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    Below ground efficiency of a parasitic wasp for Drosophila suzukii biocontrol in different soil types

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    Modeling the impact of genetically modified male mosquitoes in the spatial population dynamics of Aedes aegypti

    In the present work, we extend the base model for the spatial mosquito population dynamics24 to include wild male mosquitoes and genetically modified male mosquitoes. Thus, five populations will be considered: the aquatic mosquito population, including larvae and pupae, the egg mosquito population, the reproductive female mosquito population, the wild male mosquito population, and the genetically modified male population. Similar approaches can be found in the literature25,26.In the following system, we represent mosquito population densities (mosquitoes per m(^2)) by: E – in the egg phase, A – in the aquatic phase, F – female in the reproductive phase, M – wild males, and G – genetically modified male mosquitoes. Due to the very high resistance of the egg phase (up to 450 days27) and as we are interested in an urban spatial macro-scale modeling, we do not consider the mortality in the egg phase. The model is described by the following system of partial differential equations:$$begin{aligned} {left{ begin{array}{ll} partial _t E &{} = alpha beta F M -e E, \ partial _t A &{} = e left( 1 – dfrac{A}{k} right) E -(eta _a+{mu _a})A, \ partial _t F &{} = nabla cdot (D_m nabla F) -mu _f F + reta _{a} A, \ partial _t M &{} = nabla cdot (D_m nabla M) -mu _m M + (1-r)eta _{a} A, \ partial _t G &{} = nabla cdot (D_g nabla G) -mu _{g}G + l, end{array}right. } end{aligned}$$
    (1)
    where ( alpha ) represents the proportion of wild male mosquitoes to the total number of male mosquitoes (wild males + genetically modified males); (beta ) represents the expected quantity of eggs from the successful encounter between wild females and males; e is the egg hatching rate; k is the carrying capacity of the aquatic phase; ( eta _a ) is the emergence rate for mosquitoes from the aquatic phase to the female or male phases; ( mu _a), (mu _f), (mu _m), and (mu _{g}) are the mortality rates of mosquitoes in the aquatic phase, females, males, and genetically modified males, respectively; r is the proportion of females to males (typically (r=0.5)); (l=l(x,y,t)) is the function representing the number of genetically modified mosquitoes released in a unit of time at any point of the domain; (D_m) is the diffusion coefficient of wild mobiles females and males; (D_g) is the diffusion coefficient of genetically modified males. The proposed model (1) can naturally deal with heterogeneous parameters, such as mortality, diffusion, and carrying capacity coefficients. Thus it is possible to model the influence of rain, wind, and human action. In the context of this work, we are considering that the city neighborhood is divided into two environments: houses and streets. Due to lack of data, we restrict the investigated heterogeneity only to the carrying capacity coefficient.The proposed model can be regarded as an extension of other “economic” models20,24 in the effort to qualitatively reproduce the complex phenomena by using as few parameters as possible. Following this idea, the carrying capacity was neglected in the egg phase because of the skip oviposition phenomenon28 i.e., the female lays the number of eggs that the place holds, without more space, she migrates to other environments to finish laying the eggs. We also do not consider this coefficient in the winged phase as limitations in the winged phase were not reported in any study. On the other hand, we consider it in the aquatic phases (larvae and pupae), where it is effective29.The term ( alpha ), which multiplies the probability of encounters between male and female, represents the impact of the insertion of genetically modified males in the mosquito population to the immobile phase and is defined as$$begin{aligned} alpha = left{ begin{array}{cc} 1, &{} text{ if } M=G= 0, \ dfrac{M}{M + G}, &{} text{ otherwise }. end{array} right. end{aligned}$$
    (2)
    Similar modeling approach can be found in the literature16. As the release rate of genetically modified males increases, the alpha value decreases, and, consequently, the probability of encounter between females and wild males also decreases. Thus, there is a greater probability of encounter between genetically modified males and females. This approach presents an advantage, when compared to the models found in the literature25, as System  (1) does not present singularities at the equilibrium states, allowing mathematical analysis and numerical simulations. From the biological point of view, the increment of male wild mosquitoes over some critical value does not affect the egg deposition. At first glance, the term FM can lead to a misunderstanding that such property is not satisfied in the presented model. However, in Section “Equilibrium points considering the application of genetically modified male mosquitoes,” we argue that both male and female populations possess mathematical attractor equilibria, blocking the wild male population from growing beyond this value.Finally, any acceptable population model should be invariant in the definition domain, meaning its solution does not present senseless values. Setting the variable domain as$$begin{aligned} 0 le E(x,y,t)< infty ,;; 0 le A(x,y,t) le k, ;; 0 le F(x,y,t)< infty ,;; 0 le M(x,y,t)< infty ,;; 0 le G(x,y,t) < infty , end{aligned}$$ (3) we can verify that it is invariant under the time evolution by the System (1). To prove this statement, it is sufficient to verify that the vector field defined by the right side of (1) points into the domain when (E, A, F, M, G) approaches the domain boundary. When E approaches zero, the right side of the first equation in (1) is not negative. When A approaches zero, the right side of the second equation in (1) is not negative. When A approaches k (bottom), the first term on the right side of the second equation in (1) tends to zero, while the second term remains negative. Since the term ( nabla cdot (D_m nabla F) ) cannot change the F sign, when F approaches zero, the right side of the third equation in (1) is not negative Since the term ( nabla cdot (D_m nabla M) ) cannot change the M sign, when M approaches zero, the right side of the fourth equation in (1) is not negative. Since the term ( nabla cdot (D_g nabla G) ) cannot change the G sign, when G approaches zero, the right side of the fifth equation in (1) is not negative. In the rest of this section, let us explain how to estimate one-by-one all the parameters used in this model from experimental data available in the literature. It is a challenging task as, typically, the development of the Ae. aegypti mosquito depends on food variation30, temperature variations14,15 and rainfall31. This data is not available in the literature in the organized and systematic form. Because of that, we assume the environment is under optimal conditions of temperature, availability of food, and humidity.How to estimate emergence rate ((eta _a)) The emergence rate describes the rate at which the aquatic phase of the mosquito emerges into the adult phases. In the present model, for simplicity, it was considered that no mosquito from the crossing between genetically modified males and females reaches adulthood. Thus, the emergence rate is calculated on the crossing between females and wild males. Under optimal conditions and feeding distribution, based on the literature30, the emergence rate is 0.5596 (text{ day}^{-1}).How to estimate diffusion coefficients ((D_m,D_g)) The diffusion coefficient is one of the most important parameters describing the mosquitoes’ movement. We use the methodology proposed in the previous work24 to obtain the diffusion coefficient of adult mosquitoes (females and males) and genetically modified males.The estimate is done by assuming that all mosquitoes are released at (0, 0), and their movement is described by the corresponding equation in (1) neglecting other terms than diffusion. The population starts spreading in all directions. We define the spreading distance R(t) as the radius of the region centered in (0, 0) where (90%) of the initial mosquitoes population density is present. In Silva et al.24 it is shown that$$begin{aligned} R(t) = sqrt{4Dt} ;text {erf}^{-1}(0.9). end{aligned}$$ (4) Now corresponding diffusion coefficient is estimated by using the average flight distance of the mosquitoes and the characteristic time related to their life expectancy. Under favorable weather conditions, the average lifetime flight distance of females and males is approximately32,33 65 m, while the same for GM males is34 67.3 m. Based on the literature, we consider that the characteristic time for wild females and males32 is 7 days, and the same for genetically modified males is34 2.17 days. Using (4) we estimate the values for (D_m) and (D_g) summarized in Table 1. It would be natural to consider that the mosquitoes’ movement changes in different environments. Unfortunately, we were unable to find the corresponding experimental data, and because of that, we considered that (D_m) and (D_g) are the same in streets and house blocks.How to estimate mortality rates ((mu _a), (mu _f), (mu _m), (mu _{g}))The mortality coefficient represents an average quantity of mosquitoes in the corresponding phase dying each day. As mentioned before, we disregard the mortality rate in the egg phase, as it is negligible due to its great durability27, it does not affect the numerical results, and it complicates analytical estimates. Thus, the aquatic phase mortality rate coefficient is equal to the same for larvae’s coefficient, which is approximately29 (mu _a = 0.025) (1/day).There is no solid agreement on the mortality rate of male and female wild mosquitoes in the literature. Although some results29,30 suggest they are similar, we follow these authors and consider them equal. Considering both natural death and accidental ones, approximately (10%) of females and male mosquitoes in the adult phase die at each day35. Under optimal conditions, the mortality coefficient can be estimated from this data by using the proposed model (1) by neglecting diffusion and emergence terms in the corresponding equation; details can be found in the previous work24. The resulting parameter values are summarized in Table 1.It would be natural to consider that the mosquitoes mortality rate depends on the environment. Unfortunately, we were unable to find the corresponding experimental data, and because of that, we considered that (mu _a), (mu _f), (mu _m), and (mu _{g}) are the same in streets and house blocks.How to estimate the expected egg number ((beta ))This coefficient represents the average quantity of eggs a wild female lays per day, assuming a successful meeting with a wild male. Considering the number of times a female lays eggs in its lifetime36, the average quantity of eggs per lay and the mosquito’s life expectancy, under favorable conditions, this coefficient is estimated as (beta = 34).How to estimate the hatching rate (e)This coefficient determines the average number of eggs hatching in one day. Experimental data37 suggest that, under optimal humidity conditions, the mean value of the hatch rate coefficient is 0.24 given a temperature of 28 ((^{circ })C), which is considered ideal for mosquito development. This is the value used in the present work.How to estimate carrying capacity coefficient (k)The carrying capacity k represents the space limitation of one phase due to situations present in the environment37,38, such as competition for food among the larvae39. In general, it depends on external factors such as food availability, climate, terrain properties, making direct estimation almost impossible. In the Analytical results section, we show how to estimate this coefficient for each grid block. When considering spatial population dynamics in a heterogeneous environment, carrying capacity is one of the most influential parameters as it varies significantly. For example, house block offer more food and a shelter against natural predators resulting to a larger carrying capacity when compared with street environment. Following the literature32 we assume that the 80% of the mosquito’s breeding places are in houses resulting in the relation (k_h=5k_s), where (k_h) and (k_s) are the carrying capacities of the house blocks and in the streets.Genetically modified mosquitoes release rate (l)Function l(x, y, t) determines how many genetically modified mosquitoes are released in the location (x, y) at time t.In a normal situation, the sex ratio between males and females is 1 : 1. The increment of this proportion favoring GM males increases the probability of females to mate with these mosquitoes. As reported in the literature12,30 the initial launch size is 11 times larger than the adult female population, and it is done in some spots in the city. In this work, we analyze different release strategies maintaining the (11times 1) proportion in some scenarios.Table 1 All parameter values are directly taken or estimated from the literature as explained in section Modeling.Full size table More

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    Population density mediates induced immune response, but not physiological condition in a well-adapted urban bird

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    The sustainability movement is 50. Why are world leaders ignoring it?

    Swedish environment minister Annika Strandhäll before the start of the Stockholm +50 Climate Summit. Few world leaders will be attending.Credit: Fredrik Persson/TT News Agency/AFP/Getty

    Sustainability is now a household term, but it wasn’t always so.Fifty years ago, the United Nations held its Conference on the Human Environment in Stockholm. This landmark event gave the concept of sustainable development its first international recognition. Sweden and the UN are marking the occasion this week with Stockholm+50, an international meeting that serves as both commemoration and call to action.The world is deep in planetary and human crises, with the UN’s Sustainable Development Goals off track and multilateral agreements on climate change and biodiversity behind schedule. Governments need to integrate sustainability into economic planning — and listen to researchers, who are ready with evidence-based arguments and tools to help them do so.Fifty years ago, the time was ripe for an environmental agenda to enter the world stage. Optimistic ideas of economic growth as a driver of progress, propelled by the Industrial Revolution, needed to accommodate concerns over damage to the natural environment. Books such as Rachel Carson’s Silent Spring (1962) — which raised awareness about harms caused by pesticides — brought scientific information about environmental risks into the mainstream.In March 1972, a team of researchers and policymakers sounded another alarm in The Limits to Growth, one of the first reports to forecast catastrophic consequences if humans kept exploiting Earth’s limited supply of natural resources. The conference in Stockholm followed a few months later, steered to success by its secretary-general, Canadian industrialist Maurice Strong. That set crucial institutions in motion, starting with the establishment of the UN Environment Programme (UNEP), based in Nairobi — the first UN body to be headquartered in a developing country. UNEP went on to facilitate a new international law — the 1987 Montreal Protocol to phase out ozone-depleting substances — and co-founded the Intergovernmental Panel on Climate Change (IPCC). It assisted in establishing the first action plans for sustainable development through landmark international agreements on biodiversity, climate and desertification.But there were mistakes and missed opportunities. The establishment of multiple agencies and policy instruments created a disjointed governance system. Newly created environment ministers wielded little power. In national budgets, environmental protection was siloed away from economic development and social concerns. For a long time, action on climate change remained unfocused. And the economic drivers of environmental change were overlooked.And so, 50 years after that momentous conference, the world remains in crisis. With impending climate and biodiversity crises, the warnings issued by visionaries now hit even closer.Stockholm+50 promises “clear and concrete recommendations and messages for action at all levels”. More than 90 ministers are expected to attend, but only 10 heads of government. That’s a missed opportunity for high-level action. World leaders are needed because their presence signals that sustainability remains at the top of their agendas.Awareness of the need to embed sustainability into policymaking has broken into the mainstream, although much of it is still talk. City governments around the world are implementing ambitious climate action plans through the C40 Cities network. Some companies, too, are adopting sustainability principles, from reporting (and reducing) their carbon footprints to ensuring that investments, as far as possible, do not harm the environment.But this urgency has not ascended to heads of state and government. With a handful of exceptions — such as Finland, Iceland, New Zealand, Scotland and Wales — most nations seem unwilling to systemically integrate their economic, environmental and social policymaking.Doing so is not only good for the environment; it is also sound economics and good for well-being. The food and energy crisis driving poverty and diminishing living standards around the world might have been triggered by the shocks of a pandemic and war on Ukraine — but it is driven just as much by the depletion of natural resources.Ahead of the 1972 conference, 2,200 environmental scientists signed a letter — called the Menton Message — to then UN secretary-general U Thant. The signatories had a sense that the world was moving towards multiple crises. They urged “massive research into the problems that threaten the survival of mankind”, such as hunger, wars, environmental degradation and natural-resource depletion. The UN system went on to play a big part in building the body of knowledge that has shown why sustainability is necessary, and in creating the policy architecture to make it happen. But to do the Stockholm vision justice, there must be bolder action from heads of government and from the UN system. The planned creation of a board of science advisers to UN secretary-general António Guterres needs to be accelerated. Once established, the board must find a way to bring joined-up action on sustainability closer to world leaders.Researchers can now join a successor to the Menton Message that has been organized by the International Science Council, the global science network Future Earth and the Stockholm Environment Institute. In an open letter addressed to world citizens, the authors write: “After 50 years, pro-environmental action seems like one step forward and two back. The world produces more food than needed, yet many people still go hungry. We continue to subsidize and invest in fossil fuels, even though renewable energy is increasingly cost-effective. We extract resources where the price is lowest, often in direct disregard of local rights and values.”World leaders must listen to the research community, and accept the evidence and narrative offered to help them to navigate meaningful change. Environmental sustainability does not impede prosperity and well-being — in fact, it is vital to them. People in power need to sit up and take notice. More

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