streamlit_app.py

import streamlit as st
from scipy.integrate import odeint
import numpy as np
import matplotlib.pyplot as plt

# Assigning title and subtitle to the app
st.set_page_config(page_title="Lotka-Volterra Simulator", page_icon=":heart:")

st.title("Lotka-Volterra Model Simulator")
st.subheader("An Interactive App to learn Interspecific Population Interaction")

hide_menu_style = """
        <style>
        #MainMenu {visibility: hidden;}
        </style>
        """
st.markdown(hide_menu_style, unsafe_allow_html=True)

# Display the Lotka-Volterra competition equations
st.markdown(
    r"""
    The Lotka-Volterra competition equations describe the dynamics of two species exhibiting interspecific competition in an ecosystem. The equations are given by:

    $$\frac{dN_1}{dt} = r_1 N_1 \left( 1 - \frac{N_1 + a N_2}{K_1} \right)$$

    $$\frac{dN_2}{dt} = r_2 N_2 \left( 1 - \frac{N_2 + b N_1}{K_2} \right)$$

    where,

    $N_1$ and $N_2$ are the population size of the two competing species,

    $r_1$ and $r_2$ are the intrinsic growth rates (logistic growth) of the species, 

    $a$ is the measure of the effect of species 2 on the growth of species 1 
    
    $b$ is the measure of the effect of species 1 on the growth of species 2, and 

    $K_1$ and $K_2$ are the carrying capacities of the habitat for the species.
    """
)

# Explaining in more depth:
st.markdown("### More about the model: ")
st.markdown('''
The Lotka-Volterra competition model is a mathematical model that describes the interactions between two species in a competitive environment. The model is named after Alfred J. Lotka (1880-1949) and Vito Volterra (1860-1940), who independently developed the model in the early 20th century.

The model is based on the assumption that each species has a certain reproductive rate, which determines how quickly it can reproduce and increase its population size. The model also assumes that resources are in limited supply, due to which competition is inevitable.

The model predicts that the population sizes of both species will change over time based on their reproductive rates and resource use. However, competition coefficients and carrying capacities are assumed to be constant.

If the interaction coefficient is equal to zero, there is no competitive effect, and the equation behaves as a single-species logistic equation.

If interaction coefficients are small, both species approach an equilibrium level near their carrying capacities.
''')


# defining a formula:


def lv(y, t, r1, r2, a, b, K1, K2):
    N1 = y[0]
    N2 = y[1]
    dN1dt = r1 * N1 * (1 - (N1 + a * N2) / K1)
    dN2dt = r2 * N2 * (1 - (N2 + b * N1) / K2)
    return [dN1dt, dN2dt]


# Define the growth rates and interaction coefficients as streamlit sliders


st.sidebar.markdown("## Input Parameters")
r1 = st.sidebar.slider('Growth rate of species 1 (r1)', 0.01, 1.0, 0.13)
r2 = st.sidebar.slider('Growth rate of species 2 (r2)', 0.01, 1.0, 0.98)
K1 = st.sidebar.number_input('Carrying capacity of species 1 (K1)', value=600, step=1)
K2 = st.sidebar.number_input('Carrying capacity of species 2 (K2)', value=500, step=1)
a = st.sidebar.slider('Interaction coefficient \'a\' (effect of species 2 on species 1)', 0.0, 1.0, 0.1)
b = st.sidebar.slider('Interaction coefficient \'b\' (effect of species 1 to species 2)', 0.0, 1.0, 0.4)
N1 = st.sidebar.number_input("Population size of species 1 (N1)", value=50, step=1)
N2 = st.sidebar.number_input("Population size of species 2 (N2)", value=70, step=1)
T = st.sidebar.slider('Length of simulation', 1, 1000, 100)

# Set the time range for the simulation
t = np.linspace(0, T, 100)

# Solve the equations using the odeint function from scipy
y = odeint(lv, [N1, N2], t, args=(r1, r2, a, b, K1, K2))

# Extract the population sizes for each species
y1 = y[:, 0]
y2 = y[:, 1]

# Plot the results
st.markdown("### Plotting the values:")
fig, ax = plt.subplots()
ax.plot(t, y1, 'r', label='Species 1')
ax.plot(t, y2, 'b', label='Species 2')
ax.legend(loc='best')
ax.set_xlabel('Time')
ax.set_ylabel('Population Size(N)')
st.pyplot(fig)

st.markdown("### References: ")
st.markdown(''' https://en.wikipedia.org/wiki/Competitive_Lotka%E2%80%93Volterra_equations

A Primer of Ecology, Third Edition by Nicholas J. Gotelli''')

st.markdown("## Developed By: ")
col1, col2 = st.columns(2, gap="small")
with col1:
    st.image("https://mohit254-portfolio-cv-t4bwqw.streamlit.app/~/+/media/511fd1351113b1b2f0acc6c65d463c50c4155c521ee6fce285af2566.png", width=230)

with col2:
    st.title("Mohit Poudel")
    st.write("Bioinformatics & population genetics enthusiast, self-taught python programmer")
    st.write("Ohio University")
    st.write("Athens, Ohio")
st.markdown("##### [Know more about the developer!!](https://mohit254-portfolio-cv-t4bwqw.streamlit.app/#mohit-poudel)")