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\begin{document}

\title{``Accidents waiting to happen'' -- insights from a simple model on the
emergence of infectious agents in new hosts.}



\author[1]{Sofia Feronato}%
\author[1]{Sabrina Araujo}%
\author[1]{Walter A. Boeger}%
\affil[1]{Universidade Federal do Paraná}%


\vspace{-1em}



  
  \date{May 15, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
This study evaluates through modeling the possible individual and
combined effect of three populational parameters of pathogens
(reproduction rate; rate of novelty emergence; and propagule size) on
the colonization of new host species -- putatively the most fundamental
process leading to the emergence of new infectious diseases. The results
are analyzed under the theoretical framework of the Stockholm Paradigm
using IBM simulations to better understand the evolutionary dynamics of
the pathogen population and the possible role of Ecological Fitting. The
simulations suggest that all three parameters positively influence the
success of colonization of new hosts by a novel parasite population but
contrary to the prevailing belief, the rate of novelty emergence (e.g.
mutations) is the least important factor. Maximization of all parameters
result in a synergetic facilitation of the colonization and emulates the
expected scenario for pathogenic microorganisms. The simulations also
provide theoretical support for the retention of the capacity of
fast-evolving lineages to retro-colonize their previous host
species/lineage by ecological fitting. Capacity is, thus, much larger
than we can anticipate. Hence, the results support the empirical
observations that opportunity of encounter (i.e. the breakdown in
mechanisms for ecological isolation) is an fundamental determinant to
the emergence of new associations - in special of Emergent Infectious
Diseases - and the dynamics of host exploration, as observed in
SARS-CoV-2. Insights on the dynamics of Emergent Infectious Diseases
derived from the simulations and from the Stockholm Paradigm are
discussed.%
\end{abstract}%



\sloppy


\textbf{``Accidents waiting to happen'' -- insights from a simple model
on the emergence of infectious agents in new hosts.}

\textbf{Running Title:} A simple model for the success of emergence of
infectious pathogens

Sofia G. Feronato\textsuperscript{1}, Sabrina
Araujo\textsuperscript{1,2}, Walter A. Boeger\textsuperscript{1,3*}

\textsuperscript{1} Biological Interactions, Universidade Federal do
Paran\selectlanguage{ngerman}á, Curitiba, PR 81531-980, Brazil.

\textsuperscript{2} Dept de Física, Universidade Federal do Paraná,
Curitiba, PR 81531-980, Brazil.

\textsuperscript{3} Dept de Zoologia, Universidade Federal do Paraná,
Caixa Postal 19020, Curitiba, PR 81531-980, Brazil.

*Corresponding author: Walter A Boeger, wboeger@gmail.com, fone:
+554199985055

\textbf{Summary:} This study evaluates through modeling the possible
individual and combined effect of three populational parameters of
pathogens (reproduction rate; rate of novelty emergence; and propagule
size) on the colonization of new host species -- putatively the most
fundamental process leading to the emergence of new infectious diseases.
The results are analyzed under the theoretical framework of the
Stockholm Paradigm using IBM simulations to better understand the
evolutionary dynamics of the pathogen population and the possible role
of Ecological Fitting. The simulations suggest that all three parameters
positively influence the success of colonization of new hosts by a novel
parasite population but contrary to the prevailing belief, the rate of
novelty emergence (e.g. mutations) is the least important factor.
Maximization of all parameters result in a synergetic facilitation of
the colonization and emulates the expected scenario for pathogenic
microorganisms. The simulations also provide theoretical support for the
retention of the capacity of fast-evolving lineages to retro-colonize
their previous host species/lineage by ecological
fitting.\textbf{Capacity} is, thus, much larger than we can anticipate.
Hence, the results support the empirical observations that
\textbf{opportunity}of encounter (i.e. the breakdown in mechanisms for
ecological isolation) is an fundamental determinant to the emergence of
new associations - in special of Emergent Infectious Diseases - and the
dynamics of host exploration, as observed in SARS-CoV-2. Insights on the
dynamics of Emergent Infectious Diseases derived from the simulations
and from the Stockholm Paradigm are discussed.

\textbf{Keywords:} Individual-based model, host-switching, emerging
infectious diseases, Stockholm Paradigm.

\section*{Introduction}

{\label{introduction}}

Understanding the ecological mechanisms influencing the origin and
evolution of host-pathogen associations is fundamental and it became a
vigorous area of research in human health, agriculture, and food
security, during recent years (Heard and Hauser, 1995; Woolhouse et al.,
2005; Brooks et al., 2014). These studies are of special interest,
considering the so-called crisis of Emerging Infectious Diseases (EIDs),
present and future (Brooks et al., 2019). This crisis is the fulfilling
of the prediction that EIDs are ''accidents waiting to happen'' (Brooks
and Ferrao, 2005).

However, such studies are strongly influences by the researcher's
perspective of its accepted theoretical evolutionary framework (see a
summary of this under a historical perspective in Nylin et al. 2018;
Brooks and Boeger 2019; Brooks et al. 2019; Agosta and Brooks 2020),
often influenced by the perspective that parasites are ultimate
specialists (Agosta et al., 2010). Traditionally, the nature of
host-parasite/pathogen associations is regarded as a symmetrically
selective interaction built under a 1:1 relation in a context of strong
selective pressures (Kaltz and Shykoff, 1998). This vision generated a
paradox - the Parasite Paradox (Agosta et al., 2010). The Parasite
Paradox results from the accumulation of studies on host-parasite
evolution in the last 40 years that, even utilizing protocols strongly
biased towards co-speciation, still detected a large amount of what has
been called to this date as host-switching (Krasnov and Shenbrot 2002;
Hoberg and Brooks 2008; Agosta et al. 2010; De Vienne et al. 2013).
Increasing phylogenetic and historical evidence points out that
expansion in host range (=host repertoire according to Braga et al.
2018) is a primary dynamic in pathogen evolution and ecology. The
complex structure of host-pathogen associations strongly sustain that
the widely held evolutionary paradigm, which has been conceptually
dominant for a century, cannot accommodate the present knowledge on the
origin and evolution of symbiotic associations (Nylin et al., 2018).

The Stockholm Paradigm (Hoberg and Brooks, 2015; Brooks et al., 2019)
provides such a theoretical framework. The fundamental element of this
new perspective on the evolution and ecology of associations is the
recognition that the vast majority of ecological changes occur through
Ecological Fitting (Janzen, 1985a; Agosta and Klemens, 2008). The other
two elements of the Paradigm - the Oscillation Hypothesis (Janz and
Nylin, 2008) and the Taxon Pulse (Erwin, 1985) - are thought to
represent emergent properties of the complex system composed of species
that interact -- with other species or the environment - under the
ability to change by Ecological Fitting (Janzen, 1985; Brooks et al.,
2006; Agosta and Klemens, 2008; Brooks et al., 2019).

Under the framework of the Stockholm Paradigm, Araujo et al. (2015)
developed a mathematical model that evaluated the colonization of new
host species by an evolving population. The simulations support the
postulate that host colonization by Ecological Fitting is likely
ubiquitous. Among other conclusions, Araujo et al. (2015) also suggested
that successful colonizations are not limited to a high degree of
compatibility of the pathogen population to the new host. Support for
this perspective has been recently revealed by empirical experimentation
(Khokhlova et al., 2020). Araujo et al. (2015) also indicate that poorly
adapted pathogens can survive in a new host despite being in a
sub-optimum condition, whereas they did not explicitly explore
populational parameters that might influence the pathogen's colonization
success.

The Stockholm Paradigm was recently expanded to incorporate any process
of ecological change in evolution (Agosta and Brooks, 2020), including
invasive species (Hoberg, 2010), phytophagous insects (Agosta, 2006;
Nylin et al., 2018), ecological associations and community structuring
(Wilkinson, 2004), and plant--bird pollination (Jane\selectlanguage{polish}č\selectlanguage{english}ek et al., 2020).
Colonization of new conditions, reflecting change from the ancestral
selective pressure, most likely occur by ecological fitting in
association to environmental and ecological disruptions (Brooks et al.,
2019) and far less frequently by immediately preceding releasing
mutations (see also Morse 2001).

Hence, in the present work we expand the study of Araujo et al. (2015)
using simulations based on an individual-based model (IBM) considering
elements of the Stockholm Paradigm to explore the significance and
interaction of selected parameters that could be considered important
for the success of colonization of new host species. The model is
focused in host-pathogens systems, as Araujo t al. (2015). Although
methodologically different, it can be applied to equivalent ecological
changes, such as similar studies that developed other type of models to
study, for instance, invasive species (e.g. P\selectlanguage{romanian}ȩkalski 2003). The tested
parameters are the reproduction rate, the rate of novelty emergence
(analogous to mutation rate), and the propagule size of the founder
pathogen population, all of which are frequently considered as key
population parameters in studies of biological invasion and epidemiology
(Woolhouse, 2001; Dobson, 2004; Lockwood et al., 2005; Woolhouse et al.,
2005; Braendle and Flatt, 2006; Hoberg, 2010; Hurford et al., 2010;
Briski et al., 2012; Johnson et al., 2015; Mason, 2016; Gould and
Stinchcombe, 2017).

The resulting simulations strongly support previous accounts on the
process of colonization of new environmental conditions - in this case
of new host-pathogens associations under an ecological perspective - and
provides new insights into the process of emerging infectious diseases.
The overall result of the simulations provides instrumental support to
the recognized crisis of emergence of new infectious diseases (Fauci,
2001; Morens et al., 2004; Brooks and Ferrao, 2005; Brooks et al., 2014;
Hoberg and Brooks, 2015; Mondragon et al., 2018; Morand and Figui\selectlanguage{ngerman}é,
2018).

\section*{The model}

{\label{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).

\subsection*{Pathogen and host
descriptions:}

{\label{pathogen-and-host-descriptions}}

Each pathogen \emph{i} is described by a compound phenotype
(=\emph{fundamental} \emph{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 (=\emph{realized capacity space} of Agosta and Brooks 2020),
which can vary between 0 and G. This \emph{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 \emph{p\textsubscript{i,n}} , in which the
subscripts identify the pathogen \emph{i} of the generation \emph{n} .
For the beginning of the simulation, the sum of all ``loci'' is
identical for all propagule individuals- creating a standard
populational compound phenotype \emph{p\textsubscript{0}} at the start
of the colonization attempt.

For simplicity, as in Araujo et al. (2015), the host is characterized by
a single number (\emph{p\textsubscript{h}} ) which represents the
optimum value of the compound phenotype imposed on pathogens. It is a
fixed throughout the simulation. Here we assume
\emph{p\textsubscript{h}} = 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 \emph{K} individuals.

\subsection*{Dynamics}

{\label{dynamics}}

The dynamics starts with a propagule size of
\emph{N\textsubscript{0}}pathogen 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
phenotypes\emph{p\textsubscript{i,n=0}} =\emph{p\textsubscript{0}} \selectlanguage{english}[?]
\emph{i} -- that is, they have the same fitness in the new host but
carry different phenotypes (i.e. represent distinct \emph{fundamental
capacity space} ). Each iteration step represents a generation \emph{n}
where the pathogens will undergo \emph{Selection} and
\emph{Reproduction} (Fig 1), as detailed below.

\subsubsection*{Selection}

{\label{selection}}

The selection is imposed as the survival probability of each
pathogen\emph{i} in a given generation \emph{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
(\emph{p\textsubscript{i,n}} ) and the optimum imposed by the host
(\emph{p\textsubscript{h}} ) in units of the deviation rate (\selectlanguage{greek}σ\selectlanguage{english}). 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 \emph{p\textsubscript{0}} - the initial phenotype
distance from the propagule to the host is\emph{d\textsubscript{0}=}
(\emph{p\textsubscript{0}} -\emph{p\textsubscript{h}} )/ \selectlanguage{greek}σ. \selectlanguage{english}The model
imposes this survival probability (Eq. 1) to every individual, and the
survivors (\emph{N\textsubscript{s,n}} ) go to the next model step,
\emph{Reproduction} .

\subsubsection*{Reproduction}

{\label{reproduction}}

At this step, the pathogens that survived the previous step (\emph{Ns,n}
) produce offspring depending on the reproduction rate (\emph{b, the}
average number of descendants per parental) and the carrying capacity
(\emph{K} ). For simplicity, we assume asexual reproduction. The number
of descendants for the next generation\emph{n+1} will be
\emph{N\textsubscript{s,n}*b} if this value does not exceed \emph{K} ,
otherwise, the number of descendants is \emph{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 \selectlanguage{greek}\emph{μ} \selectlanguage{english}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 \emph{Selection} and\emph{Reproduction}
cycle (Fig 1).

The rate novelty emergence (\selectlanguage{greek}\emph{μ)}\selectlanguage{english} 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
the\emph{capacity space} of the pathogen (called \emph{information
space}in 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).

\subsubsection*{Simulations and data
analyses}

{\label{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 \emph{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
parameter\emph{p\textsubscript{0}} was always one of the varied
parameters and it varied between the fittest
(\emph{p\textsubscript{0}}=\emph{p\textsubscript{h}=G/2} ) to the least
fit value (\emph{p\textsubscript{0}} =\emph{G} ). Given that the
propagule survival probability (Eq. 1) depends only on
\emph{d\textsubscript{0}} , 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 (\selectlanguage{greek}\emph{μ} \selectlanguage{english}) are 0,
10\textsuperscript{-6},10\textsuperscript{-5}, 10\textsuperscript{-4},
10\textsuperscript{-3}, 10\textsuperscript{-2,}and
10\textsuperscript{-1}. Higher novelty values, such as
10\textsuperscript{-2} and 10\textsuperscript{-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
for\selectlanguage{greek}\emph{μ} \selectlanguage{english}represents the inferior limit of our analysis. We also
varied the reproduction rate (\emph{b} ), propagule size
(\emph{N\textsubscript{0}} ,), compound phenotype size (\emph{G} ), and
carrying capacity (\emph{K} ) (Table 1). Our simulations were
qualitatively invariable for the parameters \emph{G} and \emph{K} - only
results in varying \emph{b} , \selectlanguage{greek}\emph{μ} , \selectlanguage{english}\emph{N\textsubscript{0,}}
and\emph{d\textsubscript{0}} are presented.

\section*{Results}

{\label{results}}

We simulated the success of establishment of the pathogen population
during colonization of a new host and, when pertinent, the evolution of
its compound phenotype under the new selective pressure. Parsing these
components allowed a better understanding of the individual and combined
influence of distinct rates of novelty emergence (\selectlanguage{greek}\emph{μ} \selectlanguage{english}), propagule
size (\emph{N\textsubscript{0}} ), and reproductive rate (\emph{b}
)\emph{\_} on the success of establishment of a new association and the
behavior of the fitness and size of the population of pathogen following
colonization of a new host resource. All analyzed parameters were
evaluated under variable distance of the propagule compound phenotype
from the host (\emph{d\textsubscript{0}} ) and revealed their influence
on the probability of establishment of the pathogen population in the
new host (Fig. 2). For a single propagule (\emph{N\textsubscript{0}}
=1), the increase of \emph{d\textsubscript{0}}gradually reduces the
probability of establishment (Fig. 2a and b) -- which was an expected
result since the survival probability decays following this distance
(black curves in Figs. 2 represent Eq. 1 for the propagule,
\emph{d\textsubscript{i,n}} =\emph{d\textsubscript{0}} ). For the
pathogen population to colonize the new host, it needs to survive
successive selection events - therefore the probability of establishment
is lower than the survival probability recovered for a single colonizing
individual to persist until the first reproduction (the black curve in
Figure 1).

Greater reproduction rates (\emph{b} ) favor the pathogen establishment
(Fig. 2a). As \emph{b} increases, the establishment success approaches
the probability of one individual surviving the selective forces of the
new host species (in Fig. 2a; compare non-black probability curves
approaching the black curve as \emph{b} increases). For high
\emph{b}rates (e.g. \emph{b} = 7.5), the probability of establishment of
the pathogen population will be the same as that expected for a single
individual surviving until the first reproductive event of the
simulation - and the probability of survival will depend only on the
effect of \emph{d\textsubscript{0}} .

Only high novelty rate values (10\textsuperscript{-2} and
10\textsuperscript{-1}) had a measurable effect on the populational
probability of establishment - all other variations of novelty rate had
practically the same low effect on the probability (Fig 2b). For novelty
rates between 0.0 and 10\textsuperscript{-3}, the probability of success
practically did not differ, reaching 0 for \emph{d\textsubscript{0}}
\(\approx\)1 (propagule compound phenotype app. one standard
deviation distant from the optimum imposed). The effect of the
increasing novelty rate between these values is more evident on the
population growth; the population reaches the carrying capacity about
twice faster when\selectlanguage{greek}\emph{μ} \selectlanguage{english}=10\textsuperscript{-4} than when \selectlanguage{greek}\emph{μ} \selectlanguage{english}=0
(Fig 3). Less than 10\% of establishment success was detected for
non-synergic simulations when \emph{d\textsubscript{0}} = 2, despite the
novelty rate (Fig. 2b).

Simulations have shown that a small increase in the propagule size (from
1 to 10) greatly expanded the diversity of compound phenotypes which
resulted in a probability of success greater than 90\% for pathogens
with a \emph{d\textsubscript{0}} \textless{}0.9 (Fig. 2c). For larger
propagule sizes, this success extends up to\emph{d\textsubscript{0}}
\(\approx\)1.2. The propagule-size effect was significant for the
survival rate of the compound phenotypes that do not meet the optimum
imposed by the host, maximizing the survival rate of the neighboring
phenotypes as the propagule size increases. This high probability effect
quickly diminishes, depicting a cliff-like pattern for phenotypes
survival probabilities higher than\emph{d\textsubscript{0}}
\(\approx\)1.2, independent of the propagule size.

Finally, the simultaneous maximization of all parameters (B=7.5;\selectlanguage{greek}\emph{μ}
\selectlanguage{english}=0.1; \emph{N\textsubscript{0}} =200) resulted in a synergetic effect on
the probability of success of colonization (Fig. 2). Under this
scenario, even host lineages representing distant resources (resources
that are less compatible with the pathogen requirements/capacity) have a
high probability of colonization, far exceeding the probability observed
for the populational parameters of the pathogens tested independently
(Fig. 2).

As expected, based in every simulated scenario with a non-null \selectlanguage{greek}\emph{μ}
, \selectlanguage{english}the emergence of phenotypic novelties in the generations following
colonization allowed the compound phenotypes to evolve towards and
stabilize around the optimal fitness value imposed by the host (Fig. 3).
The greater the novelty rate (\selectlanguage{greek}\emph{μ} \selectlanguage{english}), the faster the evolution
towards the optimum, also increasing the diversity of compound
phenotypes (Fig. 3, \selectlanguage{greek}\emph{μ} \selectlanguage{english}=10\textsuperscript{-2}). During
simulations, population size rapidly reaches the established carrying
capacity. Even though higher values of \selectlanguage{greek}\emph{μ} \selectlanguage{english}favors population
growth, the carrying capacity is achieved much earlier than phenotype
stabilization for all scenarios (Fig. 3). Surprisingly, even in the
absence of novelties (Fig. 3, \selectlanguage{greek}\emph{μ=0}\selectlanguage{english} ) many simulated pathogen
populations persisted and achieved the carrying capacity in the newly
colonized host species.

Varying rates of the emergence of evolutionary novelties revealed also
an unexpected outcome on the qualitative profile of the populations,
following colonization. High rates of emergence resulted in the
retention of compound phenotypes (variants) present in the initial and
previous populations during populational growth, with correspondingly
larger load (something analogous to the concept of genetic load; Wallace
1970) (Fig. 4a). Lower rates of novelty emergence resulted in
populations that depict smaller phenotypic variability, with greater
loss of pre-existing phenotypes (Fig. 4b). By maximizing every other
parameter, the expansion of phenotypes is even larger, indicating that
the increased maintenance of ancestral phenotypes is also influenced by
other populational parameters besides \selectlanguage{greek}\emph{μ} .

\selectlanguage{english}\section*{Discussion}

{\label{discussion}}

The general result of the simulations suggests that the increase in the
rate of evolutionary novelty emergence, reproductive rate, and propagule
size influence positively the success of colonization of new hosts by a
novel pathogen population (Fig. 2). However, within the scope of the
simulations, the different values of the explored parameters resulted in
distinct impacts on this success.~By far, the most significant impact
was observed for the number of propagules; even not adapting to the
selection of the new host, due to the complete absence of emergence of
novelties imposed by the model, an initial population composed of 10
colonizers resulted in a significant increase of the probability to
thrive and persist under suboptimal fitness, even in hosts representing
relatively small compatibility (\emph{d\textsubscript{0}}
\(\approx\)1).

Indeed, propagule pressure is extensively known to positively influence
the colonization of new host species (May et al. 2001; Hatcher et al.
2012) - or geographic areas and corresponding communities in the case of
invasive species (Sax et al. 2007; Lockwood et al. 2009; Cassey et al.
2018). Large propagule sizes are usually linked with the reduction of
consequences of demographic (e.g. stochasticity and Allee effects)
(Hufbauer et al. 2013) and genetic (founder's effect) (Simberloff 2009;
Roman and Darling 2007) processes observed in small population size
during changes in ecologic and geographic distribution. Since every
simulation involving variation in propagule size used a low rate of
emergence of evolutionary novelty and the relative fitness of propagules
were kept unchanged (same \emph{d\textsubscript{0}} despite qualitative
differences in the combination of loci), the advantage conferred by
increasing propagule sizes during colonization appears to be associated
with demographic issues, most likely stochastic, as we did not model
social collaborative processes nor limitation in the encounter of mates
during reproduction (see Hufbauer et al. 2013). However, the rate of
increase in colonization success according to the imposed distance of
the compound phenotype optimum of the new host diminishes with
increasing values of the propagule size, not displaying a direct linear
relationship (Fig. 2c).

Although less evident than the simulations with variable propagule size,
increases in reproductive rate in less than 10 -- fold (from 1.5 to 7.5)
resulted in a more expressive increase in the probability of successful
colonization than 1000-fold increases in the rate of emergence of
novelties (from \selectlanguage{greek}\emph{μ} \selectlanguage{english}=10\textsuperscript{-6} to\selectlanguage{greek}\emph{μ}
\selectlanguage{english}=10\textsuperscript{-3}). This is an unexpected result, especially
considering that the emergence of new associations - such as infectious
diseases - is often linked by many to high mutation rates of the
consumer associate (Pepin et al. 2008; Selman et al. 2012; Viana et al.
2015). Hence, our results indicate that the rate of emergence of
evolutionary novelties alone (e.g. mutation rates for simple organisms
such as viruses) has secondary importance in the colonization of new
host species, as suggested in Araujo et al. (2015) and implicitly by the
Stockholm Paradigm (Brooks and Hoberg 2007; Brooks and Boeger 2019;
Brooks et al. 2019; Agosta and Brooks 2020). The accumulation of
accessible historical information - termed the \emph{information
space}by Brooks and Agosta (2012) and Agosta and Brooks (2020) - is of
greater importance for the events of host-repertoire expansion (i.e. the
evolutionarily process that precedes what is known as host-switching;
see Braga et al. 2018). It is the accumulation of heritable information
by preceding generations (and ancestors) and its retention in the
biological entities (i.e. populations, species) through time
(=phylogenetic conservatism) that will determine the ability of lineages
to endure ecological and environmental changes or to take advantage of
opportunities (e.g. explore new resources, new habitats). Since
compatibility (i.e. the distance to the actual host optimum) varies
within individuals of a diverse pathogen population, regions of
suboptimal fitness in the ancestral host - albeit potentially at low
frequency in the population - may contain pathogen variants that are
capable of reaching more distant (= more different) resources (new
hosts) than originally higher-fitness variants (see also Araujo et al.
2015; Brooks et al. 2019). Consequently, under this scenario, actual
rates of emergence of new inheritable evolutionary novelties (e.g.
mutations) are less important than the number of individuals colonizing
the new host (=propagule pressure), the rate of reproduction, and the
degree of the variability in the original donor population.

When all three parameters considered are maximized, the simulations
generate pronounced synergism (grey line in Fig. 2). The fact that this
combination of values likely compares to those observed for viruses,
particularly among RNA-viruses (Holmes 2009) is especially significant
in understanding the evolution of this group of organisms and the
corresponding emergence of infectious diseases. This outcome is
compatible with the conclusions of Geoghegan, Duch\selectlanguage{ngerman}êne, and Holmes (2017)
that ``cross-species transmission is a near universal feature of the
viruses \ldots{}, with virus-host co-divergence occurring less
frequently\ldots{}'' For instance, continuous oscillations of host
species were suggested as an intrinsically biological feature of
coronaviruses (Menachery et al. 2017), but it is likely a property of
viruses in general and perhaps of pathogenic bacteria as well. It is,
thus, understandable that viruses and bacteria are the most common
groups of organisms associated with emergent infectious diseases
(Cleaveland et al. 2001; Woolhouse and Gaunt 2007; Gubler 2010;
P\selectlanguage{polish}ę\selectlanguage{english}kala-Safi\selectlanguage{polish}ń\selectlanguage{english}ska 2018; Duarte-Neto 2019).

Since we expect that in the real-world representatives of the variants
of pathogens are continuously exploring accessible resources (e.g. host
species) (Brooks et al. 2019; Agosta and Brooks 2020) the emergence of
new associations - or colonization of new environments - is expected
when suitable matching (likely imperfect rather than perfect) between
requirements of the pathogen, the resource (i.e. host properties),
and/or environmental conditions meet. Therefore, the original host
species represents an imperfect reference - but, perhaps, the only one
accessible at this time - to describe the relative quality and the
distance of the new resources to the pathogen. Phylogenetic distance
between the host species involved in the host range expansion appears,
within limits, to estimate the multidimensional space of traits that
influence the compatibility of host and a specific pathogen lineage
(Martiny et al. 2013; Braga et al. 2015; Streicker et al. 2010; Gilbert
and Webb 2007). Since the resources defining compatibility vary
according to both host and pathogen species, phylogenetic distances
appear to be the only accessible proxy for the value
of\emph{d\textsubscript{0}} , but it should be considered parsimoniously
because evolutionary convergence of resources (Brooks and McLennan 2002)
and the variability of the pathogen and hosts may influence also the
outcome of the colonization attempts (see for instance Boeger et al.
2005; Araujo et al. 2015).

The results of the present simulations are also fundamental to expand
the understanding of the role of ecological fitting (Janzen 1985b;
Agosta 2006; Agosta and Klemens 2008) on the evolution of ecological
changes. As suggested previously by Araujo et al. (2015), newly
established populations of pathogens may survive for many generations in
a host even in the absence of adaptations. This is a more extreme
scenario of what Darwin called the survival of the adequate (Agosta and
Brooks 2020; Brooks and Agosta 2012). By surviving under these
``suboptimal'' conditions, pathogens may expand their temporal window
for the ``right'' novelty to present itself and allow an increase in the
population's fitness (adaptation) following the ecological change. For
instance, Antia et al. (2003), modeling a scenario of colonization
similar to the present simulations, suggested that early values of
R\textsubscript{0} of a new pathogen may evolve towards an
R\textsubscript{0}\textgreater{}1 subsequently, under the selective
pressure of the newly colonized host. However, after exploring the
available Sloppy Fitness Space of the pathogen population (Agosta and
Klemens 2008; Agosta et al. 2010; Brooks et al. 2019; Agosta and Brooks
2020), evolutionary novelties emerge randomly in the consumer species
(the pathogen). Thus, the perfect match may never happen (i.e. a
perfectly fit association) despite the influence of selection and the
consumer may remain in a situation of continuous suboptimal fitness
regarding its host species, a scenario analogous to that proposed by Sax
et al. (2007) for invasive species.

Another additional perspective is that the newly established population
of pathogens, although unchanged in its diversity due to the absence or
limited emergence of novelties (phenotypic or genetic), may also expand
the window of opportunity to encounter additional hosts representing
more or simply adequate resources solely by inhabiting a host species
with distinct ecological interactions with the surrounding environment.
For instance, by depicting dissimilar behaviors, the adequate new host
species may increase the probability of the new pathogen population to
encounter other potential hosts not previously available (considering
the ecology of the original host species) through a process that likely
comprises one of the mechanisms of colonization of new hosts species.
This is an empirically recognized process associated with many cases of
emergence of new symbiotic associations - contemporary (Brown 2001) and
historical (Braga et al. 2015) - including one of the possible pathways
of SARS-CoV-2 to humans during the emergence (Ji et al. 2020; Zhang et
al. 2020).

In the case of SARS-CoV-2, the scenario is even more worrisome since
humans became one of the ``stones'' in the process of host-repertoire
expansion by stepping stones (Braga et al. 2015; Brooks et al. 2019).
COVID19 has rapidly expanded to almost every part of the planet,
providing opportunities for the virus to colonize other human
populations and animal species. Presently, pets -- ferrets, cats, and
dogs -- and captive wild animals -- such as minks, tigers, lions,
macaques, Syrian hamsters, tree shrews, marmosets, and Egyptian fruit
bats (Gryseels et al. 2020; Lin et al. 2020) are known empirically to be
compatible hosts while a much greater range of host species has been
suggested through modeling (Damas et al. 2020) - from old-world monkeys
to anteaters. While many of the presently known compatible host species
are not seriously affected by the virus, they certainly represent unique
selective pressures and opportunities for broader dissemination through
ecological fitting (as suggested above). Hence, we may anticipate
influences connected with the acquisition of new host species on the
genetic make-up of SARS-CoV-2 -- among others, it may result in an
increase in its overall genetic variability and/or on the emergence of
unique haplotypes in isolated host populations (as suggested also by
Franklin and Bevins 2020). Indeed, the nature of RNA-viruses replication
influences by host and geographic expansion and isolation are already
known to generate new variants (Franklin and Bevins 2020) with
dissimilar potential virulence to humans. Such evolutionary changes may
result in new strains of the viruses with the ability to generate
diseases with symptomatic, virulence, and epidemiological
characteristics distinct from the original strains (see Jerzak et al.
2007; Border\selectlanguage{ngerman}ía, Stapleford, e Vignuzzi 2011). This epidemiological
scenario is complicated by the accumulation of evidence suggesting that
SARS-CoV-2 may take the opposite path (retro-colonizing humans), a
situation already recorded among other coronaviruses for the Siberian
musk deer \emph{(Moschus moschiferus)} and ferrets (\emph{Mustela
lutreola} ) (Hadfield et al., 2018; Van Der Hoek et al., 2004). Hence,
despite the recognition that these retro-colonization events are likely
rare (de Morais et al. 2020), they cannot be simply ignored in
epidemiological surveillance systems. The significance of such scenarios
and outcomes is further heightened given the currently expected limited
capacity for viruses to re-infect humans from domestic or synanthropic
wildlife sources. Thus, potential pathways are not under active
surveillance.

The simulations revealed yet another aspect of this host-exploration
dynamics that makes the above-proposed scenario of retro-colonization of
humans particularly important in health surveillance for EIDs. The
simulations strongly suggest that at higher values of the rate of
emergence of evolutionary novelties (e.g. mutation rates for viruses),
the genetic profile of the pathogen - although changing qualitatively
and quantitatively under the selective pressure of the new host resource
- putatively retain ``ancestral'' variants at low frequency despite
lower supposed fitness (Fig. 4B, C). This outcome provides theoretical
support for the retention of the capacity of fast-evolving lineages to
retro-colonize their previous host species/lineage by ecological fitting
(Janz and Nylin 1998; Janz et al. 2001; Brooks et al. 2019 ). RNA
viruses, such as SARS-CoV-2, are well known to evolve rapidly by
mutation and hybridization (Holland et al. 1982), and the retention of
variants may facilitate retro-colonizing of humans from recent spillover
into other animal species. This perspective in phylogenetic conservatism
analyzed along with available empirical data (such as that of
Celorio-Mancera et al. 2016) and the real nature of novelty emergence
(i.e. which includes more than just the idea that adaptation is solely
associated with random mutations - Jablonka and Lamb 1995; Jablonka et
al. 2014; Agosta and Brooks 2020) may provide a better understanding on
the process of retro-colonization of the original host species/lineages.
Hence, retro-colonization should be an important element in
epidemiological monitoring (as suggested by Favoretto et al. 2019,
Franklin e Bevins 2020, and González-Salazar, Stephens, e
Sánchez-Cordero 2017), especially in cases of recent emergence and
re-emergence of EIDs.

The combined results of this study provide further theoretical support
for the assertion that ``emerging infectious diseases are evolutionary
accidents waiting to happen'' (Brooks and Ferrao 2005). An increase in
host-repertoire by pathogens, potentially associated with the emergence
of a new infectious disease, is most likely to occur among closely
related species of hosts, but it is also possible among distantly
related hosts when the resource(s) is(are) convergent (see discussion on
specilization in Brooks and McLennan 2002). \textbf{Capacity} is much
larger than we can anticipate, and it is the \textbf{opportunity} of
encounter (i.e. the breakdown in mechanisms for ecological isolation)
that is a more essential determinant to the emergence of new
associations (Araujo et al. 2015; Brooks et al. 2019; Agosta and Brooks
2020). And opportunities are more frequent during periods of
environmental disruptions, many of which are associated with
climatological fluctuations in the past (Hoberg and Klassen 2002; Brooks
and Hoberg 2007; Hoberg and Brooks 2008, 2015; Hoberg et al. 2017).
Climatological fluctuations usually change the permeability of
pre-existing ecological barriers and promote shuffling in the
composition of organismic communities, augmenting the rate of encounter
of different host lineages, many of the same clade, fostering intense
exchange in pathogens.

In general, climate oscillation and independent or accompanying
environmental disruptions over evolutionary time have been a central
determinant of opportunities for faunal mixing and pathogen exchange
that have structured complex associations (Hoberg and Brooks, 2008).
Climate and environmental disruption occur across scales and
historically have had a substantial episodic behavior in the past
(Hoberg et al. 2017). However, during what is now characterized as the
Anthropocene, the outcomes of environmental disruption have become
significantly more prevalent due to globalization, other
human-associated actions, and also to climate change, which promote
movements of wildlife, humans, and domestic species into new geographic
range (Wilson 1995; Brooks and Boeger 2019). As a consequence, we expect
EID's to become even more frequent in the years to come (Brooks et al.
2014). We have little control over capacity, but we can, to a certain
level, monitor, avoid, and minimize the opportunity of encounter between
parasites and compatible host species. This is the principle of the
D.A.M.A. protocol (Brooks et al. 2014, 2019; Hoberg and Brooks 2015;
Brooks and Boeger 2019).

However, even with an effective D.A.M.A. protocol established, the task
to avoid the emergence of new diseases is especially difficult,
considering available empirical information. Many of the most
significant events in the history of life, and in the history of EID's,
are likely the result of unpredictable incidents when compatible
biological entities unexpectedly meet (opportunity). Attempts to
generate new associations (hosts and pathogens, in this case) likely
occur continuously, most being unsuccessful. However, a single
successful event may perpetuate the emerged association through
evolution and have a significant influence on the future
diversifications of the associates. That was likely the case for
well-known symbioses, such as those of proto-eukaryotic cells and
mitochondria, eukaryotic cells, and chloroplasts but also for many
recent EIDs, such as HIV, Ebola, Dengue, Zika, Chikungunya, and, of
course, Covid19.

Perhaps the final message from the empirical information accumulated
from the recent emergence of infectious diseases and the dynamics
revealed from the theoretical framework of the Stockholm Paradigm
(Brooks et al. 2019) and associated evolutionary models (Araujo et al.
2015) is that we cannot ``lower our guard''. These events are
evolutionarily dynamic processes, with pathogens incessantly exploring
the space of compatible host species (Brooks et al. 2019). And we -- and
other domesticated species -are certainly one of the most abundant,
available, ecologically diverse, and widespread species of potential
host on this planet.

\textbf{Acknowledgments}

This study was partially funded by the Conselho Nacional de
Desenvolvimento Científico e Tecnológico (CNPq), Brazil. ~Ethical
Statement is not applicable since the study did not involve sampling
animals nor humans, or questionnaires.~ Dr Eric Hoberg provided
pre-submission review and suggestions to the manuscript.

\textbf{Conflict of interest statement}

The authors report no conflict of interest.

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\textbf{Table 1} . Parameters, with a short definition, and all the
values analyzed during simulations. The underlined values are the fixed
values used in the presented results, while the other parameters varied.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\textbf{Parameters} & \textbf{Short Definition} & \textbf{Standard
values applied}\tabularnewline
\emph{G} & Compound phenotype size; Length of the binary characters that
define each pathogen. & 30, 40, 50, 60, 70, 80,
\emph{100}\tabularnewline
\emph{K} & Carrying capacity; The pathogen's maximum population size the
host can support & \emph{1000}, 2000, 3000, 4000, 5000\tabularnewline
\selectlanguage{greek}σ & Deviation rate for survivor probability; the higher its value the
lower the selection pressure imposed by the host on pathogens &
\emph{10}\tabularnewline
\emph{b} & Reproduction rate; average population growth per reproduction
step & \emph{1.5}, 3.5, 5.5, 7.5\tabularnewline
\selectlanguage{greek}\emph{μ} & Novelty rate per locus, probability of trait state change &
10\textsuperscript{-6},10\textsuperscript{-5},\emph{10\textsuperscript{-4}},
10\textsuperscript{-3},~10\textsuperscript{-2},10\textsuperscript{-1},
0.0.\tabularnewline
\emph{p\textsubscript{h}} & Optimum Phenotype imposed by the host &
G/2\tabularnewline
\emph{p\textsubscript{0}} & Propagule phenotype. It defines the
phenotype distance \emph{d\textsubscript{0}} between propagule and host
in the first generation of the colonization (see Eq.1) &
0\emph{\textless{}d\textsubscript{0}}\textless{}G/20\tabularnewline
\emph{N\textsubscript{0}} & Propagule size & \emph{1}, 10, 50, 100,
200\tabularnewline
& Maximum number of generations that each simulation was run &
1000\tabularnewline
& Number of simulation repetitions of a given set of parameters. &
700\tabularnewline
\bottomrule
\end{longtable}

\textbf{Legends to figures}

\textbf{Figure 1.} Flowchart of the model dynamics. The initial
population, with individuals of identical compound phenotype, is
subjected to the \emph{Selection} in the newly-colonized host. Upon
survival, the simulated pathogen population will then
undergo\emph{Reproduction} . The daughter compound phenotype will differ
from the parental phenotype according to a pre-defined rate of emergence
of evolutionary novelties (\selectlanguage{greek}\emph{μ} \selectlanguage{english}). Descendent populations are
subjected to these cyclic sequences for a pre-determined number of
generations

\textbf{Figure 2.} Probability of establishment of the pathogen
population as a function of the propagule phenotype distance
(\emph{d\textsubscript{0}} ). The graphs present the effect of (\emph{a}
) reproduction rate, (\emph{b} ) evolutionary novelty rate, and
(\emph{c} ) propagule size (\emph{N\textsubscript{0}} ) on the
probability of establishment for varying resource distances
(\emph{d\textsubscript{0}} ). Except for the specifically tested
parameter in each graph, the remaining simulation parameter values used
are defined in Table 1. The black line in every graph represents the
probability of a single pathogen individual of surviving the first
reproductive event following colonization at
each\emph{d\textsubscript{0}} - Eq (1). The grey line represents the
probability of establishment of the pathogen when all parameters are
maximized (the highest values in Table 1) in the simulations.

\textbf{Figure 3.} Evolution of compound phenotype diversity/frequency
and population size over generations. Left vertical axis indicate the
distance of the pathogen compound phenotype from the optimum value
imposed by the host, (\emph{d\textsubscript{i,n}} ), whereas the
horizontal axes indicate generation time in simulations. The orange
palette depicts compound phenotype frequency in the given generation,
warmer colors indicate greater phenotype frequency in the population.
The right vertical axis represents the population size, drawn as a blue
line - carrying capacity = 1,000 (Table 1). The vertical lines in the
last two plots correspond to the respective generation time (same
colors) depicted in Figure 3. The respective rates of novelty emergence
for each graphic are the following: (\emph{a} ) \selectlanguage{greek}\emph{μ} \selectlanguage{english}= 0.0;
(\emph{b} ) \selectlanguage{greek}\emph{μ} \selectlanguage{english}= 10\textsuperscript{-4}; and (\emph{c} ) \selectlanguage{greek}\emph{μ}
\selectlanguage{english}= 10\textsuperscript{-2} - the remaining parameter values are those
presented in Table 1.

\textbf{Figure 4.} Maintenance of original phenotypes according to the
rate of evolutionary novelties. Relative frequency of compound phenotype
as a function of the distance of the pathogen compound phenotype from
the optimum value imposed by the host, (\emph{d\textsubscript{i,n}} )
for two levels of evolutionary novelty rates and propagule size:
(\emph{a} ) \selectlanguage{greek}\emph{μ} \selectlanguage{english}=10\textsuperscript{-4} and (\selectlanguage{greek}\emph{b) μ}
\selectlanguage{english}=10\textsuperscript{-2}, \emph{N\textsubscript{0}} =1 (\emph{c}
)\selectlanguage{greek}\emph{μ} \selectlanguage{english}=10\textsuperscript{-2}, \emph{N\textsubscript{0}}
=200,\emph{b} =7.5). Each curve represents specific generation times as
follow: (\emph{a} ) 45 (yellow line), 120 (dark-orange line), 200 (red
line), 500 (brown line); (\emph{b} ) and (\emph{c} ) =10 (yellow line),
13 (light-orange line), 25 (dark-orange line), 35 (red line), 500 (brown
line). The first four temporal elements (colored lines) of each list are
highlighted by the vertical lines in Figure 3b and 3c, respectively.\selectlanguage{english}
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