Code and Data for: Importance of environmental productivity and diet quality in intraguild predation
Data files
Abstract
In the intricate network of ecological interactions, intraguild predation emerges as a fundamental community module incorporating omnivory. Classical equilibrium theory predicts the exclusion of the intraguild predator and prey at low and high environmental productivity, respectively, with the coexistence of both species occurring only at intermediate productivity levels. However, empirical studies challenge this theoretical prediction, particularly concerning the extinction of intraguild prey in highly productive environments. To address this enigmatic issue, Diehl (2003) and Abrams and Fung (2010a) explore the impact of food quality and propose that low nutritional quality of the basal resource stabilizes omnivorous systems. Yet, the influence of intermediate consumer quality remains inadequately explored. This study employs analytical and numerical bifurcation studies to investigate the effects of the quality of two diet types. Various bifurcations, including supercritical and subcritical Hopf bifurcations, saddlenode bifurcations of periodic solutions, and transcritical bifurcations of periodic solutions are observed. These bifurcations are directly linked to the destinies of intraguild prey and predators. The results reveal that, in highly productive environments, it may not be the intermediate consumer but the omnivore that faces extinction. This discovery holds significant implications for the conservation and management of omnivorous systems.
Dataset DOI: 10.5061/dryad.b8gtht7q4
Description of the data and file structure
This repository encompasses files corresponding to Fig. 1 through Fig. 6, and FigS1 through FigS4, three code scripts in the CODE folder, and this README document. The DATA folder contains subfolders labeled from Fig1 to Fig6, and FigS1 to FigS4, housing data essential for constructing bifurcation diagrams.
DATA
Equilibrium values are documented in files named REq.dat, RCEq.dat, RPEq.dat, and RCPEq.dat. Data files for insets are prefixed by “Inset,” and data files for a linear chain in Fig. 6 are prefixed by “LC_.”
Each file for equilibrium values begins with four lines specifying the model’s parameter values. The first line encompasses the intrinsic growth rate, carrying capacity of the basal resource, and mortalities of the consumer and predator. The second to fourth lines capture information on the attack rate, handling time, and conversion efficiency concerning the resource by the consumer, the resource by the predator, and the consumer by the predator, respectively.
The subsequent lines provide information on stability flags (-1 for stable, +1 for unstable), followed by the bifurcation parameter and the densities of the resource, consumer, and predator at the equilibrium point. The bifurcation parameter is the carrying capacity in Fig.1 to Fig.6, conversion efficiency eRP in Figs. S1 and S2, and conversion efficiency eCP in Figs. S3 and S4.
The files conclude with the identifier “-99999.”
In each DATA folder, files such as RCStableLimitCycle, RCUnstableLimitCycle, RPStableLimitCycle, RCPStableLimitCycle, and RCPUnstableLimitCycle contain information on limit cycles. Data files for insets are prefixed by “Inset,” and data files for a linear chain in figure 6 are prefixed by “LC_.”
Each of these files commences with the first four lines delineating parameter values of the model, following the same structure as the files for the equilibrium values. The subsequent five lines provide specific details about the limit cycle. The fifth line specifies the bifurcation parameter: the carrying capacity of the basal resource in Fig.1 to Fig.6, the conversion efficiency eRP in Figs. S1 and S2, and conversion efficiency eCP in Figs. S3 and S4. The sixth line contains information on the initial densities of the resource, consumer, and predator, along with the period of the limit cycle. The successive three lines provide details on the bifurcation parameter, and the minimum, mean, and maximum values of the resource, consumer, and predator, respectively. These five lines are iterated as necessary for a comprehensive description of the bifurcation diagram. The files conclude with the identifier “-99999.”
CODE
The CODE folder contains three C-language programs.
1. RCPLimitCycles.c
This program solves a limit cycle of three species coexistence, using Newton’s iteration method.
2. RCLimitCycles.c
This program solves a limit cycle of the basal resource and consumer, using Newton’s iteration method.
3. RPLimitCycles.c
This program solves a limit cycle of the basal resource and predator, using Newton’s iteration method.
This folder also includes six data files from sampledata3_1.dat to sampledata3_6.dat.
The first four lines of the files delineate the model’s parameter values, similarly as in files in folders from Fig1 to Fig6, FigS1 to S4. The fifth line describes the number of the candidate’s initial points. The sixth line denotes the number of candidate values of the bifurcation parameter (K in figure 3) and its initial value and increment. From the seventh line, candidate initial values are written for the basal resource and consumer in sampledata3_1.dat and sampledata3_2, for the consumer in sampledata3_3.dat and sampledata3_4, and the predator in sampledata3_5.dat and sampledata3_6.dat.
To generate Figure 3, for example, numerical explorations are conducted using the above programs. For instance, RCPLimitCycle.c is executed with sampledata3_1.dat, incorporating four candidate initial points, to obtain a coexistence limit cycle for K=22. Subsequently, substituting the seventh line of sampledata3_2.dat with the above result, the program was further executed with sampledata3_2.dat to gather information on coexistence limit cycles for K values ranging from 22 to 30.
For insights into the limit cycles of the resource and consumer, RCLimitCycles.c is utilized with sampledata3_3.dat, and the result is used to modify the seventh line of sampledata3_4.dat. Then, RCLimitCycles.c is executed with sampledata3_4.dat to find limit cycles covering K values from 22 to 30. Similarly, information on the limit cycles of the resource and predator for the same range of K values is obtained by running RPLimitCycles.c, first with sampledata3_5.dat, and next with the modified sampledata3_6.dat based on the former result.
This sequential process is iterated for K values below 22, ensuring comprehensive coverage for Figure 3. The resulting data provide a detailed depiction of the bifurcations in the ecological system under investigation.
Figs. S1 to S4 can be created using similar procedures with eRP or eCP as bifurcation parameters instead of K.
Code/software
C-language