Modeling population dynamics of yeast-like symbionts (Ascomycota: Pyrenomycetes: Clavicipitaceae) of the planthopper Delphacodes kuscheli (Hemiptera: Delphacidae)

Delphacodes kuscheli establish mutualistic relationship with yeast-like symbionts (YLS) that live in the fat body and are necessary for host survival and reproduction. We estimated for a host of age t, its body weight, W₍ₜ₎, and the number of YLS per host, YLS₍ₜ₎. The host body weight was calculated as: W₍ₜ₎ = Lm/[1+ e ⁽ᵈ–ᵏᵗ⁾], (Lm = the maximum observed weight, and d and k are constants), and the fat body was considered a fixed proportion of W₍ₜ₎. We calculated the number of YLS per unit host body mass: α₍ₜ₎ = YLS₍ₜ₎/W₍ₜ₎. We also calculated the number of YLS per host, cYLS₍ₜ₎, and analyzed the pattern of variation in both sexes adapting the expression of the logistic model: cYLS₍ₜ₎ = KNₒeʳᵗ/K+(eʳᵗ -1)Nₒ, (Nₒ = initial number of YLS, r = intrinsic per capita rate of natural increase, and K = variable carrying capacity). In females the carrying capacity varied according to a constant proportion of the host’s weight: K₍ₜ₎ = αW₍ₜ₎. In males α₍ₜ₎ was considered a decreasing function of the host age: K₍ₜ₎ = α₍ₜ₎W₍ₜ₎. The coefficients No, α, and r were subjected to parameterization. We found that the patterns of W₍ₜ₎ and YLS₍ₜ₎ of D. kuscheli were similar to other planthoppers. In females YLS increased up to the adult stage and then remained almost constant, varying similarly to individual weight. In males YLS increased up to the 5th instar nymph as the individual weight did, but the number of YLS decreased in the adult stage and the correlation was not so good. The calculated number of YLS per host matches reasonably well with the number estimated experimentally both in females and males. This is the first study that quantified and modeled the dynamics of YLS endosymbionts in a Neotropical planthopper pest. The models will be used in future studies for better understand the experimental reduction of YLS in young nymphal stages.