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8 results for “diffuse competition”
Suppression force-fields and diffuse competition: Competition de-escalation is an evolutionarily stable strategy
<p><span>Competition theory is founded on the premise that individuals benefit from harming their competitors, which helps them secure resources and prevent inhibition by neighbours. When multiple individuals compete, however, competition has complex indirect effects that reverberate through competitive neighbourhoods. The consequences of such "diffuse" competition are poorly understood. For example, competitive effects may dilute as they propagate through a neighbourhood, weakening benefits of neighbour suppression. Another possibility is that competitive effects may rebound on strong competitors, as their inhibitory effects on their neighbours benefit other competitors in the community. Diffuse competition is unintuitive in part because we lack a clear conceptual framework for understanding how individual interactions manifest in communities of multiple competitors. Here, I use mathematical and agent-based models to illustrate that diffuse interactions—as opposed to direct pairwise interactions—are likely the dominant mode of interaction among multiple competitors. Consequently, competitive effects may regularly rebound, incurring fitness costs under certain conditions, especially when kin-kin interactions are common. These models provide a powerful framework for investigating competitive ability and its evolution and produce clear predictions in ecologically realistic scenarios.</span></p>
Suppression force-fields and diffuse competition: Competition de-escalation is an evolutionarily stable strategy
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Perturbing the travelling pulse in a three-species competition-diffusion system
<p>We consider the situation where an exotic species <em>w</em> invades an ecosystem inhabited by two native species <em>u</em> and <em>v</em>. All species are competing for the same limited resource. Supposing that <em>u</em> and <em>v</em> are not able to coexist in the absence of the invader, we want to determine whether a successful invasion by <em>w</em> may allow all species to coexist (competitor-mediated coexistence). Mathematically, this problem can be modelled by the following three-species competition-diffusion system<br> <span class="math-tex">\( \left\{ \begin{alignedat}{6} u_t &= d_1 \, \Delta u &&+ (r_1 &&- u &&- b_{12} \, v &&- b_{13} \, w &&)\,u, \\ v_t &= d_2 \, \Delta v &&+ (r_2 &&- v &&- b_{21} \, u &&- b_{23} \, w &&)\,v, \\ w_t &= d_3 \, \Delta w &&+ (r_3 &&- w &&- b_{31} \, u &&- b_{32} \, v &&)\,w, \end{alignedat} \right.\)</span><br> where all parameters are positive constants.</p> <p>We are interested in the case in which the invading species is weaker than the native ones, i.e., it is not able to survive in the diffusion-free system obtained by setting <em>d</em><sub>1</sub> = <em>d</em><sub>2</sub> = <em>d</em><sub>3</sub> = 0.<br> We fix all parameters as<br> <span class="math-tex">\( \begin{aligned} & d_1 = d_2 = d_3 = 1, \\ & r_1 = r_2 = 28, \\ & \begin{aligned} b_{12} &= 22/21, & b_{13} &= 4, \\ b_{21} &= 1.87, & b_{23} &= 3/4, \\ b_{31} &= 26/21, & b_{32} &= 22/21, \\ \end{aligned} \end{aligned}\)</span><br> and leave <em>r</em><sub>3</sub>, which measures the strength of the exotic species, as a free parameter. Depending on the value of <em>r</em><sub>3</sub>, the invasion can be either successful or not and competitor-mediated coexistence may or may not occur.</p> <p>It turns out that if <em>r</em><sub>3</sub> lies in a certain range of values, the three-species competition-diffusion system admits several types of travelling wave solutions. In particular, there exists a travelling pulse which is stable for relatively high values of <em>r</em><sub>3</sub> and then becomes unstable when <em>r</em><sub>3</sub> decreases. In the movie here presented, we show the outcome of perturbing the unstable travelling pulse for <em>r</em><sub>3</sub> = 26.75. In this case, the pulse splits in two three-species waves moving in opposite directions.</p>
Breathing travelling wave solutions in a three-species competition-diffusion system
<p>We consider the situation where an exotic species <em>w</em> invades an ecosystem inhabited by two native species <em>u</em> and <em>v</em>. All species are competing for the same limited resource. Supposing that <em>u</em> and <em>v</em> are not able to coexist in the absence of the invader, we want to determine whether a successful invasion by <em>w</em> may allow all species to coexist (competitor-mediated coexistence). Mathematically, this problem can be modelled by the following three-species competition-diffusion system<br> <span class="math-tex">\( \left\{ \begin{alignedat}{6} u_t &= d_1 \, \Delta u &&+ (r_1 &&- u &&- b_{12} \, v &&- b_{13} \, w &&)\,u, \\ v_t &= d_2 \, \Delta v &&+ (r_2 &&- v &&- b_{21} \, u &&- b_{23} \, w &&)\,v, \\ w_t &= d_3 \, \Delta w &&+ (r_3 &&- w &&- b_{31} \, u &&- b_{32} \, v &&)\,w, \end{alignedat} \right.\)</span><br> where all parameters are positive constants.</p> <p>We are interested in the case in which the invading species is weaker than the native ones, i.e., it is not able to survive in the diffusion-free system obtained by setting <em>d</em><sub>1</sub> = <em>d</em><sub>2</sub> = <em>d</em><sub>3</sub> = 0.<br> We fix all parameters as<br> <span class="math-tex">\( \begin{aligned} & d_1 = d_2 = d_3 = 1, \\ & r_1 = r_2 = 28, \\ & \begin{aligned} b_{12} &= 22/21, & b_{13} &= 4, \\ b_{21} &= 1.87, & b_{23} &= 3/4, \\ b_{31} &= 26/21, & b_{32} &= 22/21, \\ \end{aligned} \end{aligned}\)</span><br> and leave <em>r</em><sub>3</sub>, which measures the strength of the exotic species, as a free parameter. Depending on the value of <em>r</em><sub>3</sub>, the invasion can be either successful or not and competitor-mediated coexistence may or may not occur.</p> <p>It turns out that if <em>r</em><sub>3</sub> lies in a certain range of values, the three-species competition-diffusion system admits a breathing travelling wave solution, i.e., a travelling pulse whose width is oscillating. Such a breathing wave is originated from a standard travelling pulse which is destabilized through a Hopf bifurcation. The period <em>T</em> of the breathing wave depends on the free parameter <em>r</em><sub>3</sub> and goes to infinity at one end of the solution branch.</p> <p>The movie "Breathing Travelling Wave Orbits" shows the evolution of the spatial profile of the breathing wave. After one period, the value of the parameter <em>r</em><sub>3</sub> is changed and the next solution on the breathing wave branch is displayed. Please note that the solution is plotted in a reference frame moving at the velocity of the breathing wave.</p> <p>The movie "Breathing Travelling Wave Features" shows several features of the breathing wave as <em>r</em><sub>3</sub> is changed. The first plot in the third row shows the current value of <em>r</em><sub>3</sub> and the position on the solution branch. The first row shows the space-time profiles of the solution. The first plot of the second row shows the evolution of the pulse width during one period. The remaining plots on the second row show the instantaneous velocities of the back and leading fronts of the oscillating pulse, while the plots immediately below show the density of the invading species <em>w</em> in correspondence of those two fronts.</p>
Interaction of one-dimensional trivial and non-trivial travelling waves in a three-species competition-diffusion system
<p>We consider the situation where an exotic species <em>w</em> invades an ecosystem inhabited by two native species <em>u</em> and <em>v</em>. All species are competing for the same limited resource. Supposing that <em>u</em> and <em>v</em> are not able to coexist in the absence of the invader, we want to determine whether a successful invasion by <em>w</em> may allow all species to coexist (competitor-mediated coexistence). Mathematically, this problem can be modelled by the following three-species competition-diffusion system<br> <span class="math-tex">\( \left\{ \begin{alignedat}{6} u_t &= d_1 \, \Delta u &&+ (r_1 &&- u &&- b_{12} \, v &&- b_{13} \, w &&)\,u, \\ v_t &= d_2 \, \Delta v &&+ (r_2 &&- v &&- b_{21} \, u &&- b_{23} \, w &&)\,v, \\ w_t &= d_3 \, \Delta w &&+ (r_3 &&- w &&- b_{31} \, u &&- b_{32} \, v &&)\,w, \end{alignedat} \right.\)</span><br> where all parameters are positive constants.</p> <p>We are interested in the case in which the invading species is weaker than the native ones, i.e., it is not able to survive in the diffusion-free system obtained by setting <em>d</em><sub>1</sub> = <em>d</em><sub>2</sub> = <em>d</em><sub>3</sub> = 0.<br> We fix all parameters as<br> <span class="math-tex">\( \begin{aligned} & d_1 = d_2 = d_3 = 1, \\ & r_1 = r_2 = 28, \\ & \begin{aligned} b_{12} &= 22/21, & b_{13} &= 4, \\ b_{21} &= 1.87, & b_{23} &= 3/4, \\ b_{31} &= 26/21, & b_{32} &= 22/21, \\ \end{aligned} \end{aligned}\)</span><br> and leave <em>r</em><sub>3</sub>, which measures the strength of the exotic species, as a free parameter. Depending on the value of <em>r</em><sub>3</sub>, the invasion can be either successful or not and competitor-mediated coexistence may or may not occur.</p> <p>It turns out that if <em>r</em><sub>3</sub> lies in a certain range of values, the three-species competition-diffusion system admits two planarly stable travelling wave solutions. In the movies here presented, the result of the interaction of these two waves in one spatial dimension is reported for several value of <em>r</em><sub>3</sub>. For relatively higher values of the free parameter, the relative velocity of the interacting waves is small and they merge into a single travelling pulse. As <em>r</em><sub>3</sub> decreases, the relative velocity of the two waves becomes larger and they merge into a breathing wave (a travelling pulse whose width is oscillating). If <em>r</em><sub>3</sub> is even smaller, the trivial wave is reflected as a leftward-moving non-trivial wave.</p>
Invasion by an exotic species in a three-species competition-diffusion system
<p>We consider the situation where an exotic species <em>w</em> invades an ecosystem inhabited by two native species <em>u</em> and <em>v</em>. All species are competing for the same limited resource. Supposing that <em>u</em> and <em>v</em> are not able to coexist in the absence of the invader, we want to determine whether a successful invasion by <em>w</em> may allow all species to coexist (competitor-mediated coexistence). Mathematically, this problem can be modelled by the following three-species competition-diffusion system<br> <span class="math-tex">\( \left\{ \begin{alignedat}{6} u_t &= d_1 \, \Delta u &&+ (r_1 &&- u &&- b_{12} \, v &&- b_{13} \, w &&)\,u, \\ v_t &= d_2 \, \Delta v &&+ (r_2 &&- v &&- b_{21} \, u &&- b_{23} \, w &&)\,v, \\ w_t &= d_3 \, \Delta w &&+ (r_3 &&- w &&- b_{31} \, u &&- b_{32} \, v &&)\,w, \end{alignedat} \right.\)</span><br> where all parameters are positive constants.</p> <p>We are interested in the case in which the invading species is weaker than the native ones, i.e., it is not able to survive in the diffusion-free system obtained by setting <em>d</em><sub>1</sub> = <em>d</em><sub>2</sub> = <em>d</em><sub>3</sub> = 0.<br> We fix all parameters as<br> <span class="math-tex">\( \begin{aligned} & d_1 = d_2 = d_3 = 1, \\ & r_1 = r_2 = 28, \\ & \begin{aligned} b_{12} &= 22/21, & b_{13} &= 4, \\ b_{21} &= 1.87, & b_{23} &= 3/4, \\ b_{31} &= 26/21, & b_{32} &= 22/21, \\ \end{aligned} \end{aligned}\)</span><br> and leave <em>r</em><sub>3</sub>, which measures the strength of the exotic species, as a free parameter. Depending on the value of <em>r</em><sub>3</sub>, the invasion can be either successful or not and competitor-mediated coexistence may or may not occur, as can be seen in the movies here presented. The species <em>u</em>, <em>v</em> and <em>w</em> are denoted by the red, green and blue colours respectively. The yellow line marks the interface between the species <em>u</em> and <em>v</em>. We remark that competitor-mediated coexistence only occurs for intermediate values of <em>r</em><sub>3</sub>.</p>
Interaction of planarly stable trivial and non-trivial travelling waves in a three-species competition-diffusion system
<p>We consider the situation where an exotic species <em>w</em> invades an ecosystem inhabited by two native species <em>u</em> and <em>v</em>. All species are competing for the same limited resource. Supposing that <em>u</em> and <em>v</em> are not able to coexist in the absence of the invader, we want to determine whether a successful invasion by <em>w</em> may allow all species to coexist (competitor-mediated coexistence). Mathematically, this problem can be modelled by the following three-species competition-diffusion system<br> <span class="math-tex">\( \left\{ \begin{alignedat}{6} u_t &= d_1 \, \Delta u &&+ (r_1 &&- u &&- b_{12} \, v &&- b_{13} \, w &&)\,u, \\ v_t &= d_2 \, \Delta v &&+ (r_2 &&- v &&- b_{21} \, u &&- b_{23} \, w &&)\,v, \\ w_t &= d_3 \, \Delta w &&+ (r_3 &&- w &&- b_{31} \, u &&- b_{32} \, v &&)\,w, \end{alignedat} \right.\)</span><br> where all parameters are positive constants.</p> <p>We are interested in the case in which the invading species is weaker than the native ones, i.e., it is not able to survive in the diffusion-free system obtained by setting <em>d</em><sub>1</sub> = <em>d</em><sub>2</sub> = <em>d</em><sub>3</sub> = 0.<br> We fix all parameters as<br> <span class="math-tex">\( \begin{aligned} & d_1 = d_2 = d_3 = 1, \\ & r_1 = r_2 = 28, \\ & \begin{aligned} b_{12} &= 22/21, & b_{13} &= 4, \\ b_{21} &= 1.87, & b_{23} &= 3/4, \\ b_{31} &= 26/21, & b_{32} &= 22/21, \\ \end{aligned} \end{aligned}\)</span><br> and leave <em>r</em><sub>3</sub>, which measures the strength of the exotic species, as a free parameter. Depending on the value of <em>r</em><sub>3</sub>, the invasion can be either successful or not and competitor-mediated coexistence may or may not occur.</p> <p>It turns out that if <em>r</em><sub>3</sub> lies in a certain range of values, the three-species competition-diffusion system admits two planarly stable travelling wave solutions. In the movies here presented, the result of the interaction of these two waves in two spatial dimensions is reported for several value of <em>r</em><sub>3</sub>. The species <em>u</em>, <em>v</em> and <em>w</em> are denoted by the red, green and blue colours respectively. The yellow line marks the interface between the species <em>u</em> and <em>v</em>. As the value of the free parameter decreases, we observe a transition from a regular spiral pattern, to a breathing spiral and finally to a complex spatio-temporal pattern born from the break-up of the spiral. This complex pattern may be either periodic or chaotic in the long run, as can be seen in the movies for longer time intervals <em>T</em>.</p>
RNAseq reveals that Pseudomonas aeruginosa mounts medium-dependent competitive responses when sensing diffusible cues from Burkholderia cenocepacia
GEO Series GSE224821. Pseudomonas aeruginosa PAO1. 18 samples. Type: Expression profiling by high throughput sequencing.
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