an omnivorous ciliated protist that feeds on smaller protozoa species as well as bacteria (Naeem & Li, 1998). T. pyriformis is a smaller (~50mm) ciliated protist that naturally feeds on bacteria and grows approximately logistically in the absence of other ciliates (Doerder & Brunk, 2012). Didinium is a voracious predator that naturally feeds on both Colpidium and Paramaecium in natural systems (Holyoak, 2000; Veilleux, 1979). All these protist species naturally co-occur in aquatic environments and form trophically structured communities (McGrady-Steed et al. 1997).

Individual protist microcosm “communities” were 175mL or 32mL polypropylene Nalgene bottles that were linked by silicon rubber tubing that allows for natural, active movement of materials and individuals to bottles they are connected to. Each network has its own unique design and connections but were generally attached using 11cm tube lengths except when geometric constraints prevented this in the ring lattice treatment (Figure 1k). For all experiments, each network had four replicates. The protist medium used in experiments varied among a higher and lower productivity medium and was used as a factor potentially explaining differences in persistence times. Medium was composed of 1000mL of water, 0.2g of reptile food, and either 1) 1.28g of protozoan pellet (high productivity) or 2) 0.56g of protozoan pellet (medium productivity). Twenty-four hours after autoclaving the protist medium, three freshwater species of bacteria were inoculated in this medium: Bacillus subtillis, Bacillus cereus, and Serratia macescens.

Each Nalgene bottle was filled with either 50mL or 30mL, depending on the size of Nalgene bottle used, of protist medium with associated bacteria species and one boiled wheat seed, which provides ample nutrients to bacteria throughout the experiment. Prey species were initially added to the experiment from a stock culture at carrying capacity. After two days, predator species were added in low densities from a stock culture at carrying capacity to all bottles. Sampling of experiments followed standard protist microcosm procedures (Altermatt et al., 2015) and consisted of mixing the community, pipetting five to ten μl drops (~0.032 mL/drop) of the community, weighing the sample, and counting the total number of each species under a microscope. For studies involving Didinium, 3mL of the community was sampled for predator densities. Sampling of protist microcosms occurred three times per week for a period of more than 75 day. Each week, sterile medium (without bacteria) was replaced in each microcosm to remove waste buildup, replenish carbon supply, and replace sampled medium.

Due to differences in experimental time among treatments, we cut off experiments at day 75 as all experiments ran at a minimum for this time length. We controlled for differences in the size of bottles used among Holyoak (2000) and Anderson lab (unpublished) experiments, by using the number of bottles as a proxy for metacommunity size. Because the total number of bottles and total volume were highly correlated, we used total number of bottles to represent metacommunity size. For response variables, species density accounted for differences in the volume used amongst experiments although we did not correct for difference in volumes for occupancy as it is a binomial variable.

Spatial Metrics: Connectivity was defined as nearest neighbors’ connectivity, where for each focal bottle, the average number of connections for directly connected neighbors was taken (Gilarranz & Bascompte, 2012; Melián & Bascompte, 2002). Metacommunity size was determined by the total number of bottles per spatial network. Although the volume varied among experimental treatments from 50mL to 32mL in local communities, total volume was highly correlated with total number of bottles and is more reflective of that used in the literature. We also used spectral theory to characterize spatial structures, which we call network synchrony. This approach utilizes the eigenvalues (λ) and eigenvectors generated from the spatial structure matrix as a Laplacian matrix. The eigenratio, or the largest eigenvalue to the smallest non-zero eigenvalue , can determine the stability of a metacommunity’s synchronized state (Barahona & Pecora, 2002; Barrat et al., 2008; Hayes & Anderson, 2018; Yeakel et al., 2014).