Research ArticlePARASITOLOGY

Host-parasite Red Queen dynamics with phase-locked rare genotypes

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Science Advances  04 Mar 2016:
Vol. 2, no. 3, e1501548
DOI: 10.1126/sciadv.1501548
  • Fig. 1 Population density time series illustrating Red Queen dynamics with phase-locked rare types (K = 40, σ = 0).

    Host 1 (parasite 1) and host 2 (parasite 2) have out-of-phase cycles with dominant amplitude, whereas the rest are inferior and phase-locked. We call the cyclic dominance between the two dominant species types as “Red Queen binary oscillations.” Some inferior phase-locked population plots are not visible because they have almost similar periods and amplitudes as the time series plotted in front of them. The qualitative behaviors of both host and parasite population time series follow Red Queen binary oscillations. (A) n = 3. (B) n = 5. (C) n = 10.

  • Fig. 2 Effects of host basal growth rate (ri = r) and parasite mortality rate (dj = d) on the generation of Red Queen binary oscillations (K = 40, σ = 0).

    Vertical alternating colors characterize oscillations. (A) A high host basal growth rate r favors the occurrence of Red Queen binary oscillations (for example, r > 0.5; d = 0.5). A lower basal growth rate may result in host extinction or in population dynamics where only one type is dominant. (B) An intermediate parasite mortality rate d favors the occurrence of Red Queen binary oscillations (for example, d = 0.5; r = 1). Relatively low and high death rates may result in host extinction or in population dynamics where only one host type is dominant.

  • Fig. 3 Illustration of Red Queen dynamics with noise (n = 3, K = 25, σ = 15%).

    Here, Red Queen dynamics are represented by winnerless coevolution between two dominant cyclic host/parasite types (binary oscillations). The evolution due to random noise is characterized by a stochastic transition event where a rare cyclic host/parasite type (H3, P3) replaces one of the dominant cyclic types (H2, P2). The transition event is a result of the accumulated effect of random noise representing uncertain physical-environmental perturbations.

  • Fig. 4 Evolutionary landscape separated into two regions by an entrapment barrier.

    The height of the landscape characterizes the population density of species types (balls). The barrier limits the number of dominant cyclic types and constrains subordinate/rare cyclic types to enter the optimal region where Red Queen dynamics occur. In the optimal region, a dominant cyclic type can attain maximum growth potential near its carrying capacity. The population dynamics of the species oscillate (phase-locked subordinate cycles and Red Queen dynamics) as a result of parasitism (the paths of broken arrow lines illustrate oscillatory behavior). (A) Rare cyclic types remain rare because they are trapped at a suboptimal region. Only two species types undergo cyclic dominance of Red Queen dynamics. The population dynamics of rare cyclic types do not exhibit Red Queen dynamics but rather are phase-locked (synchronized). (B) Physical-environmental variability can allow a rare cyclic type to escape the suboptimal region and enter the optimal region by hurdling the evolutionary entrapment barrier. However, the optimal region only allows two dominant cyclic types; hence, one of the types needs to leave the optimal region to accommodate the succeeding rare type (red and green balls).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/3/e1501548/DC1

    Supporting text

    Table S1. Summary of state variables and model parameters.

    Fig. S1. Example of canonical Red Queen dynamics (Red Queen n-ary oscillations) where all host and parasite types undergo dominance switching.

    Fig. S2. Oscillatory behavior expected to occur when α has a lower value (that is, there is a higher level of parasite specificity).

    Fig. S3. Parameter diagram showing the effects of increasing the host’s carrying capacity K on the oscillation patterns of host and parasite population densities (σ = 0, t = 0 to 50,000).

    Fig. S4. Increasing the carrying capacity K increases the amplitude of population density (for example, compare the graphs associated with K = 3 and K = 10; σ = 0).

    Fig. S5. Host population density time series showing the effects of stochastic noise (n = 4, K = 16).

    Fig. S6. Host population pattern illustrating the effects of stochastic noise on a system with 10 host types and 10 parasite types (K = 40, σ = 10%).

    Fig. S7. Additional illustrations of some population dynamics that can arise from our host-parasite interaction system (σ = 0).

  • Supplementary Materials

    This PDF file includes:

    • Supporting text
    • Table S1. Summary of state variables and model parameters.
    • Fig. S1. Example of canonical Red Queen dynamics (Red Queen n-ary oscillations) where all host and parasite types undergo dominance switching.
    • Fig. S2. Oscillatory behavior expected to occur when α has a lower value (that is, there is a higher level of parasite specificity).
    • Fig. S3. Parameter diagram showing the effects of increasing the host’s carrying capacity K on the oscillation patterns of host and parasite population densities (σ = 0, t = 0 to 50,000).
    • Fig. S4. Increasing the carrying capacity K increases the amplitude of population density (for example, compare the graphs associated with K = 3 and K = 10; σ = 0).
    • Fig. S5. Host population density time series showing the effects of stochastic noise (n = 4, K = 16).
    • Fig. S6. Host population pattern illustrating the effects of stochastic noise on a system with 10 host types and 10 parasite types (K = 40, σ = 10%).
    • Fig. S7. Additional illustrations of some population dynamics that can arise from our host-parasite interaction system (σ = 0).

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