The model

An individual-based model (IBM) was designed to investigate the influence of some populational parameters on the colonization success of a new host species. During simulations, pathogens with variable propagule sizes, reproduction rates, and rates of emergence of phenotypic novelties were challenged by new host species representing different levels of compatibility (which are related to the selection pressure that the new host represents). The consumer-resource system can be applied to several different types of symbioses and ecological associations; for simplicity, hereafter we will designate these as the host-pathogen interaction. The model (written in Fortran) is available through Github (https://github.com/sofiagalvao2020/SimpleHost_switching).

Pathogen and host descriptions:

Each pathogen i is described by a compound phenotype (=fundamental capacity space as defined in Agosta and Brooks 2020) of G binary individual phenotypes. The binary phenotypes can assume the values of either one or zero, which can be understood as the expression of two distinct traits within the same locus or set of loci. The sum of all characters defines the individual’s compound phenotype (=realized capacity space of Agosta and Brooks 2020), which can vary between 0 and G. This capacity space is composed by inheritable features, subjected to change over generations, and under selection according to its compatibility to the host. The compound phenotype is labeled as pi,n , in which the subscripts identify the pathogen i of the generation n . For the beginning of the simulation, the sum of all “loci” is identical for all propagule individuals- creating a standard populational compound phenotype p0 at the start of the colonization attempt.
For simplicity, as in Araujo et al. (2015), the host is characterized by a single number (ph ) which represents the optimum value of the compound phenotype imposed on pathogens. It is a fixed throughout the simulation. Here we assume ph = G/2. Besides defining an interaction pressure around this optimum value, the host is also represented by a carrying capacity on the pathogen population of K individuals.

Dynamics

The dynamics starts with a propagule size of N0pathogen individuals challenged to colonize the host - there is only one colonization attempt per simulation. For simplicity, their phenotypes are randomly defined, but when more than one pathogen individual is considered, they present identical compound phenotypespi,n=0 =p0i – that is, they have the same fitness in the new host but carry different phenotypes (i.e. represent distinct fundamental capacity space ). Each iteration step represents a generation n where the pathogens will undergo Selection and Reproduction (Fig 1), as detailed below.

Selection

The selection is imposed as the survival probability of each pathogeni in a given generation n and it follows a normal distribution:
\(P_{\text{survival}}=exp\left[\frac{-{{d{}^{2}}_{i,n}}}{2}\right]\), (1)
where
\(d_{i,n}=\frac{p_{i,n}-\text{\ p}_{h}}{\sigma}\) (2)
is the distance between the pathogen compound phenotype (pi,n ) and the optimum imposed by the host (ph ) in units of the deviation rate (σ). The deviation rate represents the selection strength imposed by the new host - the larger the deviation rate, the larger is the diversity of phenotypes that are capable of surviving on that specific host (Fig 1). For the propagule population - with all individuals presenting the same compound phenotype p0 - the initial phenotype distance from the propagule to the host isd0= (p0 -ph )/ σ. The model imposes this survival probability (Eq. 1) to every individual, and the survivors (Ns,n ) go to the next model step, Reproduction .

Reproduction

At this step, the pathogens that survived the previous step (Ns,n ) produce offspring depending on the reproduction rate (b, the average number of descendants per parental) and the carrying capacity (K ). For simplicity, we assume asexual reproduction. The number of descendants for the next generationn+1 will be Ns,n*b if this value does not exceed K , otherwise, the number of descendants is K . Random individuals of the surviving population are selected to generate one offspring with reposition - the progenitor can be selected more than once. This process is repeated until the total number of descendants is achieved. Each descendant inherits the same chain of characters of its progenitor with a probability μ of incorporating a novelty per locus (i.e. changing from 0 to 1 or from 1 to 0). After all reproduction events, the progenitors die and the descendants constitute the next generation that will be subjected to the new Selection andReproduction cycle (Fig 1).
The rate novelty emergence (μ) refers to any kind of novelty introduced into the pool of capacity of the individual, indirectly influencing the pathogen’s fitness to the host. These evolutionary novelties can emerge, accumulate, and be maintained throughout generations simulating inheritance mechanisms, comprising thecapacity space of the pathogen (called information spacein Brooks and Agosta 2012, Jablonka et al. 2014, Brooks et al. 2019; see also Agosta and Brooks 2020). We refrain from using “mutation rate” - as opposed to “rate of emergence of evolutionary novelty” - to avoid the strictly genetic meaning of the expression used in the Modern Synthesis (see Brooks and Agosta 2012; Laland et al. 2015; Agosta and Brooks 2020).

Simulations and data analyses

For each parameter combination, we ran 700 simulation repetitions for 1,000 generations or until the pathogen population went extinct. We then calculated the proportion of simulations without extinction and defined it as the probability of successful establishment . The sensibility of the probability of successful establishment to each parameter was calculated by varying two of them and fixing the remaining ones (the fixed values are highlighted in Table 1). The parameterp0 was always one of the varied parameters and it varied between the fittest (p0=ph=G/2 ) to the least fit value (p0 =G ). Given that the propagule survival probability (Eq. 1) depends only on d0 , we fixed\(\sigma=10\ \)and, as a consequence, the propagule compound phenotype distance from the host varied according to\(0{\leq d}_{0}\leq G/20\). The investigated values of novelty rate (μ ) are 0, 10-6,10-5, 10-4, 10-3, 10-2,and 10-1. Higher novelty values, such as 10-2 and 10-1 are considered analogs of the high mutation rates observed in viruses (e.g. Drake and Holland 1999). Furthermore, although biologically unreal, the null value forμ represents the inferior limit of our analysis. We also varied the reproduction rate (b ), propagule size (N0 ,), compound phenotype size (G ), and carrying capacity (K ) (Table 1). Our simulations were qualitatively invariable for the parameters G and K - only results in varying b , μ , N0, andd0 are presented.