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|
namespace quetzal {
namespace demography {
namespace strategy {
/*!
* \brief Traits class for individual based demographic history simulation, strategy suited for small number of individuals in the landscape (small populations).
* \ingroup demography
*
* \details Simulate the demographic history with an individual-based strategy: each
* individual is dispersed individually.
* \par History Initialization:
* The population size history\f$N\f$ is initialized by setting \f$N(.,t_0)\f$, the initial distribution of individuals across demes at the
* first time of the history \f$t_0\f$. Typically for a biological invasion,
* this is restricted to the introduction site(s) with the number of introduced
* individuals. For endemic species, paleoclimatic distribution can be considered
* as starting points.
*
* \par Growth:
* The offspring number \f$ \tilde{N}_{x}^{t} \f$ in each deme is freely defined by the user. It can for example be
* sampled in a distribution conditionally to a function of the local density of
* parents. Non-overlapping generations are considered (the parents die just after reproduction).
*
* \par Dispersal:
* The children dispersal is done by sampling their destination in a multinomial
* law, that defines \f$ \Phi_{x,y}^t \f$, the number of individuals going from
* \f$x\f$ to \f$y\f$ at time \f$t\f$:
*
* \f[ (\Phi_{x,y}^{t})_{y\in X} \sim \mathcal{M}(\tilde{N}_{x}^{t},(m_{xy})_y) ~. \f]
*
* The term \f$ (m_{xy})_y \f$ denotes the parameters of the multinomial law,
* giving for an individual in \f$x\f$ its proability to go to \f$y\f$.
* These probabilities are given by the dispersal law with parameter \f$\theta\f$:
*
* \f[
* \begin{array}{cclcl}
* m & : & X^2 & \mapsto & R_{+} \\
* & & (x,y) & \mapsto & m^{\theta}(x,y) ~. \\
* \end{array}
* \f]
*
* After migration, the number of individuals in deme \f$x\f$ is defined by
* the total number of individuals converging to \f$x\f$:
*
* \f[
* N(x,t+1) = \displaystyle \sum_{i\in X} \Phi_{i,x}^{t}~.
* \f]
* \section Example
* \snippet demography/test/History/Individual_based_history_test.cpp Example
* \section Output
* \include demography/test/History/Individual_based_history_test.output
*/
struct individual_based {
using value_type = unsigned int;
};
/*!
* \brief Traits class for simulating the demographic history of importnat masses of populations.
* \ingroup demography
*
* \details Simulate the demographic history by considering that populations of individuals are divisible masses,
* leading to faster simulations.
*
* \par Intialization:
* \f$N\f$ is initialized by setting \f$N(.,t_0)\f$ the initial distribution
* of individuals across demes at the first time \f$t_0\f$.
* Typically for a biological invasion, this is restricted to the introduction site(s)
* with the number of introduced individuals. For endemic species, paleoclimatic
* distribution can be considered as starting points.
*
* \par Growth:
* The offspring number \f$\tilde{N}_{x}^{t}\f$ in each deme is freely defined by
* the user. For example, it can be sampled in a distribution conditionally
* to a function of the local density of parents. Non-overlapping generations
* are considered (the parents die just after reproduction).
*
* \par Dispersal:
* The children dispersal is done by splitting the population masses according
* to their migration probabilities, defining
* \f$ \Phi_{x,y}^t \f$, the population flow going from \f$x\f$ to \f$y\f$ at time \f$t\f$:
* \f[ (\Phi_{x,y}^{t})_{y\in X} = (\tilde{N}_{x}^{t} \times m_{xy})_{y\in X} ~. \f]
* The term \f$ m_{xy} \f$ denotes the parameters of the transition kernel,
* giving for an individual in \f$x\f$ its probability to go to \f$y\f$.
* These probabilities are given by the dispersal law with parameter \f$\theta\f$:
* \f[
* \begin{array}{cclcl}
* m & : & X^2 & \mapsto & R_{+} \\
* & & (x,y) & \mapsto & m^{\theta}(x,y) ~. \\
* \end{array}
* \f]
* After migration, the population size in deme \f$x\f$ is defined by the sum of population flows converging to \f$x\f$:
* \f[
* N(x,t+1) = \displaystyle \sum_{i\in X} \Phi_{i,x}^{t}~.
* \f]
* \section Example
* \snippet demography/test/History/Mass_based_history_test.cpp Example
* \section Output
* \include demography/test/History/Mass_based_history_test.output
*/
struct mass_based {
using value_type = double;
};
}
/*!
* \brief Base class for spatially explicit and forward-in time population history simulators.
*
* \tparam Space Demes identifiers.
* \tparam Time EqualityComparable, CopyConstructible.
* \tparam Strategy Strategy use for simulating populations dynamics
*
* \details Is used as an implementation base of the specialized simulation strategies.
*
* \ingroup demography
*
*/
template<typename Space, typename Time, typename Strategy>
class BaseHistory {
public:
//! \typedef strategy used for simulating populations dynamics
using strategy_type = Strategy;
//! \typedef type of the population flows database
using flow_type = Flow<Space, Time, typename strategy_type::value_type>;
//! \typedef type of the population size database
using pop_sizes_type = PopulationSize<Space, Time, typename strategy_type::value_type>;
//! \typedef space type
using coord_type = Space;
//! \typedef time type
using time_type = Time;
//! \typedef type of the discrete distribution used inside the backward dispersal kernel
using discrete_distribution_type = quetzal::random::DiscreteDistribution<coord_type>;
//! \typedef Backward dispersal kernel type
using backward_kernel_type = quetzal::random::TransitionKernel<time_type, discrete_distribution_type>;
protected:
// Need to be accessed by the expand method
std::unique_ptr<pop_sizes_type> m_sizes;
std::unique_ptr<flow_type> m_flows;
std::vector<Time> m_times;
std::unique_ptr<backward_kernel_type> m_kernel;
private:
auto make_backward_distribution(coord_type const& x, time_type const& t) const
{
std::vector<double> weights;
std::vector<coord_type> support;
weights.reserve(m_flows->flux_to(x,t).size());
support.reserve(m_flows->flux_to(x,t).size());
for(auto const& it : m_flows->flux_to(x,t) )
{
support.push_back(it.first);
weights.push_back(static_cast<double>(it.second));
}
return discrete_distribution_type(std::move(support),std::move(weights));
}
public:
/**
* \brief Constructor initializing the demographic database.
* \param x the coordinate of introduction
* \param t the introduction time
* \param N the population size at coordinate x at time t
* \section Example
* \snippet demography/test/History/History_test.cpp Example
* \section Output
* \include demography/test/History/History_test.output
*/
BaseHistory(coord_type const& x, time_type const& t, typename strategy_type::value_type N):
m_sizes(std::make_unique<pop_sizes_type>()),
m_flows(std::make_unique<flow_type>()),
m_kernel(std::make_unique<backward_kernel_type>())
{
m_sizes->operator()(x,t) = N;
m_times.push_back(t);
}
/**
* \brief Read-only access to the demographic flows database
*/
flow_type const& flows() const
{
return *m_flows;
}
/**
* \brief Read and write access to the demographic flows database
*/
flow_type & flows()
{
return *m_flows;
}
/**
* \brief Read-only access to the demographic sizes database.
* \remark Can be used for composition into time dependent growth functions.
*/
const pop_sizes_type & pop_sizes() const
{
return *m_sizes;
}
/**
* \brief Read-and-write access to the demographic sizes database
*/
pop_sizes_type & pop_sizes()
{
return *m_sizes;
}
/**
* \brief First time recorded in the foward-in-time database history.
*/
time_type const& first_time() const
{
return m_times.front();
}
/**
* \brief Last time recorded in the foward-in-time database history.
*/
time_type const& last_time() const
{
return m_times.back();
}
/**
* \brief Samples a coordinate from the backward-in-time transition matrix
*
* \details The transition matrix is computed from the demographic flows
* database. The returned coordinate object will basically answer the question:
* when an individual is found in \f$x\f$ at time \f$t\f$, where could it
* have been at time \f$t-1\f$ ?
* Let \f$ X \f$ be the geographic space and \f$\Phi_{x,y}^t\f$ be the number of individuals going
* from coordinate \f$x \in X \f$ to coordinate \f$y\f$ at time \f$t\f$.
* Knowing that a child node \f$c\f$ is found in \f$ j \in X \f$, the probability for its parent
* \f$p\f$ to be in \f$i\in X \f$ is: \f$ P( p \in i ~|~ e \in j) = \frac{\Phi_{i, j}^{t}}{ \sum_{k} \Phi_{k, j}^{t} } ~.\f$
* \section Example
* \snippet demography/test/History/Mass_based_history_test.cpp Example
* \section Output
* \include demography/test/History/Mass_based_history_test.output
*/
template<typename Generator>
coord_type backward_kernel(coord_type const& x, time_type t, Generator& gen)
{
--t;
assert(m_flows->flux_to_is_defined(x,t));
if( ! m_kernel->has_distribution(x, t))
{
m_kernel->set(x, t, make_backward_distribution(x, t));
}
return m_kernel->operator()(gen, x, t);
}
};
/**
* \brief Demographic history simulated from an individual-based strategy (each individual is dispersed individually).
*
* \tparam Space Demes identifiers.
* \tparam Time EqualityComparable, CopyConstructible.
* \tparam Strategy Strategy used for simulating populations dynamics
*
* \details Inherit from this class and specialize the Strategy template parameter
*
* \ingroup demography
*
*/
template<typename Space, typename Time, typename Strategy>
class History : public BaseHistory<Space, Time, Strategy>
{
};
/**
* \brief Demographic history simulated from an individual-based strategy (each individual is dispersed individually).
*
* \tparam Space Demes identifiers.
* \tparam Time EqualityComparable, CopyConstructible.
*
* \ingroup demography
*
* \details $N$ is initialized by setting \f$ N(.,t_0) \f$ the initial distribution
* of individuals across demes at the first time \f$ t_0 \f$.
* Typically for a biological invasion, this is restricted to the introduction site(s)
* with the number of introduced individuals. For endemic species, paleoclimatic
* distribution can be considered as starting points. The number of descendants
* \f$ \tilde{N}_{x}^{t} \f$ in each deme is sampled in a distribution conditionally
* to a function of the the local density of parents. Non-overlapping generations
* are considered (the parents die just after reproduction). The children dispersal
* is done by sampling their destination in a multinomial law, that defines
* \f$ \Phi_{x,y}^t \f$ the number of individuals going from \f$ x \f$ to \f$ y \f$ at time \f$ t \f$:
* \f[ (\Phi_{x,y}^{t})_{y\in X} \sim \mathcal{M}(\tilde{N}_{x}^{t},(m_{xy})_y) ~. \f]
* The term \f$ (m_{xy})_y \f$ denotes the parameters of the multinomial law,
* giving for an individual in \f$x\f$ its proability to go to \f$y\f$.
* These probabilities are given by the dispersal law with parameter \f$\theta\f$:
* \f[
* \begin{array}{cclcl}
* m & : & X^2 & \mapsto & R_{+} \\
* & & (x,y) & \mapsto & m^{\theta}(x,y) ~. \\
* \end{array}
* \f]
* After migration, the number of individuals in deme \f$x\f$ is defined by the total number of individuals converging to \f$x\f$:
* \f[
* N(x,t+1) = \displaystyle \sum_{i\in X} \Phi_{i,x}^{t}~.
* \f\]
*
* \section Example
* \snippet demography/test/History/History_test.cpp Example
* \section Output
* \include demography/test/History/History_test.output
*/
template<typename Space, typename Time>
class History<Space, Time, strategy::individual_based> : public BaseHistory<Space, Time, strategy::individual_based>
{
using BaseHistory<Space, Time, strategy::individual_based>::BaseHistory;
public:
/**
* \brief Expands the demographic database.
*
* \tparam Space Demes identifiers.
* \tparam Time EqualityComparable, CopyConstructible.
*
* \exception std::domain_error if the population goes extincted before the simulation is completed.
*
* \param nb_generations the number of generations to simulate
* \param sim_growth a functor simulating \f$\tilde{N}_{x}^{t}\f$.
*
* The functor can possibly internally use a reference on the population sizes database to represent the time dependency.
* The signature of the function should be equivalent to the following:
* `unsigned int sim_growth(Generator &gen, const coord_type &x, const time_type &t);`
*
* \param kernel a functor representing the dispersal location kernel that simulates the coordinate of the next location conditionally to the current location.
* The signature should be equivalent to `coord_type kernel(Generator &gen, const coord_type &x, const time_type &t);`
*
* \section Example
* \snippet demography/test/History/History_test.cpp Example
* \section Output
* \include demography/test/History/History_test.output
*/
template<typename Growth, typename Dispersal, typename Generator>
void expand(unsigned int nb_generations, Growth sim_growth, Dispersal kernel, Generator& gen)
{
for(unsigned int g = 0; g < nb_generations; ++g)
{
auto t = this->last_time();
auto t_next = t; ++ t_next;
this->m_times.push_back(t_next);
unsigned int landscape_individuals_count = 0;
// TODO : optimize the definition_space function (for loop)
for(auto x : this->m_sizes->definition_space(t) )
{
auto N_tilde = sim_growth(gen, x, t);
landscape_individuals_count += N_tilde;
if(N_tilde >= 1)
{
for(unsigned int ind = 1; ind <= N_tilde; ++ind)
{
auto y = kernel(gen, x, t);
this->m_flows->add_to_flux_from_to(x, y, t, 1);
this->m_sizes->operator()(y, t_next) += 1;
}
}
}
if(landscape_individuals_count == 0)
{
throw std::domain_error("Landscape populations went extinct before sampling");
}
}
}
};
/**
* \brief Demographic history where populations levels are assumed high enough to be considered as divisible masses.
*
* \ingroup demography
*
* \tparam Space Demes identifiers.
* \tparam Time EqualityComparable, CopyConstructible.
*
* \details $N$ is initialized by setting \f$N(.,t_0)\f$ the initial distribution
* of individuals across demes at the first time \f$t_0\f$.
* Typically for a biological invasion, this is restricted to the introduction site(s)
* with the number of introduced individuals. For endemic species, paleoclimatic
* distribution can be considered as starting points. The number of descendants
* \f$\tilde{N}_{x}^{t}\f$ in each deme is sampled in a distribution conditionally
* to a function of the the local density of parents. Non-overlapping generations
* are considered (the parents die just after reproduction). The children dispersal
* is done by sampling their destination in a multinomial law, that defines
* \f$ \Phi_{x,y}^t \f$ the number of individuals going from \f$x\f$ to \f$y\f$ at time \f$t\f$:
* \f[ (\Phi_{x,y}^{t})_{y\in X} \sim \mathcal{M}(\tilde{N}_{x}^{t},(m_{xy})_y) ~. \f]
* The term \f$ (m_{xy})_y \f$ denotes the parameters of the multinomial law,
* giving for an individual in \f$x\f$ its probability to go to \f$y\f$.
* These probabilities are given by the dispersal law with parameter \f$\theta\f$:
* \f[
* \begin{array}{cclcl}
* m & : & X^2 & \mapsto & R_{+} \\
* & & (x,y) & \mapsto & m^{\theta}(x,y) ~. \\
* \end{array}
* \f]
* After migration, the number of individuals in deme \f$x\f$ is defined by the total number of individuals converging to \f$x\f$:
* \f[
* N(x,t+1) = \displaystyle \sum_{i\in X} \Phi_{i,x}^{t}~.
* \f\]
*
* \section Example
* \snippet demography/test/History/History_test.cpp Example
* \section Output
* \include demography/test/History/History_test.output
*/
template<typename Space, typename Time>
class History<Space, Time, strategy::mass_based> : public BaseHistory<Space, Time, strategy::mass_based>{
using BaseHistory<Space, Time, strategy::mass_based>::BaseHistory;
public:
/**
* \brief Expands the demographic database,
* \details $N$ is initialized by setting \f$N(.,t_0)\f$ the initial distribution
* of individuals across demes at the first time \f$t_0\f$.
* Typically for a biological invasion, this is restricted to the introduction site(s)
* with the number of introduced individuals. For endemic species, paleoclimatic
* distribution can be considered as starting points. The number of descendants
* \f$\tilde{N}_{x}^{t}\f$ in each deme is sampled in a distribution conditionally
* to a function of the the local density of parents. Non-overlapping generations
* are considered (the parents die just after reproduction). The children dispersal
* is done by sampling their destination in a multinomial law, that defines
* \f$ \Phi_{x,y}^t \f$ the population flow going from \f$x\f$ to \f$y\f$ at time \f$t\f$:
* \f[ (\Phi_{x,y}^{t})_{y\in X} = (\tilde{N}_{x}^{t}*m_{xy})_{y\in X} ~. \f]
* The term \f$ m_{xy} \f$ denotes the parameters of the transition kernel,
* giving for an individual in \f$x\f$ its probability to go to \f$y\f$.
* These probabilities are given by the dispersal law with parameter \f$\theta\f$:
* \f[
* \begin{array}{cclcl}
* m & : & X^2 & \mapsto & R_{+} \\
* & & (x,y) & \mapsto & m^{\theta}(x,y) ~. \\
* \end{array}
* \f]
* After migration, the population size in deme \f$x\f$ is defined by the sum of population flows converging to \f$x\f$:
* \f[
* N(x,t+1) = \displaystyle \sum_{i\in X} \Phi_{i,x}^{t}~.
* \f\]
* \param nb_generations the number of generations to simulate
* \param sim_growth a functor simulating \f$\tilde{N}_{x}^{t}\f$.
* The functor can possibly internally use a reference on the population sizes database to represent the time dependency.
* The signature of the function should be equivalent to the following:
* `double sim_growth(Generator &gen, const coord_type &x, const time_type &t);`
* \param kernel a functor representing the dispersal location kernel that simulates the coordinate of the next location conditionally to the current location.
* The signature should be equivalent to `coord_type kernel(Generator &gen, const coord_type &x, const time_type &t);`.
* The expression `kernel.support(time_type const& t)` must be valid and return an iterable container of geographic coordinates
* indicating the transition kernel state space at time \f$t\f$.
* \section Example
* \snippet demography/test/History/History_test.cpp Example
* \section Output
* \include demography/test/History/History_test.output
*/
template<typename Growth, typename Dispersal, typename Generator>
void expand(unsigned int nb_generations, Growth sim_growth, Dispersal kernel, Generator& gen)
{
for(unsigned int g = 0; g < nb_generations; ++g)
{
auto t = this->last_time();
auto t_next = t; ++ t_next;
this->m_times.push_back(t_next);
for(auto x : this->m_sizes->definition_space(t) )
{
auto N_tilde = sim_growth(gen, x, t);
for(auto y : kernel.state_space(t) )
{
auto m = kernel(x, y, t);
this->m_flows->set_flux_from_to(x, y, t, m*N_tilde);
this->m_sizes->operator()(y, t_next) += m*N_tilde;
}
}
}
}
};
} // namespace demography
} // namespace quetzal
#endif |
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A méditer: La solution la plus simple est toujours la moins compliquée
Bon, j'attend un peu avant de mettre le sujet en résolu mais apparemment c'est tout bon ! 
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