Publisher Correction: Modeling the ecology of parasitic plasmids

Correction to: The ISME Journal

10.1038/s41396-021-00954-6

Owing to errors in production, the original version of this article unfortunately contained mistakes. The equations were not properly labeled:

$$\frac{d\rho }{dt}=\alpha C\rho -{\gamma }_{\mathrm{c}}\rho {\rho }_{\mathrm{p}}+p_{\ell }\left(1-\mathrm{\Delta }\right)\alpha C{\rho }_{\mathrm{p}}-\delta \rho ,$$ 1

$$\frac{d{\rho }_{\mathrm{p}}}{dt}=\left(1-\mathrm{\Delta }\right)\alpha C{\rho }_{\mathrm{p}}+{\gamma }_{\mathrm{c}}\rho {\rho }_{\mathrm{p}}-p_{\ell }\left(1-\mathrm{\Delta }\right)\alpha C{\rho }_{\mathrm{p}}-\delta {\rho }_{\mathrm{p}},$$ 2

$$\frac{dC}{dt}=S-\alpha C\rho -\left(1-\mathrm{\Delta }\right)\alpha C{\rho }_{\mathrm{p}}.$$ 3

$${\gamma }_{\mathrm{c}}{\rho }^{*}>\delta \mathrm{\Delta }+\delta p_{\ell }\left(1-\mathrm{\Delta }\right),$$ 4

$$\frac{d\rho }{dt}=\alpha C\rho -{\gamma }_{\mathrm{t}}\rho P+p_{\ell }\left(1-\mathrm{\Delta }\right)\alpha C{\rho }_{\mathrm{p}}-\delta \rho ,$$ 5

$$\frac{d{\rho }_{\mathrm{p}}}{dt}=\left(1-\mathrm{\Delta }\right)\alpha C{\rho }_{\mathrm{p}}+{\gamma }_{\mathrm{t}}\rho P-p_{\ell }\left(1-\mathrm{\Delta }\right)\alpha C{\rho }_{\mathrm{p}}-\delta {\rho }_{\mathrm{p}},$$ 6

$$\frac{dC}{dt}=S-\alpha C\rho -\left(1-\mathrm{\Delta }\right)\alpha C{\rho }_{\mathrm{p}},$$ 7

$$\frac{dP}{dt}=n_{\mathrm{eff}}\delta {\rho }_{\mathrm{p}}-{\gamma }_{\mathrm{t}}\rho P-{\delta }_{\mathrm{p}}P.$$ 8

$${\gamma }_{\mathrm{t}}{\rho }^{*}>{\delta }_{\mathrm{p}}\left(\frac{\mathrm{\Delta }+p_{\ell }\left(1-\mathrm{\Delta }\right)}{n_{\mathrm{eff}}-\mathrm{\Delta }-p_{\ell }\left(1-\mathrm{\Delta }\right)}\right).$$ 9

$$p_i=\frac{n_0{w}_0\left(1-q\right)}{{\sum }_{j=0}^{\infty }{n}_j{w}_j}i=0,$$ 10

$$p_i=\frac{n_i{w}_i\left(1-q\right)+n_{i-1}{w}_{i-1}q}{{\sum }_{j=0}^{\infty }{n}_j{w}_j}i>0.$$ 11

The original article has been corrected.